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Mindfulness in Measurement:
            Reconsidering the Measurable in Mindfulness Practice
                                               Sharon G. Solloway
                                               Bloomsburg University
                                               Bloomsburg, PA, USA

                                              William P. Fisher, Jr.1
                                              Avatar International, Inc.
                                                 Sanford, FL, USA


          Can an organic partnership of qualitative and quantitative data confirm the value of mind-
          fulness practice as an assignment in undergraduate education? Working from qualitative
          evidence suggesting the existence of potentially measurable mindfulness effects expressed in
          ruler measures, a previous study calibrated a mathematically invariant scale of mindfulness
          practice effects with substantively and statistically significant differences in the measures
          before and after the assignment. Current efforts replicated these results. The quantitative
          model is described in measurement terms defined at an introductory level. Detailed figures
          and appendices are provided, and a program of future research is proposed.




T
         he value of mindfulness practice as contributing    present moment. These journal entry responses link
         to psychological strength has a long history of     themselves to a number of important self-care issues: the
         supporting anecdotal evidence. A rich legacy of     quality of the inner-life suggested by Seligman and Csik-
such research exists in Buddhist literature as far back as   szentmihalyi (2000), self-determination (Ryback, 2006),
the seventh century BCE. Buddhist practitioners today        emotional balance (Goleman, 1995), stress-reduction,
in both the East and West are actively engaged in broad-     and empathy (Kabat-Zinn, 2005) to name a few. Solloway
ening this legacy via a scientific research agenda. This     (the first author) teaches in higher education, and holds
agenda seeks to document the physiological effects of        both a meditation practice and an orientation to mind-
meditation and mindfulness practice using methods            fulness practice when not meditating. Her daily experi-
that meet the technical standards expected of precision      ence of witnessing the debilitating effects of emotional
measurement and experimental design. The activities of       imbalances, stress, and prejudicial orientations to present
the Dalai Lama’s Mind and Life Institute (http://www.        moment experience in the lives of university students
mindandlife.org), among others, demonstrate the current      awakened her compassion. Offering assignments in mind-
vigor of this interest.                                      fulness practice became her compassionate intervention.
         Mindfulness practice has been described as          Developing documentation of the effects strengthened
non-judgmental awareness of both internal and external       the argument for such assignments.
experience, moment to moment, “…an open, undivided                     The use of mindful awareness as a method of
observation of what is occurring both internally and         immersion (Moustakas, 1990) for reading and responding
externally rather than a particular cognitive approach to    to students’ journal entries across several semesters
external stimuli” (Brown & Ryan, 2000, p. 823). One of       gave Solloway insight into recurring themes associated
the psychological strengths of mindfulness is the capacity   with powerful individual transformations across the
to maintain an emotional balance within any particular       assignment’s duration. The students were different each
life moment, whatever that happens to be. Novice mind-       semester but the effects of mindfulness practice emerged
fulness practitioners (Solloway, 1999, 2000, 2001, 2004)     through similar themes and ranges each time. The
were asked to describe their experience of mindfulness       journal entries were anecdotal self-reports of those effects
practice as a non-judgmental focus of attention in the       for each student and were in themselves powerful voices

58    International Journal of Transpersonal Studies 26, 2007, pp. 58-81
                                             Studies,
for the value of this compassionate intervention. Growth        patterns emerged regarding students’ depths of engage-
was palpable…like noticing that the worn patch on your          ment in the project (see Appendix A). The journal entries
son’s jeans no longer matches where his knee was a few          suggested a range of depth of engagement in the practice;
months ago. You don’t have to measure his height to             consistent reports of specific categories of experience
know he has grown, but the availability of an instrument        began to suggest patterns of “Beginning,” “Intermediate,”
to provide that measure certainly brings valuable infor-        and “Advanced” engagement. These labels only refer to an
mation to bear when selecting a pair of jeans with a better     accumulation of patterns among the self-reported experi-
fit. The journal entries, like the jeans, showed evidence of    ences of these novice practitioners. But the accumulation
individual growth, but the question arose as to whether it      of journal entries seemed to indicate that the participants
was possible to calibrate a ruler to provide more specific      in this project semester to semester “grew,” some more
information about each individual’s growth.                     than others.
          The most well-known mindfulness instruments                     Could an instrument be constructed that
are the Mindfulness Attention Awareness Scale (Brown            reflected the common themes in the journals and also
& Ryan, 2003), the Kentucky Inventory of Mindfulness            created a ruler measuring growth across the themes? In
Skills (Baer, Smith, Hopkins, Krietemeyer, & Toney,             other words, could these patterns be corroborated by a
2006; Baer, Smith, & Allen, 2004), and the Toronto              quantitative measure requiring experimental tests of the
Mindfulness Scale (Lau, Bishop, Segal, Buis, Anderson,          hypothesis that the variable of interest is in fact quantita-
Carlson, Shapiro, & Carmody, 2006). Solloway’s (1999,           tive, that is, that the variable is divisible into the additive
2000, 2001, 2004) roots as a qualitative researcher             magnitudes necessary for meaningful numeric represen-
influenced her desire to develop a scale directly out of        tations? This would require a model that pitted the diffi-
her students’ journal entries rather than select a scale        culty of each item against the ability of the participant
developed from other sources. Could the cumulative              without any other influences. This is the same problem
voices of her students be translated into a scale that would    Rasch (1960) saw when he contemplated the problem
corroborate their journal entries retaining the individu-       of statistical methods most often used in psychometric
ality of experience just as the journal entries did? Fisher’s   methods that are group-centered rather than ones
(2000, 2003a, 2003b, 2004) experience with developing
                                                                    in which each individual is characterized separately
instruments from qualitative data takes advantage of
                                                                    and from which, given adequate data, the individual
Rasch models to give ruler measures of the qualitative
                                                                    parameters can be estimated. It is further essential
construct without compromising the integrity of the
                                                                    that comparisons between individuals become inde-
individual measured, thus opening the door to collabora-
                                                                    pendent of which particular instruments – tests or
tion toward an answer.
                                                                    items or other stimuli – within the class consid-
                                                                    ered have been used. Symmetrically, it ought to be
                  The Present Research
                                                                    possible to compare stimuli belonging to the same
         The first study (Solloway & Fisher, 2007) grew
                                                                    class – “measuring the same thing” – independent of
out of Solloway’s seven-semester experience of coaching
                                                                    which particular individuals within a class considered
novice mindfulness practitioners (students in a pre-
                                                                    were instrumental for the comparison. This is a huge
service undergraduate teacher education course) through
                                                                    challenge, but once the problem has been formulated
an eight-week introduction to mindfulness practice.
                                                                    it does seem possible to meet it. (Rasch, 1960, p. xx)
These students used the breath as an anchor for attention
in the present moment all day one day a week for eight          Rasch models enable one to imagine a methodology that
weeks. At the end of each day of practice, the student          embraces both the contemplative and compassionate
submitted an email journal entry describing the expe-           found in qualitative work describing the experiential
rience of mindfulness practice that day. Solloway, a            without sacrificing the rigor of measurement required
vipassana practitioner since 1996, mindfully read each          in experimental science. Yet Rasch models have their
journal entry. Out of this deep listening, she responded        opponents as well. The following section will describe
to each journal entry within 24-hours of receiving it,          what happened when Solloway’s mindfulness practice
providing encouragement that seemed appropriate to              entered the Present Moment of Fisher’s tutelage on the
the individual entry. Across the seven semesters, obvious       subject.

                                                                International Journal of Transpersonal Studies 59
Mindfulness in Measurement
repeatedly proven themselves essential to science over
Fisher’s Two-Year Mentorship of Solloway
          Rasch measurement practitioners are sometimes       the course of its history. The identification of anomalies
accused of an over-zealous advocacy of their methods,         is fundamental to allowing exceptions to prove (in the
as a kind of method idolatry. Sometimes, however, such        sense of testing) rules. It is said that nature reveals herself
accusations have less to say about the accused than           by her exceptions, but when mathematical models incor-
they do about quick judgments foreclosing prematurely         porate interaction terms and do not require invariantly
on the opportunity to see something new. Instead of           separable parameters, as do many IRT and statistical
dismissing what seems on the face of it to be an unrea-       models, these exceptions are hidden within summary
sonable position—strong advocacy of either (1) one            statistics, where they are either ignored or very difficult
method among many equivalent methods, or (2) math-            to find. Rasch models, in contrast, have been associ-
ematical invariance requirements that can seem unreal-        ated from their inception with a variety of graphical
istically rigid to those unfamiliar with them—perhaps         and statistical methods for identifying and evaluating
a more sympathetic attitude, or one more sensitive to         anomalies (Smith, 2000). For more information on this
the ambiguities of interpretation, as outlined by Kuhn        controversy, see Wright (1977a, 1984), Fisher (1994), or
(1977, pp. xi-xii), would lead to insights as to why and      Andrich (1988, 2002, 2004).
how reasonable people might take an apparently unrea-                      Taking another tack on this issue, there are
sonable position.                                             others who contend that methods such as Confirmatory
          For instance, there are those who contend that      Factor Analysis (CFA) can be as informative as a Rasch
Rasch models are fine to apply when they happen to fit        model in the identification of unidimensional constructs.
data, but they often do not, and so other, more flexible      Though this is true in limited applications (Reise,
models are then required (van der Linden & Hambleton,         Widaman, Pugh, 1993), (1) CFA lacks a stochastic frame
1997). But generality in the measurement of a construct       of reference, meaning that there are no error terms for the
requires the identification of patterns of invariance that    factor loadings; (2) secondary factors can be completely
hold up across data sets (Rogosa, 1987; Michell, 1990,        dependent on the particular error distribution that just
2000). As Embretson (1996, p. 211) puts it,                   happens to be present in one data set, but not in others;
                                                              (3) CFA does not provide the desired additive unit of
     It is sometimes maintained that the Rasch model is
                                                              measurement, since the raw scores are usually assumed to
     too restrictive and does not fit real test data suffi-
                                                              provide it (and though a logistic regression of the scores
     ciently well. However, even if a more complex IRT
                                                              on the loadings might come close), and (4) CFA does not
     model is required to fit the data, the total score
                                                              provide any means of identifying or evaluating anomalous
     scale would not provide a relatively better metric. In
                                                              individual responses. These four shortcomings of CFA as
     fact, if item discrimination parameters are required
                                                              a measurement model mean that multimodal data will
     to obtain fit, total score is not even monotonically
                                                              produce multifactorial results, even if the data analyzed
     related to the IRT theta parameters. The IRT trait
                                                              are a subset of a larger data matrix previously shown by
     score, even for equal total scores, would depend on
                                                              CFA to be a single unidimensional factor (Smith, 1996;
     which items were answered correctly.
                                                              Wright, 1988, 1991).
                                                                        Finally, raw scores from tests and surveys are
These kinds of confoundings can occur because multi-
                                                              typically interpreted as though they are meaningful repre-
parameter IRT models are internally inconsistent,
                                                              sentations of quantitative amounts, when they demon-
asserting unidimensionality even while allowing item
                                                              strably are not. Scores summed from two sets of items
characteristic curves to cross (Lumsden, 1978; Andrich,
                                                              drawn from different agreeability or difficulty ranges of
1988; Wright, 1984).
                                                              the same survey, test, or assessment do not and cannot
         Rasch (1960, pp. 37-8) was certainly aware of
                                                              plot in a straight line. Centimeter and inch measures of
the problems of interactions, and wrote, “models are not
                                                              the same object lengths do plot in a straight line, as the
meant to be true,” since no data ever fit a model exactly.
                                                              relation between the two number systems is dominated
Models are meant to be useful and meaningful, however,
                                                              by the invariance of the objects’ amounts of length.
and abstract heuristic ideals, such as Plato’s redefini-
                                                                        If nonarbitrary, invariant measures of constant
tion of the elements of geometry, Galileo’s frictionless
                                                              amounts could be obtained from tests and surveys,
plane, or Carnot’s perfectly reversible heat engine, have

60    International Journal of Transpersonal Studies                                                  Solloway & Fisher
would not these be worth obtaining? Might it be that           tics that are sufficient in the sense of summarizing data
those who dismiss Rasch’s models for measurement as            with no loss of information.
just one approach among many equivalent approaches are                  What this means is that, “if there exists a
missing something important, perhaps even something            minimal sufficient statistic for the individual parameter
essential?                                                     Theta which is independent of the item parameters, then
          The fact is that data scaled via fit to a Rasch      the raw score is the minimal sufficient statistic and the
model can plot linearly, in close approximations to the        model is the Rasch model” (Andersen 1977, p. 72). As
way quantitative amounts dominate the relation between         Wright (1977b) pointed out, it then follows that
centimeters and inches, or grams and ounces. Further-
                                                                   Unweighted scores are appropriate for person
more, this kind of a plot is defined as the hallmark of
                                                                   measurement if and only if what happens when a
quantitative meaningfulness by philosophers and theo-
                                                                   person responds to an item can be usefully approxi-
reticians who are unconcerned with and not informed
                                                                   mated by a Rasch model.... Ironically, for anyone
about Rasch’s models. Finally, it has been shown that,
                                                                   who claims skepticism about ‘the assumptions’ of
insofar as a score from a test or survey provides a useful
                                                                   the Rasch model, those who use unweighted scores
basis for measurement, the model that it must fit is a
                                                                   are, however unwittingly, counting on the Rasch
Rasch model.
                                                                   model to see them through. Whether this is useful
          Thus we have measurement theoreticians and
                                                                   in practice is a question not for more theorizing, but
philosophers (Falmagne & Narens, 1983; Narens, 2002;
                                                                   for empirical study. (p. 114)
Roberts, 1985, 1999) investigating the meaningfulness
of quantitative statements, and arriving at the essential      In other words, if a count of correct answers or a sum
importance of invariance as a fundamental criterion for        of ratings can provide a meaningful basis for invariant,
telling sense from nonsense. Mundy (1986), for instance,       additive quantification, then a Rasch model holds.
summarizes this work in terms applicable to the differ-                  Even when data are not evaluated for fit to a
ence between curved raw score plots and linear length          Rasch model, even when the invariance and additivity
plots, saying,                                                 properties of quantitative measurement are ignored, use
                                                               of test, survey, or assessment scores as though they are
    The hallmark of a meaningless proposition is that
                                                               measures inherently implies acceptance of Rasch’s sepa-
    its truth-value depends on what scale or coordinate
                                                               rability theorem. This is because the parameter separation
    system is employed, whereas meaningful proposi-
                                                               theorem is nothing more or less than a formal representa-
    tions have truth-value independent of the choice
                                                               tion of the rigorous independence of figure and meaning,
    of representation, within certain limits. The formal
                                                               or of name and concept, that must be assumed in any
    analysis of this distinction leads, in all three areas
                                                               honest effort at communication (Fisher, 2003a, 2003b,
    [measurement theory, geometry, and relativity], to
                                                               2004), even in the discourses of deconstruction (Ricoeur,
    a rather involved technical apparatus focusing upon
                                                               1977, p. 293; Derrida, 1982, p. 229; Derrida, 1989, p.
    invariance under changes of scale or changes of coor-
                                                               218; Gasché, 1987, p. 5). Rasch’s mathematics make tests
    dinate system. (p. 392)
                                                               of the qualitative hypothesis of quantitative meaningful-
Hall, Wijsman, and Ghosh (1965) show “that the set of          ness (Michell, 1990; Narens, 2002) more accessible and
invariant rules based on a sufficient statistic is an essen-   practical than most work in this area. And in so doing,
tially complete subclass of the class of invariant rules”      Rasch taps deeply into the history of measurement and
(Arnold, 1985, p. 275). Rasch models are valued for the        deploys rich possibilities for mathematical thinking that
fact that counts of correct responses or sums of ratings       remain largely unexplored (Wright, 1988, 1997a).
are minimally sufficient statistics (Andersen, 1977; van
der Linden, 1992). Rasch learned of sufficient statis-         Solloway’s Study
tics from their inventor, Ronald Fisher (1922), and                     This study operationalizes mindfulness as a
considered this work the high mark of Fisher’s accom-          construct, evaluates stability over time and across groups
plishments (Andrich, 1997; Wright, 1980). In a Rasch           receiving and not receiving mindfulness training, and
model, ordinal scores are minimally sufficient, and thus       establishes a metric for measuring change in amounts
necessary, since they are functions of all the other statis-   of mindfulness. The experience of novice mindfulness

                                                               International Journal of Transpersonal Studies 61
Mindfulness in Measurement
practitioners is taken as a basis for the nurturing of an       include the possibility of unifying research communities
organically integrated conceptualization of the measured        via a consensus focus on experimentally demonstrated
construct.                                                      common objects of investigation that are furthermore
                                                                measured in the common mathematical language of
                                                                instruments all traceable to reference standard metrics
                         Method
                                                                (Fisher, 2004).
Instrument
         Fundamental measurement-based guidelines                        This research tests for the separability of a
for developing high quality survey items (Fisher, 2006)         parameter associated with student mindfulness measures
were followed in the development of the instrument. A           from two parameters associated with mindfulness item
bank of thirty assessment items were constructed from           and rating scale calibrations. In other words, the substan-
the students’ journal entries (a database of over 350 sets      tive hypothesis tested in this research can be expressed
of journal entries). Three more items were added to the         as
instrument after the completion of the original study, in
                                                                             ln(Pnij /Pnij-1) = Sn - Mi - Rj
the Fall, 2006, administration. The items were grouped
in three categories of hypothesized mindfulness practice        that is, that the natural logarithm of the response odds
development: Beginning, Intermediate, and Advanced              (the probability P for any student n on any item i in
(Appendix B). Items were randomized for the final draft         response category j relative to category j-1) of any student
of the instrument (Appendix C).                                 n’s response to any item i on the self-assessment is due
         Eight response options (Absolutely Disagree,           only to the difference between that student n’s measure
Very Strongly Disagree, Strongly Disagree, Disagree,            S of the effects of mindfulness practice and the calibra-
Agree, Strongly Agree, Very Strongly Agree, Absolutely          tion M of the mindfulness practice effects item i and
Agree) were provided.                                           the agreeability calibration R of the response category
                                                                j (Andrich, 1978; Wright & Masters, 1982; Wright &
Measurement Theory                                              Mok, 2000).
         Criteria for obtaining objectivity in measure-                   In short, the model tests the hypothesis that
ment comparisons include conjoint additivity (Luce &            mindfulness is the primary construct dominating the
Tukey, 1964), statistical sufficiency (Arnold, 1985; Hall,      question and answer exchange. Analysis of the model
Wijsman, & Ghosh, 1965), invariance (Krantz, Luce,              residuals then aids in identifying individual responses,
Suppes, & Tversky, 1971), conditional independence              students, and items as influenced by something different
(Kolmogorov, 1950), and infinite divisibility (Levy, 1937).     other than the primary construct.
All of these are embodied in the criterion of parameter
separation (Rasch, 1960), as has been shown over the            Research Participants
course of number of analyses and proofs (Andersen,                        Study participants were 338 unique preservice
1977; Andrich, 1988; Fischer, 1995; Perline, Wright, &          education students enrolled in several different teacher
Wainer, 1979; Wright, 1985, 1997b, 1999). These criteria        education courses over a four-semester period extending
for objectivity in measurement have been found useful in        from the Fall of 2005 through the Spring of 2007 (see
the study of a wide variety of applications in education,       Table 1). Though the vast majority of students provided
health care, and psychology (Bezruczko, 2005; Bond &            both pre- and post-instruction measures every semester,
Fox, 2007; Fisher & Wright, 1994; Wilson, 2005).                not all did, resulting in a total of 647 measures for the
         In general, psychologists do not test or even state    two time points across semesters.
the hypothesis that the variable of interest in a study is                In the first semester of the study, in the Fall of
quantitative (Cliff, 1992; Guttman, 1985; Michell, 1990,        2005, and only in this semester, two different instruc-
1997a, 1997b, 1999, 2000; Wilson, 1971; Wright, 1984).          tors taught three of these courses. The class lists were
In so doing, their research results remain tied to arbitrary,   cross checked for participants who had previously taken
local, idiosyncratic, sample- and scale-dependent,              the first instructor’s course or who were simultaneously
ordinal comparisons, and are cut off from the benefits          enrolled in both the first and second instructors’ courses;
that would accrue from nonarbitrary, general, universal,        these students were removed from the second instructor’s
uniform, and invariant linear comparisons. These benefits       list. Therefore, none of the participants had previous

62    International Journal of Transpersonal Studies                                                  Solloway & Fisher
practice. About half of the students (88) participated in
                                                                                      mindfulness training as described in Appendix D, and
                          Table 1
                                                                                      about half (83) served as a control. The experimental group
                      Demographics
                                                                                      received positive feedback for each journal entry submitted
              338 Total Student Participants
                                                                                      during the eight weeks. Both groups responded to the
   (Due to missing data, not all category groups sum to 338)
                                                                                      survey items twice, using an eight-point rating scale, once
                                                                                      before the experimental group underwent eight weeks of
                            Fall     Spring        Fall   Spring             Valid
                            2005      2006         2006    2007    Total    Percent
                                                                                      mindfulness practice (T1=Pre), and again at the end of
                                                                                      those eight weeks (T2=Post).
Sex
 Male                        16     5              14     16       51        15.2%
 Female                     155     35             41     54       285       84.8%
                                                                                      Analyses
                                                                                                All scaling and fit analyses were performed using
Age
  17-21                     106     27             38     53       224       68.7%
                                                                                      the Winsteps software (Linacre, 2006), implementing a
  22-31                     44      11             16     11       82        25.2%
                                                                                      probabilistic conjoint model of fundamental measurement
 32-41                      6       1              0      2        9          2.8%
                                                                                      for rating scales (Andrich, 1978, 1988; Wright & Mok,
 42-51                      5       1              0      4        10         3.1%
 Other                      1       0              0      0        1           .3%
                                                                                      2000), and testing for the invariant internal consistency of
                                                                                      the data using information-weighted and outlier-sensitive
Ethnic Group
                                                                                      mean square model fit statistics (Smith, R. M., 2000;
 Caucasian American         151     39             53     68       311       98.4%
 African American           0       1              0      2        3           .9%
                                                                                      Wright & Masters, 1982), and principal components
 Asian American             1       0              0      0        1           .3%
                                                                                      factor analysis of the model residuals (Smith, R. M., 1996;
 Hispanic American          1       0              0      0        1           .3%
                                                                                      Linacre, 1998; Smith, E., 2002). Measures are reported in
Curriculum
 Mindfulness                87      40             55     70       252       74.6%
                                                                                      “logits.”
 Non-Mindfulness            86                                     86        25.4%

                                                                                          “Logit” is a contraction of “Log-Odds Unit”. It is no
Pre- or Post-Instruction * Semester and Year Cross Tabulation
                                                                                          more obscure a measurement unit of an underlying
                                                                                          and invisible variable than an “Ampère” is of invisible
                                   Fall       Spring      Fall     Spring
                                                                             Total
                                                                                          electric current. The essential ingredient of Amps and
                                   2005        2006       2006      2007

                                                                                          logits is that they be additive.
   Pre-Instruction Count           171        37          56       71       335
                                                                                               Real apples are not additive. One Apple + One
                                                                                          Apple = Two Apples. But Two Apples are twice as
   Post-Instruction Count          153        38          53       68       312
                                                                                          much as One Apple only when the Two Apples are
                                                                                          perfectly identical. Real apples are not perfectly
           Total                   324        75          109      139      647
                                                                                          identical. When we say One Amp + One Amp = Two
                                                                                          Amps, we say “all Amps are identical,” wherever they
                                                                                          appear on the Ammeter. Logits form an equal interval
instruction in mindfulness practice or assignments in
                                                                                          linear scale, just like Amps. When any pair of logit
mindfulness practice within their teacher education
                                                                                          measurements have been made with respect to the
programs prior to the study.
                                                                                          same origin on the same scale, the difference between
         Students in the mindfulness instructor’s course
                                                                                          them is obtained merely by subtraction and is also in
were assured every semester that credit for the assign-
                                                                                          Logits. (Wright, 1997c, p. 288)
ment would be awarded simply by participation. In other
                                                                                      Measures and calibrations from Winsteps were then studied
words, any level of participation would receive full credit.
                                                                                      statistically and graphically using SPSS v. 14 (2005).
The students in the second instructor’s courses acted as a
control group.
                                                                                                                 Results
                                                                                               The data from the later three semesters reproduced
Procedure
                                                                                      the same rating scale structure as the initial first semester’s
         The mindfulness project opted for mindfulness
                                                                                      study. The optimization of the rating scale based on the
practice one day a week following Thich Nhat Hahn’s
                                                                                      first semester’s results was thus retained.
(1967) projected potential benefits of one day a week


                                                                                      International Journal of Transpersonal Studies 63
Mindfulness in Measurement
Mindfulness Item Calibrations from Pre-Instruction Sample
                                 (n=171)




                                                                      Mindfulness Item Calibrations from Post-Instruction Sample (n=153)
             Figure 1. Scatter Plot of Fall 2005 Pre-Instruction and Post-Instruction Item Calibrations

                                                                                                     supported by the meaningfulness of the item order on the
Scaling
                                                                                                     variable.
          The 8-point rating scale was optimized (Andrich,
                                                                                                               Due to an error in survey production, item 29
1996; Linacre, 1999, 2002) to three categories, with all of
                                                                                                     was rephrased in late 2006, resulting in exceptionally high
the disagree categories (25% of the responses) combined
                                                                                                     calibrations and mean square outlier-sensitive fit statis-
together, the Agree category (37% of the responses) left
                                                                                                     tics in the Fall 2006 and Spring 2007 semesters. It is the
intact, and three most extreme Agree categories (37%)
                                                                                                     only item to fall repeatedly outside the 95% confidence
also combined. The transition from category 1 (All
                                                                                                     intervals in scatter plots of item calibrations by semester
disagree categories) to category 2 (Agree) calibrated to 6.9
                                                                                                     and year. The rephrasing resulted in the item’s calibration
rescaled units (0.69 logits) below matching measures and
                                                                                                     changing by about two logits. Since the item was already
calibrations, while the threshold between categories 2 and
                                                                                                     near the top of the scale, the new text changed its position
3 (all other agree categories) calibrated to 6.9 units above
                                                                                                     on the scale to a level far above all other items. This large
matching measures and calibrations.
                                                                                                     effect size resulted in all unexpected responses becoming
          Overall respondent measurement separation reli-
                                                                                                     statistically significant.
ability ranged from 0.90 to 0.93, depending on how error
                                                                                                               The Fall 2006 and Spring 2007 data for item 29
is estimated, and item calibration separation reliability
                                                                                                     were therefore removed from the calibration database.
was 0.99. Logits were transformed to a roughly 0-100
                                                                                                     New data will be added in the future, and the item will be
scale from their default values by multiplying by 10 and
                                                                                                     restored to its original phrasing.
adding 50. The same scale was produced when the items
                                                                                                               The items were calibrated on multiple separate
were separately calibrated on the T1 and T2 groups (R =
                                                                                                     subsamples of the data, determined by curriculum type,
0.91), as shown in Figure 1. The model fit statistics do not
                                                                                                     pre- or post-intervention time points, the semester and
falsify the hypothesis that the thirty items measure a single
                                                                                                     year, or simply the first half of the respondent data entered
construct of mindfulness practice. Construct validity was


64    International Journal of Transpersonal Studies                                                                                        Solloway & Fisher
vs. the second half. Correlations of the resulting 41 pairs     resulting measures, suggesting that there is no substantive
    of separate-sample calibrations range from 0.85 to 0.99.        significance to the items’ statistically significant changes
             In contrast with item 29’s two-semester explain-       in position.
    able aberration, items 28 and 6 were repeatedly identi-
    fied by the model fit statistics, the graphical scatter         Experimental
    plots of separate-sample item calibrations (see Figure 1),               In the initial Fall 2005 study of the mindful-
    and the principal components analysis of the residuals          ness measures (Solloway & Fisher, 2007), the control
    as provoking responses inconsistent with the overall            group (receiving no mindfulness instruction) had nearly
    common construct. These two items changed positions             identical average measures at the beginning and end of
    on the scale to a statistically significant degree, depending   the semester (about 50, with an error of 4). The treatment
    primarily on whether the response was made at T1 (Time          group (receiving mindfulness instruction) had an average
    1 or Pre Test) or T2 (Time 2 or Post Test). Omitting the        T1 measure of 51, with an error of 4, but finished the
    items from the scale makes virtually no difference in the       semester with an average T2 measure of 68, 17 units, or




Key:
                                                                    S2S06: Mindfulness Curriculum, Post-Instruction, Spring, 2006
A1F05: Non-mindfulness Curriculum, Pre-Instruction, Fall, 2005
                                                                    S1F06: Mindfulness Curriculum, Pre-Instruction, Fall, 2006
A2F05: Non-mindfulness Curriculum, Post-Instruction, Fall, 2005
                                                                    S2F06: Mindfulness Curriculum, Post-Instruction, Fall, 2006
S1F05: Mindfulness Curriculum, Pre-Instruction, Fall, 2005
                                                                    S1S07: Mindfulness Curriculum, Pre-Instruction, Spring, 2007
S2F05: Mindfulness Curriculum, Post-Instruction, Fall, 2005
                                                                    S2S07: Mindfulness Curriculum, Post-Instruction, Spring, 2007
S1S06: Mindfulness Curriculum, Pre-Instruction, Spring, 2006


                        Figure 2. Pre- and Post-Mindfulness Instruction Measures

                                                                    International Journal of Transpersonal Studies 65
    Mindfulness in Measurement
more than four errors of measurement, higher on the                      The distribution of measures relative to the item
scale. As previously reported, the T2 measures were             hierarchy and optimized rating categories is shown hori-
different from the T1 measures to a statistically signifi-      zontally across the bottom of Figure 3, with the mean,
cant degree for the treatment group, but not for the            and first and second standard deviations, indicated by
control group.                                                  M, S, and T, respectively. The counts of students at each
          Replicating the previously reported Fall 2005         measure are read vertically; i.e., there are 36 students
results, the pre- and post-mindfulness instruction              with measures at the mean. The same information is
measures differ by 16, 19, and 11 units, respectively, for      conveyed in Figure 4, but with both the measures and
the Spring 2006, Fall 2006, and Spring 2007 semesters           the response category-level item calibrations plotted
(see Figure 2). The average T2 measures across the four         vertically.
semesters were consistent over the first three semesters, at             The average T1 measure for the students in the
68, 68, and 70.                                                 mindfulness curriculum over the four semesters is 51.
          The average gain from T1 to T2 dropped                Drawing a vertical line through Figure 3 at 50 on the
markedly in the Spring of 2007, though students started         horizontal scale shows what the expected responses to
with about the same average measure as in the previous          the items are for a student with that measure. Students
semesters. Spring 2007 was unusual in that, due to the          with these initial, uninformed experiences of mindful-
sudden departure of a colleague, Solloway was asked to          ness practice’s effects strongly acknowledge that mindful-
teach his four sections of Language Arts in addition to         ness makes for more attentive listening, and more mildly
her usual responsibilities. It was a difficult time and the     acknowledge a wide range of other effects, from positive
strain is reflected, we believe, in the drop in mindfulness     effects on others to more self control to a new kind of
measures that semester.                                         happiness, with a decreasing likelihood of agreement as
          Even with this exception, however, every semes-       one reads up the scale. Three items involving sensations
ter’s differences in the mindfulness effects measures are       (smell, touch, and sight) are more likely to elicit disagree-
highly significant, in both substantive and statistical         able responses than agreeable ones, for T1 measures, on
terms. The overall average pre-instruction measure for          average. Using the Pre/Post measures for Students A,
students enrolled in the mindfulness curriculum is 51,          B, and C given at the end of Appendix A, the expected
and the overall average post-instruction measure for those      responses for individuals may be seen in the same way in
students is 67. ANOVA shows this difference of 16 units         Figure 3.
(4 errors of measurement) to be statistically significant                The average T2 measure for the students in the
(F(1,495)=184.06, p < .001). The Pre- and Post-Instruc-         mindfulness curriculum over the four semesters is 67.
tion differences shown in Figure 2 are similarly all statis-    Again imagining a vertical line drawn through Figure
tically significant, ranging from the low of the Spring         3, this time at 67 on the scale, we now expect strong
2007 11-unit difference (F(1,137)=24.63, p < .001) to the       agreement with all but the top six of the mindfulness
high of the Fall 2006 19-unit difference (F(1,107)=75.26,       practice effects, and mild agreement is expected for
p < .001).                                                      these.
            The statistical power of the design for all the              The substantive meaning of the experimental
mindfulness curriculum comparisons was 1.00, since all          intervention of training in mindfulness practice is
of the statistically significant differences are most of, all   expressed in terms of the difference between these
of, or more than the pooled standard deviations in size,        expected response patterns. The difference between the
with one degree of freedom and p < .01.                         overall T1 measures and the experimental group’s T2
                                                                measures is about 16. At T1, with an average measure of
                                                                50, the item with the highest calibration with which all
Substantive Interpretation
         Figures 3 and 4 show the order of the items            students typically strongly agree is item 22, mindfulness
on the variable relative to the optimized rating catego-        makes me a more attentive listener, which calibrates at
ries and measures. The item hierarchy exhibits a mean-          38. At T2, with an average measure of 67, the item with
ingful progression ranging from simple noticing to more         the highest calibration with which the experimental
intensely understanding and experiencing, and then to           group typically strongly agrees with is item 8, reduces
heightened awareness and sensation.                             my stress, which calibrates at 55.


66    International Journal of Transpersonal Studies                                                   Solloway & Fisher
10   20         30        40         50        60         70         80       90 100
                                                    |-----+-----+-----+-----+-----+-----+-----+-----+-----|                                NUM    ITEM
                                                    A                                A        :           E            :        F      F    19*   1 heightens my sense of smell
                                                    A                               A       :           E            :        F        F    23*   3 I feel like I’m seeing for the first time
                                                    A                               A       :          E           :        F          F    15*   1 heightens my sense of touch.
                                                    A                             A       :            E           :        F          F     6*   2 I notice that time loses its meaning
                                                    A                           A        :           E          :         F            F    29*   3 I handle all experiences with equanimity
                                                    A                       A        :            E           :        F               F    32    3 I see how to transform my own anger and hurt
                                                    A                       A        :          E           :        F                 F    21*   2 I notice more of my body sensations
                                                    A                      A        :           E         :          F                 F     8*   1 reduces my stress
                                                    A                      A        :           E         :          F                 F    18*   1 makes me feel peaceful
                                                    A                    A        :           E           :        F                   F     4*   3 I observe my thoughts without being caught up in them
                                                    A                    A        :           E           :        F                   F    14*   2 I notice that I experience a kind of happiness that’s different




  Mindfulness in Measurement
                                                    A                  A        :           E           :        F                     F    27*   3 I notice that ordinary experiences seem extraordinary
                                                    A                  A        :           E          :        F                      F    20*   3 I observe things objectively
                                                    A                  A        :         E            :        F                      F    31    3 Anger and hurt can be transformed into compassion
                                                    A                A        :           E            :        F                      F    10*   3 I increase my power to intensely examine my life
                                                    A                A        :           E          :        F                        F    24*   3 I observe the way things constantly change from moment to moment
                                                    A                A        :           E          :        F                        F    28*   2 I notice that my mind wanders frequently
                                                                                                                                                  3 Seeing ”a world in a grain of sand” is a quality of looking deeply I cultivate day by day
                                                    A               A         :          E           :        F                        F    33
                                                    A               A       :            E         :          F                        F    30*   2 I notice things about myself I never knew before
                                                    A             A         :          E           :        F                          F     3*   1 notice things in nature that I never noticed before
                                                    A             A         :          E           :        F                          F    17*   1 teaches me to experience the world in an entirely new way
                                                    A             A        :           E           :        F                          F    25*   1 is harder than I first thought it would be
                                                    A             A        :           E           :        F                          F     7*   3 I often find great peace and joy in ordinary experiences
                                                    A           A          :         E            :       F                            F    26*   3 I observe experiences while I participate in them
                                                    A           A        :           E            :       F                            F     2*   2 I notice the causes of my emotions
                                                    A           A        :           E            :       F                            F    11*   3 I have more insights
                                                    A           A        :           E          :         F                            F     5*   1 feel thankful for things I usually take for granted
                                                    A           A        :           E          :       F                              F    16*   1 can be learned
                                                    A         A          :          E           :       F                              F    12*   2 I notice more control over my responses
                                                    A         A        :            E           :       F                              F    13*   2 I notice I feel more positive about the tasks I accomplish
                                                    A        A       :            E         :          F                               F     1*   2 I notice my emotions as they change during the day
                                                    A      A         :          E           :        F                                 F     9*   2 I notice that other people seem to like it when I listen this way
                                                    A    A        :         E            :        F                                    F    22*   1 makes me a more attentive listener
                                                    |-----+-----+-----+-----+-----+-----+-----+-----+-----|                                NUM    ITEM
                                                    10   20         30        40         50        60         70         80       90 100

                                                                          122231443333312121111 11     1                              1
                                                    5      1       3 11563548707525326162223097972678115                        2     8    PERSONS
                                                                 T          S        M         S         T

                                                    Illustrated by an observed category. Expected score: Mean. Each “:” indicates Rasch-half-point threshold. Number directly to the left of the
                                                    statement denotes the researcher’s hypothesized level of mindfulness engagement based on novice mindfulness practitioner journal entries: 1
                                                    = Beginning, 2 = Intermediate, 3 = Advanced. Read vertical numbers of student distribution as two-digits; for example, the “M” (Mean) = 36. S
                                                    = 1 Standard Deviation, T = 2 Standard Deviations.




International Journal of Transpersonal Studies 67
                                                    Figure 3. Mindfulness Practice Wright Construct Map
MAP OF PERSONS AND ITEMS
     MEASURE               | BOTTOM P=50% | MEASURE        | TOP P=50%       MEASURE
      <more> ------PERSONS-+-ITEMS        -+-ITEMS        -+-ITEMS            --- <rare>
      100            .#### +               +               +                   100
                           |               |               |
                           |               |               |
                           |               |               |
                         .|                |               |
                           |               |               |
       90                  +               +               +                    90
                           |               |               |
                      .### |               |               |
                         .|                |               |
                         .|                |               |
                        ## |               |               |
       80               .# +               +               +                    80
                        .# |               |               |
                       ### |               |               |
                     .#### |               |               |
                       .## |               |               |X
                     .#### |               |               |X
       70            .#### +               +               + XX                 70
                       .## |               |               |X
                      .### |               |               |
                    .##### |               |X              |X
                       ### |               |X              | XXX
                    .##### |               | XX            | XX
       60             #### +               +X              + XX                 60
                  .####### |               |               | XXXX
                 ######### | X             |X              | XX
                  ######## | X             | XXX           | XXXX
                 .######## | XX            | XX            | XXXXX
                 .######## | X             | XX            | XX
       50      .########## +               + XXXX          +X                   50
              .########### | X             | XX            |X
                     .#### | XXX           | XXXX          |X
                  .####### | XX            | XXXXX         |
                   .###### | XX            | XX            |
                   ####### | XXXX          |X              |
       40           ###### + XX            +X              +                    40
                      .### | XXXX          |X              |
                         . | XXXXX         |               |
                        .# | XX            |               |
                        .# | X             |               |
                         .|X               |               |
       30                .+X               +               +                    30
                           |               |               |
                         .|                |               |
                           |               |               |
                           |               |               |
                           |               |               |
       20                  +               +               +                    20
                         .|                |               |
                           |               |               |
                           |               |               |
                           |               |               |
                           |               |               |
       10               .# +               +               +                    10
      <less> ------PERSONS-+-ITEMS        -+-ITEMS        -+-ITEMS            <frequ>
     EACH ‘#’ IN THE PERSON COLUMN IS   4 PERSONS: EACH ‘.’ IS 1 TO    3




Figure 4. Mindfulness Practice Wright Map
68    International Journal of Transpersonal Studies                       Solloway & Fisher
Notice that item 8, at 55, is 17 units higher                  If then the student acknowledges that mind-
up the scale than item 22, at 38. After taking the 4-          fulness can be learned (item 16), and experiences some
unit error of measurement into account, we see that the        gratification in noticing what is usually taken for granted
same unit difference distinguishing the T1 from the T2         (item 5), then she or he is ready and able to experience
measures also distinguishes the differences between the        the “taken for granted things” in the group 2 and 3 items
two groups’ response likelihoods, respective to any pair       right above these. When the student in due course breaks
of items on the scale. These relationships constitute the      through the next group of category 1 items, a new level
substantive meaning of the quantitative comparisons            of critical awareness or attunement is obtained, which
facilitated by the scale. Any unit difference between          supports receptivity to the following group of largely
any two points on the scale will translate into substan-       group 3 items. Sticking with that critical attunement then
tively meaningful contrasts illustrated by the content         leads to the next group 1 transition into reduced stress
of the items and optimized rating scale. The constancy         (item 8), and the associated group 2 and 3 new balance,
of this relationship is itself substantiated by the fit to     centering, and enhanced physical sensations.
the measurement model, and the high correlations and
linear plots of the items’ scale values across sub sample                              Discussion
calibrations.                                                            Our replication of the first study offer further
                                                               scientific evidence and theory supporting the substan-
                                                               tive conjecture that the effects of mindfulness practice
Theory-Data Convergence
          The numbers 1, 2, and 3 in the first column          are teachable, learnable, and amenable to measure-
of the item names in Figure 3 indicate the pre-experi-         ment. Making “non-arbitrary measures” possible in
mental theoretically predicted calibration ranges. These       psychometrics was Rasch’s “outstanding contribution,”
predicted calibration ranges correlate 0.03 to 0.10 with the   according to Jane Loevinger (1965, p. 151). Loevinger
multiple independent subsample recalibrations of the 30        further observed that, “When his (Rasch’s) model fits,
items. The respondents’ ordering of the items thus differs     the results are independent of the sample of persons and
from the researcher’s original conceptualization of that       of the particular items within some broad limits. Within
hierarchy, offering an opportunity for rethinking theory       these limits, generality is, one might say, complete” (p.
and possibly establishing closer theory-data congruence.       151). This specific generality makes successful applica-
          The theoretical order was derived from several       tions of science possible and is crucial to meaningful,
years’ experience reading students’ mindfulness journals.      linked conversations among the interested parties.
It seemed evident that the empirical frequency with                      In this context, the historian of science, Bruno
which students mentioned or described various effects          Latour, remarked, “Every time you hear about a successful
of mindfulness practice in their journals followed the         application of science, look for the progressive extension
pattern described by the three assigned categories, with 1     of a network” (Latour, 1987, p. 249). The extension
emerging earliest, and 3, latest.                              of metrological networks in psychosocial science has
         But does the empirical order of emergence neces-      been effectively blocked by instrument-dependent and
sarily imply a hierarchy of effects? Perhaps the effects       arbitrary numerical representations of its measured
initially noticed are landmarks or a general structure         constructs. The non-arbitrary measures calibrated in this
within which the experience of later effects are catego-       study begin the work of investigating the possibility that
rized. The group 1 items in fact span the entire calibration   mindfulness may be characterized by lawful regularities
range, and seem to be marking out significantly different      in its patterns of presence and absence. Insofar as those
ranges in the items, with the content of the group 1 item      lawful regularities are not found to be dependent on the
signifying a theme common to the group 2 and 3 items           particulars of this study, a common language for inter-
falling in that range.                                         preting and reading qualitatively-informed amounts of
           That is, if a student is experiencing enhanced      mindfulness presence and absence will emerge.
listening ability as an effect (item 22, at the bottom of                The first requirement for any network of
the scale), then it becomes possible to do the “noticing”      relations is a medium or a common language. The
(category 2) items right above it, each of which may be in     mindfulness ruler calibrated in this study is a first step
some degree entailed by the first item.                        in establishing a non-arbitrary common language and

                                                               International Journal of Transpersonal Studies 69
Mindfulness in Measurement
an invitation for further meaningfully linked conversa-       program at one particular time? The population might
tions. Such common languages are in various stages of         be expanded to include college students in general, or
emergence in different areas of psychology, education,        adults in general, but this will be determined only by
and health care (Dawson, 2002a, 2002b; Fisher, 1997a,         additional research that focuses specifically on these
1997b; Stenner, 1994).                                        issues.
          What these studies have in common is that                    Establishing a common language of mind-
scatter plots illustrating the measured relationships         fulness practice effects that researchers can think in
are linear. A plot illustrating one-to-one relationships      together requires more than having different samples of
between amounts of length measured in centimeters and         respondents reproduce the calibrations of the items from
amounts of length measured in inches is linear because        one instrument. It must also be possible for different
amounts of length remain invariant across the numerical       samples of items from the infinite universe of all possible
representations of it. Measures exhibiting the properties     mindfulness practice effects items—that is, different
of conjoint additivity, invariance, sufficiency, parameter    mindfulness practice effects instruments—to produce
separation, and others which accordingly emerge from          linearly comparable measures that could be expressed in
data fitting a Rasch model, are linear in the same way.       a common metric. Scientific research, properly under-
          A scatter plot illustrating a typical correlation   stood, makes a fundamental priority of this kind of
of about 0.91 between separate sample calibrations of         collectively distributed care for the unity and sameness
the mindfulness self-assessment is shown in Figure 1.         of what is studied.
The constant amounts of mindfulness practice’s effects                 Human beings, like any form of life, exist in
across the samples measured are illustrated in the way        ecological webs of relations. Physical, emotional, social,
the pairs of item calibrations fall together in a consis-     and spiritual forms of well-being are experienced as
tently orderly pattern roughly along the identity line (an    projected from networked webs of relations. Susser and
imaginary line extending from the lower left corner to        Susser (1996) called the future of epidemiology eco-
the upper right). Though the item order is constant from      epidemiology, acknowledging the necessity of mean-
T1 to T2, the calibrations are somewhat skewed away           ingful communication across molecular, individual, and
from the identity line because, at T1, the students are       societal levels of organization.
inexperienced with the construct and unable to distin-                 Similarly, our findings point to the convergence
guish among the effects of mindfulness practice as well       of mindfulness effects across all three ecological levels
as they can after training. This gain in construct defini-    of relations in positive psychology (Figure 5), and so
tion has been documented in other research, with the          acknowledge and incorporate the ecological implica-
suggestion that the items be anchored at their outcome        tions of mindfulness practice. Substantial growth in
values in practical applications (Bezruczko, 2005).           psychological strengths was demonstrated with only
          The pattern is, in addition, not as narrow and      one day a week of intentional practice. These effects
linear as a plot of centimeter vs. inch measures of the       converge simultaneously with several of The Five Basic
same objects would be, but it still provides us with a        Postulates of Humanistic Psychology (Greening, n.d.)
precision of more than four statistically distinct ranges     and are reflected as well in Figure 5. This strengthening
(when reliability is greater than 0.94). These ranges are     of emotional balance integrated itself positively across
sections of the measurement continuum that have centers       the subjective, individual, and social levels. That our
three errors apart (Wright & Masters, 1982, p. 96), and       calibrated ruler now offers non-arbitrary measures of
so establish the precision of the calibrations that can be    this growth opens the possibility for testing the efficacy
expected to be reliably reproduced for this instrument        of methods of mindfulness instruction in developing
by samples of about these sizes from the population.          psychological strengths within and between individ-
          The nature of the population remains an             uals, ecologically. Might one future of the exploration
issue for further investigation. Is it the population of      of mindfulness practice be defined by developments in
all possible students in preservice teacher education         the direction of an eco-positive psychology facilitated by
programs? Or is it only students in one particular preser-    non-arbitrary measures?
vice teacher education program? Or will the population                 Indeed, we have dedicated much space to the
studied in this project turn out to be just students in one   details of the quantitative aspects of the study. As the


70    International Journal of Transpersonal Studies                                               Solloway & Fisher
Positive Psychology/Subjective Level—Valued Subjective Experiences:
  Well-being, contentment, satisfaction, happiness
   •	 Notice	I	feel	more	positive	about	the	tasks	I	accomplish	(Postulates	3,	5)	
   •	 Feel	thankful	for	things	I	usually	take	for	granted	(Postulates	3,	4,	5)
   •	 I	often	find	great	peace	and	joy	in	ordinary	experiences	(Postulates	3,	5)
   •	 Notice	that	I	experience	a	kind	of	happiness	that’s	different	(Postulate	3)
   •	 Makes	me	feel	peaceful	(Postulate	3)
  Positive Psychology/Individual Level—Positive Individual Traits:
  Capacity for Vocation
    •	 Notice	I	feel	more	positive	about	the	tasks	I	accomplish	(Postulates	3,	5)
    •	 Reduces	my	stress	(Postulate	3)	
  Interpersonal skill
     •	 Makes	me	a	more	attentive	listener	(Postulates	3,	4)
     •	 Notice	that	other	people	like	it	when	I	listen	to	them	this	way	(Postulates	3,	4,	5)
     •	 Notice	more	control	over	my	responses	(Postulates	3,	4,	5)
     •	 Notice	the	causes	of	my	emotions	(Postulate	3)
  Aesthetic Sensibility
    •	 Notice	things	in	nature	I	never	noticed	before	(Postulate	3)
    •	 Feel	thankful	for	things	I	usually	take	for	granted	(Postulates		3,	4,	5)
  Wisdom
    •	 I	have	more	insights	(Postulate	3)
    •	 Increases	my	power	to	intensely	examine	my	life	(Postulates,	3,	5)
    •	 Can	observe	my	thoughts	without	being	caught	up	in	them	(Postulates	3,	4,	5)
    •	 Feel	thankful	for	things	I	usually	take	for	granted	(Postulates	3,	4,	5)
  Positive Psychology/Group Level—Civic Virtues and the Institutions Toward Better Citizenship:
  Responsibility, Nurturance, Moderation, Tolerance, Civility, Work Ethic
    •	 Notice	more	control	over	my	responses	(Postulates	3,	4,	5)
    •	 Notice	I	feel	more	positive	about	the	tasks	I	accomplish	(Postulates	3,	5)	


  Correlations	between	Seligman	&	Csikszentmihalyi’s	(2000)	Positive	Psychology	Definition,	
  Five	Postulates	of	Humanistic	Psychology	(Greening,	n.d.),	and	Novice	Practitioners’	Descriptions	
  of	Effects	of	Mindfulness	Practice


  Figure 5. Positive Psychology and Five Basic Postulates of Humanistic
  Psychology Link to Effects of Mindfulness Practice for Novice Practitioners


                                                        International Journal of Transpersonal Studies 71
Mindfulness in Measurement
value of qualitative work in the history of mindfulness                                Conclusions
practice is well established, it seemed more important                    The study is innovative in at least three ways.
to deeply describe our quantitative process. As a quali-       First, it demonstrates mindfulness practice as measurable,
tative researcher, Solloway is well aware of the initial       as teachable and learnable, and as an object of experi-
prejudice she herself brought to Fisher’s early introduc-      mental research. Second, it does so through a rich herme-
tion of the idea that a quantitative corroboration could       neutic integration of qualitative and quantitative processes
enhance this work. It was her meditation practice in           (Fisher, 2003a, 2003b, 2004). One of Rasch’s probabilistic
support of her mindfulness practice that brought her           conjoint models of fundamental measurement is shown to
face to face with that prejudice. Solloway’s commitment        entertain uncertainty and chance in conversation, in order
to truly and openly entering the present moment with           for what is known to converge with differences that make
curiosity dismantled that prejudice in order to more           a difference across ecological webs of relations. Third, the
non-judgmentally investigate Rasch models as possibili-        study is innovative in its qualitative evidence corrobo-
ties for discovering the organic partnership between her       rated by quantitative evidence of the value of mindful-
qualitative data and the quantitative ruler that data were     ness practice as an assignment in the university classroom.
ready to construct with Fisher’s help. We have worked to       Future research will seek to generalize these findings to
make that process as transparent as possible.                  other mindfulness settings and measures.
                                                                          The way has never been more open for researchers
                                                               to work back and forth between qualitative evidence and
               Issues for Future Research
         Several issues present themselves for further         more fully mathematical, quantitative measures. To do so
study. First, can the effects measured here be reproduced      with integrity, care must be taken to retain the contempla-
elsewhere by others? Second, can the revised substantive       tive and compassionate in the best qualitative work while
theory of the variable be used to improve the instrument?      at the same time holding quantitative methodologies to
Third, DIF analysis shows that items 25 and 28 differ          the rigorous requirements of fundamental measurement.
significantly by sex; this contrast is confounded a bit by     Important obstacles to meaningful conversations have
the repetition of the same people across two time points.      been removed; the way has opened for the proliferation of
This issue should be addressed in a later study. Fourth,       invitations for meaningful conversations and the means for
the participants’ overall growth in mindfulness practice       sustaining those conversations is at hand. We suggest that
as defined by the survey items demonstrates the growth         this work supports not a “type of scientism [which] can be
predicted in several sections of the operational defini-       termed methodolatry, the undue elevation of a method to
tion of mindfulness proposed by Bishop, Lau, Shapiro,          a sacred artifact” (Friedman, 2003), but rather a research/
Anderson, Carmody, Segal, Abbey, Speca, Velting, &             living stance of a curiosity open to the present moment.
Devins (2004). Follow-up studies can further corrobo-
rate this finding. Fifth, what is the nature of the gap                                     Endnotes
separating the five items at the top of the scale from those    1. Portions of this paper were presented at the International Objective
                                                                   Measurement Workshop, April, 2006, Berkeley, CA; American Asso-
lower down? Sixth, the suggestive connections between              ciation for the Advancement of Curriculum Studies, April, 2006,
novice practitioners’ interest in positive and humanistic          Berkeley, CA; and the American Educational Research Association
                                                                   Conference, April, 2006, San Francisco, CA.
psychologies might be further investigated with other
                                                                         We thank the reviewers for their helpful insights.
studies providing different mindfulness instructions but
comparable with non-arbitrary measures. Seventh, the
corroboration of the journal entries and the mindful-                                Appendix A:
ness ruler to show growth by university students in their      Journal Entry Samples with Instructor Responses and Pre/
ability to mediate the debilitating effects of emotional                  Post Measures for Students A, B, C
imbalances, stress, and prejudicial orientations to present
moment experience provides important validation for            Week 1
the inclusion of mindfulness assignments at the univer-
                                                               Student A—
sity. Future research should address these corroborations
                                                                        Usually when I awake in the morning, my mind
and analyze the differences using rigorous measurement
                                                               is racing with thoughts of everything I need to get done.
models.


72    International Journal of Transpersonal Studies                                                        Solloway & Fisher
Taking deep breaths and trying to clear my mind proved a bit       Good Morning, _____________!
difficult. Lying in bed, trying to be in the now, I could hear              Best wishes for your next mindfulness day. Be sure to
my heart beating, and my ears ringing. I could feel that my        put something close to your bed to remind you as soon as you
eyes were itchy, my teeth were throbbing (I grind them in my       awake that it is your mindfulness day. Take that first conscious
sleep), and my throat was sore. I thought that I must be doing     breath of the morning and begin your mindfulness day. Be
this wrong, this wasn’t fun. Relax more, take another breath,      gentle with yourself. Be happy at whatever number of times
concentrate. Now I noticed that everything has a rhythm,           you remember during the day to use your breath as an anchor
and as I listened and felt that rhythm, I was soothed. Eating      for your attention. In your journal entry, describe at least one
my bowl of Kashi, I had to slow down, put my spoon down            mindful moment and analyze how it was different from ordinary
between bites, and concentrate on each mouthful. I could feel      moments…I look forward to what you learn…ss
and enjoy the coolness of the milk, the taste and texture of the
cereal, the weight and smoothness of the spoon. This was chal-     Student C—
lenging and unnatural for me as I am usually not that aware of               Today while trying to be mindful I realized it could
eating breakfast. The day continued to be a challenge. Many        be harder than I thought. It was hard at first because I usually
times I had to stop, breathe, and pay attention to the rhythm      daydream and aren’t very attentive to what is going on around
to clear my mind. What stands out for me is how easily dis-        me. As I paid closer attention to breathing and clearing my head
tracted I am from the moment. Interruptions from my son,           of the daydreaming, I was more attentive to what was actually
my dogs, the phone, but mostly from my own mind, seem a            going on around me. I noticed the bird’s chirping, I noticed
huge obstacle. I need to incorporate all of these into “happen-    other people talking as they walked by me, I noticed the con-
ings of the now” instead of intrusions. Being in the moment        struction worker’s noise, and in class I was more attentive to the
seemed easier in the evening. Perhaps my mind was tired, or I      professor and fellow classmates. I was more mindful of what
was less distracted now that the day was near an end. Playing      they said and of what I said when talking to them. When talking
cards with my husband, it was simpler to enjoy just doing          to my friends I paid more attention to what they were saying
what I was doing, and not thinking about anything else. For        instead of half listening and half daydreaming at the same time.
some reason, this day seemed longer than most. Maybe it was        It was a clear feeling being mindful all day. It was a nice feeling
because I became disappointed with myself every time my            to actually be in the present when I needed to be.
mind wandered, which was often. I hope, as the mindful days
progress, that “being in the now” will become more natural         Good Evening, ________,
for me.                                                                     Yes, the practice of keeping attention focused in the
                                                                   present moment seems simple. But as you discovered, the mind
Good Afternoon, ____________,                                      constantly dashes out of the moment taking our thoughts
          You wrote: “Maybe it was because I became disap-         elsewhere. Best wishes for your next mindfulness day…ss
pointed with myself every time my mind wandered, which
was often.” Remember that it is NORMAL for the mind to             Week 4
wander. Mindfulness practice is about NOTICING that. If
you notice it OFTEN, that means that you are practicing            Student A—
mindfulness…try to just notice without judging yourself or                    Thanks to your input from last week, and the revela-
anything else in the moment…let me know what happens……             tion that what was really driving my busy mind was a need for
Best wishes for your next mindfulness day…ss                       approval, I have found it much easier to focus on the now. It’s
Student B—                                                         funny that once I was aware of this, I find being mindful, and my
          The first mindfulness day didn’t go as well as I would   entire day, less stressful. I think I was just seeking exterior goals,
have liked. I didn’t stop and pull myself back as much as I        the shell as it were, when really, inside I was seeking control of
would have liked. The one time I really did experience it was      my day. But by keeping my mind on what I am presently doing,
after work and classes. I came home and lay down to take a         instead of what also needs to be done later, each undertaking has
nap. As I lay there, I thought about being mindful and was         become so much more enjoyable and freeing. Do you believe
able to bring myself back into the moment. It was nice to just     you can actually enjoy a task as mundane as folding laundry?
lay there and hear myself breathe and feel the breeze come in      When you’re in the moment, you can feel the warmth, feel the
though my open window and fall asleep.                             textures, smell the fresh scents. Meals taste better, are more plea-


                                                                   International Journal of Transpersonal Studies 73
Mindfulness in Measurement
surable, and I think you actually eat less because you realize        Week 8
when you’ve had your fill.
          Listening during conversations is gratifying, because       Student A—
you are no longer obsessed with your own agendas, or what                        With the holidays approaching, I was afraid I might
you’d rather be doing. It’s not that I no longer seek approval, but   backslide, start to panic about what needs to be done before
from my new viewpoint, I no longer need to chase after it. My         family arrives. My need for approval, my old mental habit, might
mind still wanders from the moment, but I can relax, cleanse          rear its ugly head. But that hasn’t happened. This mindfulness
my mind with a breath, and bring it back. Or, if I am thinking        is like a natural tranquilizer. It’s not that I’m numb or blasé. I’m
about something, I become aware and allow myself to think. I          excited and looking forward to sharing the holidays. It’s more
have to do this every day now, not just one day a week. It’s not      like I am at ease, aware of my own mental connections with
that this is a radical change, but my patterns of thinking are        what’s around me. Life is touching me, and I’m allowing it.
changing, and you can’t just turn that on once a week.                With the “approval monster” banished, I am free to be sensitive
                                                                      to a whole new realm, and enjoy each experience and mindful
Good Evening, _______,                                                moment as it comes. From past experience, I had connected
         You wrote, “Do you believe you can actually enjoy            family gatherings with a certain amount of stress; trying to
a task as mundane as folding laundry? When you’re in the              make sure everything was perfect (nothing is ever perfect, so
moment, you can feel the warmth, feel the textures, smell             that was unrealistic to begin with). And what for? Approval.
the fresh scents.” YES! One of the most lovely benefits of            And why was approval important? Because it made me feel
mindfulness practice is the way it lets you experience the            good, like I should be admired or something. Once I realized
AWE and WONDER of ordinary tasks or experiences!                      how egotistical this really was, and how it was cutting me off, I
This nourishes the soul and we feel more energy for our lives!...     could clear my mind and end the pursuit. While I was chasing
Best wishes for your next mindfulness day…ss                          self-satisfaction, life was passing by unnoticed. And like I said
                                                                      before, nothing in life is perfect--but that is okay. Something
Student B—                                                            doesn’t have to be perfect to be enjoyed. You just have to
          I was actually very pleased with my mindfulness             ignore your old impulse to fix everything, and instead become
this week. Before leaving the house I caught myself at least          comfortable with the reality. No matter what reality brings, it
twice and was able to bring myself back into the moment. The          can be beautiful. You don’t have to analyze it, manage it, or
rest of the day I forgot to do it.                                    improve upon it - just be part of it. This holiday season is going
                                                                      to be the best one since childhood.
Good Morning, _________!
        In your next journal entry, try to describe one               Good Morning, _______,
mindful moment in your day and analyze how it was different                     Well, this is your last mindfulness journal entry.
from ordinary moments….ss                                             Thank you for letting me share in this journey with you. It has
                                                                      been a joy….Best wishes for your CONTINUED mindfulness
Student C—                                                            practice…ss
          This week my mindfulness brought me back to the
senses of walking around campus. Since being sick it is hard          Student B—
to keep focus but I have since recovered and while walking                      My last mindfulness day was very successful. I have
to class this week I was happy that I was finally feeling better      come such a long way since the first day of this project. On
and therefore had a better outlook on things. I once again            this day, I was able to successfully catch myself at least ten
noticed the chatter of people talking and the leaves blowing          times and bring myself back. It was an amazing feeling!
and rustling and the clatter of high heels clicking along and         Good Afternoon, _______!
the construction going on. It is nice being able to walk and                    Yes, what we cannot change is that you can only
listen with a clear head!!                                            live ONE moment at a time AND that the mind constantly
                                                                      wanders! And mindfulness practice empowers you to
Good Morning, ________,                                               NOTICE that the mind has wandered, bring it back, and
        Glad you are feeling better. Best wishes for your             then live that moment with crystal clear energy and wisdom!
next mindfulness day…ss                                               Best wishes for your continued use of mindfulness practice
                                                                      with ever more expertise beyond this assignment…ss

74     International Journal of Transpersonal Studies                                                            Solloway & Fisher
S Solloway Fisher2007 Mindfulness
S Solloway Fisher2007 Mindfulness
S Solloway Fisher2007 Mindfulness
S Solloway Fisher2007 Mindfulness
S Solloway Fisher2007 Mindfulness
S Solloway Fisher2007 Mindfulness
S Solloway Fisher2007 Mindfulness

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S Solloway Fisher2007 Mindfulness

  • 1. Mindfulness in Measurement: Reconsidering the Measurable in Mindfulness Practice Sharon G. Solloway Bloomsburg University Bloomsburg, PA, USA William P. Fisher, Jr.1 Avatar International, Inc. Sanford, FL, USA Can an organic partnership of qualitative and quantitative data confirm the value of mind- fulness practice as an assignment in undergraduate education? Working from qualitative evidence suggesting the existence of potentially measurable mindfulness effects expressed in ruler measures, a previous study calibrated a mathematically invariant scale of mindfulness practice effects with substantively and statistically significant differences in the measures before and after the assignment. Current efforts replicated these results. The quantitative model is described in measurement terms defined at an introductory level. Detailed figures and appendices are provided, and a program of future research is proposed. T he value of mindfulness practice as contributing present moment. These journal entry responses link to psychological strength has a long history of themselves to a number of important self-care issues: the supporting anecdotal evidence. A rich legacy of quality of the inner-life suggested by Seligman and Csik- such research exists in Buddhist literature as far back as szentmihalyi (2000), self-determination (Ryback, 2006), the seventh century BCE. Buddhist practitioners today emotional balance (Goleman, 1995), stress-reduction, in both the East and West are actively engaged in broad- and empathy (Kabat-Zinn, 2005) to name a few. Solloway ening this legacy via a scientific research agenda. This (the first author) teaches in higher education, and holds agenda seeks to document the physiological effects of both a meditation practice and an orientation to mind- meditation and mindfulness practice using methods fulness practice when not meditating. Her daily experi- that meet the technical standards expected of precision ence of witnessing the debilitating effects of emotional measurement and experimental design. The activities of imbalances, stress, and prejudicial orientations to present the Dalai Lama’s Mind and Life Institute (http://www. moment experience in the lives of university students mindandlife.org), among others, demonstrate the current awakened her compassion. Offering assignments in mind- vigor of this interest. fulness practice became her compassionate intervention. Mindfulness practice has been described as Developing documentation of the effects strengthened non-judgmental awareness of both internal and external the argument for such assignments. experience, moment to moment, “…an open, undivided The use of mindful awareness as a method of observation of what is occurring both internally and immersion (Moustakas, 1990) for reading and responding externally rather than a particular cognitive approach to to students’ journal entries across several semesters external stimuli” (Brown & Ryan, 2000, p. 823). One of gave Solloway insight into recurring themes associated the psychological strengths of mindfulness is the capacity with powerful individual transformations across the to maintain an emotional balance within any particular assignment’s duration. The students were different each life moment, whatever that happens to be. Novice mind- semester but the effects of mindfulness practice emerged fulness practitioners (Solloway, 1999, 2000, 2001, 2004) through similar themes and ranges each time. The were asked to describe their experience of mindfulness journal entries were anecdotal self-reports of those effects practice as a non-judgmental focus of attention in the for each student and were in themselves powerful voices 58 International Journal of Transpersonal Studies 26, 2007, pp. 58-81 Studies,
  • 2. for the value of this compassionate intervention. Growth patterns emerged regarding students’ depths of engage- was palpable…like noticing that the worn patch on your ment in the project (see Appendix A). The journal entries son’s jeans no longer matches where his knee was a few suggested a range of depth of engagement in the practice; months ago. You don’t have to measure his height to consistent reports of specific categories of experience know he has grown, but the availability of an instrument began to suggest patterns of “Beginning,” “Intermediate,” to provide that measure certainly brings valuable infor- and “Advanced” engagement. These labels only refer to an mation to bear when selecting a pair of jeans with a better accumulation of patterns among the self-reported experi- fit. The journal entries, like the jeans, showed evidence of ences of these novice practitioners. But the accumulation individual growth, but the question arose as to whether it of journal entries seemed to indicate that the participants was possible to calibrate a ruler to provide more specific in this project semester to semester “grew,” some more information about each individual’s growth. than others. The most well-known mindfulness instruments Could an instrument be constructed that are the Mindfulness Attention Awareness Scale (Brown reflected the common themes in the journals and also & Ryan, 2003), the Kentucky Inventory of Mindfulness created a ruler measuring growth across the themes? In Skills (Baer, Smith, Hopkins, Krietemeyer, & Toney, other words, could these patterns be corroborated by a 2006; Baer, Smith, & Allen, 2004), and the Toronto quantitative measure requiring experimental tests of the Mindfulness Scale (Lau, Bishop, Segal, Buis, Anderson, hypothesis that the variable of interest is in fact quantita- Carlson, Shapiro, & Carmody, 2006). Solloway’s (1999, tive, that is, that the variable is divisible into the additive 2000, 2001, 2004) roots as a qualitative researcher magnitudes necessary for meaningful numeric represen- influenced her desire to develop a scale directly out of tations? This would require a model that pitted the diffi- her students’ journal entries rather than select a scale culty of each item against the ability of the participant developed from other sources. Could the cumulative without any other influences. This is the same problem voices of her students be translated into a scale that would Rasch (1960) saw when he contemplated the problem corroborate their journal entries retaining the individu- of statistical methods most often used in psychometric ality of experience just as the journal entries did? Fisher’s methods that are group-centered rather than ones (2000, 2003a, 2003b, 2004) experience with developing in which each individual is characterized separately instruments from qualitative data takes advantage of and from which, given adequate data, the individual Rasch models to give ruler measures of the qualitative parameters can be estimated. It is further essential construct without compromising the integrity of the that comparisons between individuals become inde- individual measured, thus opening the door to collabora- pendent of which particular instruments – tests or tion toward an answer. items or other stimuli – within the class consid- ered have been used. Symmetrically, it ought to be The Present Research possible to compare stimuli belonging to the same The first study (Solloway & Fisher, 2007) grew class – “measuring the same thing” – independent of out of Solloway’s seven-semester experience of coaching which particular individuals within a class considered novice mindfulness practitioners (students in a pre- were instrumental for the comparison. This is a huge service undergraduate teacher education course) through challenge, but once the problem has been formulated an eight-week introduction to mindfulness practice. it does seem possible to meet it. (Rasch, 1960, p. xx) These students used the breath as an anchor for attention in the present moment all day one day a week for eight Rasch models enable one to imagine a methodology that weeks. At the end of each day of practice, the student embraces both the contemplative and compassionate submitted an email journal entry describing the expe- found in qualitative work describing the experiential rience of mindfulness practice that day. Solloway, a without sacrificing the rigor of measurement required vipassana practitioner since 1996, mindfully read each in experimental science. Yet Rasch models have their journal entry. Out of this deep listening, she responded opponents as well. The following section will describe to each journal entry within 24-hours of receiving it, what happened when Solloway’s mindfulness practice providing encouragement that seemed appropriate to entered the Present Moment of Fisher’s tutelage on the the individual entry. Across the seven semesters, obvious subject. International Journal of Transpersonal Studies 59 Mindfulness in Measurement
  • 3. repeatedly proven themselves essential to science over Fisher’s Two-Year Mentorship of Solloway Rasch measurement practitioners are sometimes the course of its history. The identification of anomalies accused of an over-zealous advocacy of their methods, is fundamental to allowing exceptions to prove (in the as a kind of method idolatry. Sometimes, however, such sense of testing) rules. It is said that nature reveals herself accusations have less to say about the accused than by her exceptions, but when mathematical models incor- they do about quick judgments foreclosing prematurely porate interaction terms and do not require invariantly on the opportunity to see something new. Instead of separable parameters, as do many IRT and statistical dismissing what seems on the face of it to be an unrea- models, these exceptions are hidden within summary sonable position—strong advocacy of either (1) one statistics, where they are either ignored or very difficult method among many equivalent methods, or (2) math- to find. Rasch models, in contrast, have been associ- ematical invariance requirements that can seem unreal- ated from their inception with a variety of graphical istically rigid to those unfamiliar with them—perhaps and statistical methods for identifying and evaluating a more sympathetic attitude, or one more sensitive to anomalies (Smith, 2000). For more information on this the ambiguities of interpretation, as outlined by Kuhn controversy, see Wright (1977a, 1984), Fisher (1994), or (1977, pp. xi-xii), would lead to insights as to why and Andrich (1988, 2002, 2004). how reasonable people might take an apparently unrea- Taking another tack on this issue, there are sonable position. others who contend that methods such as Confirmatory For instance, there are those who contend that Factor Analysis (CFA) can be as informative as a Rasch Rasch models are fine to apply when they happen to fit model in the identification of unidimensional constructs. data, but they often do not, and so other, more flexible Though this is true in limited applications (Reise, models are then required (van der Linden & Hambleton, Widaman, Pugh, 1993), (1) CFA lacks a stochastic frame 1997). But generality in the measurement of a construct of reference, meaning that there are no error terms for the requires the identification of patterns of invariance that factor loadings; (2) secondary factors can be completely hold up across data sets (Rogosa, 1987; Michell, 1990, dependent on the particular error distribution that just 2000). As Embretson (1996, p. 211) puts it, happens to be present in one data set, but not in others; (3) CFA does not provide the desired additive unit of It is sometimes maintained that the Rasch model is measurement, since the raw scores are usually assumed to too restrictive and does not fit real test data suffi- provide it (and though a logistic regression of the scores ciently well. However, even if a more complex IRT on the loadings might come close), and (4) CFA does not model is required to fit the data, the total score provide any means of identifying or evaluating anomalous scale would not provide a relatively better metric. In individual responses. These four shortcomings of CFA as fact, if item discrimination parameters are required a measurement model mean that multimodal data will to obtain fit, total score is not even monotonically produce multifactorial results, even if the data analyzed related to the IRT theta parameters. The IRT trait are a subset of a larger data matrix previously shown by score, even for equal total scores, would depend on CFA to be a single unidimensional factor (Smith, 1996; which items were answered correctly. Wright, 1988, 1991). Finally, raw scores from tests and surveys are These kinds of confoundings can occur because multi- typically interpreted as though they are meaningful repre- parameter IRT models are internally inconsistent, sentations of quantitative amounts, when they demon- asserting unidimensionality even while allowing item strably are not. Scores summed from two sets of items characteristic curves to cross (Lumsden, 1978; Andrich, drawn from different agreeability or difficulty ranges of 1988; Wright, 1984). the same survey, test, or assessment do not and cannot Rasch (1960, pp. 37-8) was certainly aware of plot in a straight line. Centimeter and inch measures of the problems of interactions, and wrote, “models are not the same object lengths do plot in a straight line, as the meant to be true,” since no data ever fit a model exactly. relation between the two number systems is dominated Models are meant to be useful and meaningful, however, by the invariance of the objects’ amounts of length. and abstract heuristic ideals, such as Plato’s redefini- If nonarbitrary, invariant measures of constant tion of the elements of geometry, Galileo’s frictionless amounts could be obtained from tests and surveys, plane, or Carnot’s perfectly reversible heat engine, have 60 International Journal of Transpersonal Studies Solloway & Fisher
  • 4. would not these be worth obtaining? Might it be that tics that are sufficient in the sense of summarizing data those who dismiss Rasch’s models for measurement as with no loss of information. just one approach among many equivalent approaches are What this means is that, “if there exists a missing something important, perhaps even something minimal sufficient statistic for the individual parameter essential? Theta which is independent of the item parameters, then The fact is that data scaled via fit to a Rasch the raw score is the minimal sufficient statistic and the model can plot linearly, in close approximations to the model is the Rasch model” (Andersen 1977, p. 72). As way quantitative amounts dominate the relation between Wright (1977b) pointed out, it then follows that centimeters and inches, or grams and ounces. Further- Unweighted scores are appropriate for person more, this kind of a plot is defined as the hallmark of measurement if and only if what happens when a quantitative meaningfulness by philosophers and theo- person responds to an item can be usefully approxi- reticians who are unconcerned with and not informed mated by a Rasch model.... Ironically, for anyone about Rasch’s models. Finally, it has been shown that, who claims skepticism about ‘the assumptions’ of insofar as a score from a test or survey provides a useful the Rasch model, those who use unweighted scores basis for measurement, the model that it must fit is a are, however unwittingly, counting on the Rasch Rasch model. model to see them through. Whether this is useful Thus we have measurement theoreticians and in practice is a question not for more theorizing, but philosophers (Falmagne & Narens, 1983; Narens, 2002; for empirical study. (p. 114) Roberts, 1985, 1999) investigating the meaningfulness of quantitative statements, and arriving at the essential In other words, if a count of correct answers or a sum importance of invariance as a fundamental criterion for of ratings can provide a meaningful basis for invariant, telling sense from nonsense. Mundy (1986), for instance, additive quantification, then a Rasch model holds. summarizes this work in terms applicable to the differ- Even when data are not evaluated for fit to a ence between curved raw score plots and linear length Rasch model, even when the invariance and additivity plots, saying, properties of quantitative measurement are ignored, use of test, survey, or assessment scores as though they are The hallmark of a meaningless proposition is that measures inherently implies acceptance of Rasch’s sepa- its truth-value depends on what scale or coordinate rability theorem. This is because the parameter separation system is employed, whereas meaningful proposi- theorem is nothing more or less than a formal representa- tions have truth-value independent of the choice tion of the rigorous independence of figure and meaning, of representation, within certain limits. The formal or of name and concept, that must be assumed in any analysis of this distinction leads, in all three areas honest effort at communication (Fisher, 2003a, 2003b, [measurement theory, geometry, and relativity], to 2004), even in the discourses of deconstruction (Ricoeur, a rather involved technical apparatus focusing upon 1977, p. 293; Derrida, 1982, p. 229; Derrida, 1989, p. invariance under changes of scale or changes of coor- 218; Gasché, 1987, p. 5). Rasch’s mathematics make tests dinate system. (p. 392) of the qualitative hypothesis of quantitative meaningful- Hall, Wijsman, and Ghosh (1965) show “that the set of ness (Michell, 1990; Narens, 2002) more accessible and invariant rules based on a sufficient statistic is an essen- practical than most work in this area. And in so doing, tially complete subclass of the class of invariant rules” Rasch taps deeply into the history of measurement and (Arnold, 1985, p. 275). Rasch models are valued for the deploys rich possibilities for mathematical thinking that fact that counts of correct responses or sums of ratings remain largely unexplored (Wright, 1988, 1997a). are minimally sufficient statistics (Andersen, 1977; van der Linden, 1992). Rasch learned of sufficient statis- Solloway’s Study tics from their inventor, Ronald Fisher (1922), and This study operationalizes mindfulness as a considered this work the high mark of Fisher’s accom- construct, evaluates stability over time and across groups plishments (Andrich, 1997; Wright, 1980). In a Rasch receiving and not receiving mindfulness training, and model, ordinal scores are minimally sufficient, and thus establishes a metric for measuring change in amounts necessary, since they are functions of all the other statis- of mindfulness. The experience of novice mindfulness International Journal of Transpersonal Studies 61 Mindfulness in Measurement
  • 5. practitioners is taken as a basis for the nurturing of an include the possibility of unifying research communities organically integrated conceptualization of the measured via a consensus focus on experimentally demonstrated construct. common objects of investigation that are furthermore measured in the common mathematical language of instruments all traceable to reference standard metrics Method (Fisher, 2004). Instrument Fundamental measurement-based guidelines This research tests for the separability of a for developing high quality survey items (Fisher, 2006) parameter associated with student mindfulness measures were followed in the development of the instrument. A from two parameters associated with mindfulness item bank of thirty assessment items were constructed from and rating scale calibrations. In other words, the substan- the students’ journal entries (a database of over 350 sets tive hypothesis tested in this research can be expressed of journal entries). Three more items were added to the as instrument after the completion of the original study, in ln(Pnij /Pnij-1) = Sn - Mi - Rj the Fall, 2006, administration. The items were grouped in three categories of hypothesized mindfulness practice that is, that the natural logarithm of the response odds development: Beginning, Intermediate, and Advanced (the probability P for any student n on any item i in (Appendix B). Items were randomized for the final draft response category j relative to category j-1) of any student of the instrument (Appendix C). n’s response to any item i on the self-assessment is due Eight response options (Absolutely Disagree, only to the difference between that student n’s measure Very Strongly Disagree, Strongly Disagree, Disagree, S of the effects of mindfulness practice and the calibra- Agree, Strongly Agree, Very Strongly Agree, Absolutely tion M of the mindfulness practice effects item i and Agree) were provided. the agreeability calibration R of the response category j (Andrich, 1978; Wright & Masters, 1982; Wright & Measurement Theory Mok, 2000). Criteria for obtaining objectivity in measure- In short, the model tests the hypothesis that ment comparisons include conjoint additivity (Luce & mindfulness is the primary construct dominating the Tukey, 1964), statistical sufficiency (Arnold, 1985; Hall, question and answer exchange. Analysis of the model Wijsman, & Ghosh, 1965), invariance (Krantz, Luce, residuals then aids in identifying individual responses, Suppes, & Tversky, 1971), conditional independence students, and items as influenced by something different (Kolmogorov, 1950), and infinite divisibility (Levy, 1937). other than the primary construct. All of these are embodied in the criterion of parameter separation (Rasch, 1960), as has been shown over the Research Participants course of number of analyses and proofs (Andersen, Study participants were 338 unique preservice 1977; Andrich, 1988; Fischer, 1995; Perline, Wright, & education students enrolled in several different teacher Wainer, 1979; Wright, 1985, 1997b, 1999). These criteria education courses over a four-semester period extending for objectivity in measurement have been found useful in from the Fall of 2005 through the Spring of 2007 (see the study of a wide variety of applications in education, Table 1). Though the vast majority of students provided health care, and psychology (Bezruczko, 2005; Bond & both pre- and post-instruction measures every semester, Fox, 2007; Fisher & Wright, 1994; Wilson, 2005). not all did, resulting in a total of 647 measures for the In general, psychologists do not test or even state two time points across semesters. the hypothesis that the variable of interest in a study is In the first semester of the study, in the Fall of quantitative (Cliff, 1992; Guttman, 1985; Michell, 1990, 2005, and only in this semester, two different instruc- 1997a, 1997b, 1999, 2000; Wilson, 1971; Wright, 1984). tors taught three of these courses. The class lists were In so doing, their research results remain tied to arbitrary, cross checked for participants who had previously taken local, idiosyncratic, sample- and scale-dependent, the first instructor’s course or who were simultaneously ordinal comparisons, and are cut off from the benefits enrolled in both the first and second instructors’ courses; that would accrue from nonarbitrary, general, universal, these students were removed from the second instructor’s uniform, and invariant linear comparisons. These benefits list. Therefore, none of the participants had previous 62 International Journal of Transpersonal Studies Solloway & Fisher
  • 6. practice. About half of the students (88) participated in mindfulness training as described in Appendix D, and Table 1 about half (83) served as a control. The experimental group Demographics received positive feedback for each journal entry submitted 338 Total Student Participants during the eight weeks. Both groups responded to the (Due to missing data, not all category groups sum to 338) survey items twice, using an eight-point rating scale, once before the experimental group underwent eight weeks of Fall Spring Fall Spring Valid 2005 2006 2006 2007 Total Percent mindfulness practice (T1=Pre), and again at the end of those eight weeks (T2=Post). Sex Male 16 5 14 16 51 15.2% Female 155 35 41 54 285 84.8% Analyses All scaling and fit analyses were performed using Age 17-21 106 27 38 53 224 68.7% the Winsteps software (Linacre, 2006), implementing a 22-31 44 11 16 11 82 25.2% probabilistic conjoint model of fundamental measurement 32-41 6 1 0 2 9 2.8% for rating scales (Andrich, 1978, 1988; Wright & Mok, 42-51 5 1 0 4 10 3.1% Other 1 0 0 0 1 .3% 2000), and testing for the invariant internal consistency of the data using information-weighted and outlier-sensitive Ethnic Group mean square model fit statistics (Smith, R. M., 2000; Caucasian American 151 39 53 68 311 98.4% African American 0 1 0 2 3 .9% Wright & Masters, 1982), and principal components Asian American 1 0 0 0 1 .3% factor analysis of the model residuals (Smith, R. M., 1996; Hispanic American 1 0 0 0 1 .3% Linacre, 1998; Smith, E., 2002). Measures are reported in Curriculum Mindfulness 87 40 55 70 252 74.6% “logits.” Non-Mindfulness 86 86 25.4% “Logit” is a contraction of “Log-Odds Unit”. It is no Pre- or Post-Instruction * Semester and Year Cross Tabulation more obscure a measurement unit of an underlying and invisible variable than an “Ampère” is of invisible Fall Spring Fall Spring Total electric current. The essential ingredient of Amps and 2005 2006 2006 2007 logits is that they be additive. Pre-Instruction Count 171 37 56 71 335 Real apples are not additive. One Apple + One Apple = Two Apples. But Two Apples are twice as Post-Instruction Count 153 38 53 68 312 much as One Apple only when the Two Apples are perfectly identical. Real apples are not perfectly Total 324 75 109 139 647 identical. When we say One Amp + One Amp = Two Amps, we say “all Amps are identical,” wherever they appear on the Ammeter. Logits form an equal interval instruction in mindfulness practice or assignments in linear scale, just like Amps. When any pair of logit mindfulness practice within their teacher education measurements have been made with respect to the programs prior to the study. same origin on the same scale, the difference between Students in the mindfulness instructor’s course them is obtained merely by subtraction and is also in were assured every semester that credit for the assign- Logits. (Wright, 1997c, p. 288) ment would be awarded simply by participation. In other Measures and calibrations from Winsteps were then studied words, any level of participation would receive full credit. statistically and graphically using SPSS v. 14 (2005). The students in the second instructor’s courses acted as a control group. Results The data from the later three semesters reproduced Procedure the same rating scale structure as the initial first semester’s The mindfulness project opted for mindfulness study. The optimization of the rating scale based on the practice one day a week following Thich Nhat Hahn’s first semester’s results was thus retained. (1967) projected potential benefits of one day a week International Journal of Transpersonal Studies 63 Mindfulness in Measurement
  • 7. Mindfulness Item Calibrations from Pre-Instruction Sample (n=171) Mindfulness Item Calibrations from Post-Instruction Sample (n=153) Figure 1. Scatter Plot of Fall 2005 Pre-Instruction and Post-Instruction Item Calibrations supported by the meaningfulness of the item order on the Scaling variable. The 8-point rating scale was optimized (Andrich, Due to an error in survey production, item 29 1996; Linacre, 1999, 2002) to three categories, with all of was rephrased in late 2006, resulting in exceptionally high the disagree categories (25% of the responses) combined calibrations and mean square outlier-sensitive fit statis- together, the Agree category (37% of the responses) left tics in the Fall 2006 and Spring 2007 semesters. It is the intact, and three most extreme Agree categories (37%) only item to fall repeatedly outside the 95% confidence also combined. The transition from category 1 (All intervals in scatter plots of item calibrations by semester disagree categories) to category 2 (Agree) calibrated to 6.9 and year. The rephrasing resulted in the item’s calibration rescaled units (0.69 logits) below matching measures and changing by about two logits. Since the item was already calibrations, while the threshold between categories 2 and near the top of the scale, the new text changed its position 3 (all other agree categories) calibrated to 6.9 units above on the scale to a level far above all other items. This large matching measures and calibrations. effect size resulted in all unexpected responses becoming Overall respondent measurement separation reli- statistically significant. ability ranged from 0.90 to 0.93, depending on how error The Fall 2006 and Spring 2007 data for item 29 is estimated, and item calibration separation reliability were therefore removed from the calibration database. was 0.99. Logits were transformed to a roughly 0-100 New data will be added in the future, and the item will be scale from their default values by multiplying by 10 and restored to its original phrasing. adding 50. The same scale was produced when the items The items were calibrated on multiple separate were separately calibrated on the T1 and T2 groups (R = subsamples of the data, determined by curriculum type, 0.91), as shown in Figure 1. The model fit statistics do not pre- or post-intervention time points, the semester and falsify the hypothesis that the thirty items measure a single year, or simply the first half of the respondent data entered construct of mindfulness practice. Construct validity was 64 International Journal of Transpersonal Studies Solloway & Fisher
  • 8. vs. the second half. Correlations of the resulting 41 pairs resulting measures, suggesting that there is no substantive of separate-sample calibrations range from 0.85 to 0.99. significance to the items’ statistically significant changes In contrast with item 29’s two-semester explain- in position. able aberration, items 28 and 6 were repeatedly identi- fied by the model fit statistics, the graphical scatter Experimental plots of separate-sample item calibrations (see Figure 1), In the initial Fall 2005 study of the mindful- and the principal components analysis of the residuals ness measures (Solloway & Fisher, 2007), the control as provoking responses inconsistent with the overall group (receiving no mindfulness instruction) had nearly common construct. These two items changed positions identical average measures at the beginning and end of on the scale to a statistically significant degree, depending the semester (about 50, with an error of 4). The treatment primarily on whether the response was made at T1 (Time group (receiving mindfulness instruction) had an average 1 or Pre Test) or T2 (Time 2 or Post Test). Omitting the T1 measure of 51, with an error of 4, but finished the items from the scale makes virtually no difference in the semester with an average T2 measure of 68, 17 units, or Key: S2S06: Mindfulness Curriculum, Post-Instruction, Spring, 2006 A1F05: Non-mindfulness Curriculum, Pre-Instruction, Fall, 2005 S1F06: Mindfulness Curriculum, Pre-Instruction, Fall, 2006 A2F05: Non-mindfulness Curriculum, Post-Instruction, Fall, 2005 S2F06: Mindfulness Curriculum, Post-Instruction, Fall, 2006 S1F05: Mindfulness Curriculum, Pre-Instruction, Fall, 2005 S1S07: Mindfulness Curriculum, Pre-Instruction, Spring, 2007 S2F05: Mindfulness Curriculum, Post-Instruction, Fall, 2005 S2S07: Mindfulness Curriculum, Post-Instruction, Spring, 2007 S1S06: Mindfulness Curriculum, Pre-Instruction, Spring, 2006 Figure 2. Pre- and Post-Mindfulness Instruction Measures International Journal of Transpersonal Studies 65 Mindfulness in Measurement
  • 9. more than four errors of measurement, higher on the The distribution of measures relative to the item scale. As previously reported, the T2 measures were hierarchy and optimized rating categories is shown hori- different from the T1 measures to a statistically signifi- zontally across the bottom of Figure 3, with the mean, cant degree for the treatment group, but not for the and first and second standard deviations, indicated by control group. M, S, and T, respectively. The counts of students at each Replicating the previously reported Fall 2005 measure are read vertically; i.e., there are 36 students results, the pre- and post-mindfulness instruction with measures at the mean. The same information is measures differ by 16, 19, and 11 units, respectively, for conveyed in Figure 4, but with both the measures and the Spring 2006, Fall 2006, and Spring 2007 semesters the response category-level item calibrations plotted (see Figure 2). The average T2 measures across the four vertically. semesters were consistent over the first three semesters, at The average T1 measure for the students in the 68, 68, and 70. mindfulness curriculum over the four semesters is 51. The average gain from T1 to T2 dropped Drawing a vertical line through Figure 3 at 50 on the markedly in the Spring of 2007, though students started horizontal scale shows what the expected responses to with about the same average measure as in the previous the items are for a student with that measure. Students semesters. Spring 2007 was unusual in that, due to the with these initial, uninformed experiences of mindful- sudden departure of a colleague, Solloway was asked to ness practice’s effects strongly acknowledge that mindful- teach his four sections of Language Arts in addition to ness makes for more attentive listening, and more mildly her usual responsibilities. It was a difficult time and the acknowledge a wide range of other effects, from positive strain is reflected, we believe, in the drop in mindfulness effects on others to more self control to a new kind of measures that semester. happiness, with a decreasing likelihood of agreement as Even with this exception, however, every semes- one reads up the scale. Three items involving sensations ter’s differences in the mindfulness effects measures are (smell, touch, and sight) are more likely to elicit disagree- highly significant, in both substantive and statistical able responses than agreeable ones, for T1 measures, on terms. The overall average pre-instruction measure for average. Using the Pre/Post measures for Students A, students enrolled in the mindfulness curriculum is 51, B, and C given at the end of Appendix A, the expected and the overall average post-instruction measure for those responses for individuals may be seen in the same way in students is 67. ANOVA shows this difference of 16 units Figure 3. (4 errors of measurement) to be statistically significant The average T2 measure for the students in the (F(1,495)=184.06, p < .001). The Pre- and Post-Instruc- mindfulness curriculum over the four semesters is 67. tion differences shown in Figure 2 are similarly all statis- Again imagining a vertical line drawn through Figure tically significant, ranging from the low of the Spring 3, this time at 67 on the scale, we now expect strong 2007 11-unit difference (F(1,137)=24.63, p < .001) to the agreement with all but the top six of the mindfulness high of the Fall 2006 19-unit difference (F(1,107)=75.26, practice effects, and mild agreement is expected for p < .001). these. The statistical power of the design for all the The substantive meaning of the experimental mindfulness curriculum comparisons was 1.00, since all intervention of training in mindfulness practice is of the statistically significant differences are most of, all expressed in terms of the difference between these of, or more than the pooled standard deviations in size, expected response patterns. The difference between the with one degree of freedom and p < .01. overall T1 measures and the experimental group’s T2 measures is about 16. At T1, with an average measure of 50, the item with the highest calibration with which all Substantive Interpretation Figures 3 and 4 show the order of the items students typically strongly agree is item 22, mindfulness on the variable relative to the optimized rating catego- makes me a more attentive listener, which calibrates at ries and measures. The item hierarchy exhibits a mean- 38. At T2, with an average measure of 67, the item with ingful progression ranging from simple noticing to more the highest calibration with which the experimental intensely understanding and experiencing, and then to group typically strongly agrees with is item 8, reduces heightened awareness and sensation. my stress, which calibrates at 55. 66 International Journal of Transpersonal Studies Solloway & Fisher
  • 10. 10 20 30 40 50 60 70 80 90 100 |-----+-----+-----+-----+-----+-----+-----+-----+-----| NUM ITEM A A : E : F F 19* 1 heightens my sense of smell A A : E : F F 23* 3 I feel like I’m seeing for the first time A A : E : F F 15* 1 heightens my sense of touch. A A : E : F F 6* 2 I notice that time loses its meaning A A : E : F F 29* 3 I handle all experiences with equanimity A A : E : F F 32 3 I see how to transform my own anger and hurt A A : E : F F 21* 2 I notice more of my body sensations A A : E : F F 8* 1 reduces my stress A A : E : F F 18* 1 makes me feel peaceful A A : E : F F 4* 3 I observe my thoughts without being caught up in them A A : E : F F 14* 2 I notice that I experience a kind of happiness that’s different Mindfulness in Measurement A A : E : F F 27* 3 I notice that ordinary experiences seem extraordinary A A : E : F F 20* 3 I observe things objectively A A : E : F F 31 3 Anger and hurt can be transformed into compassion A A : E : F F 10* 3 I increase my power to intensely examine my life A A : E : F F 24* 3 I observe the way things constantly change from moment to moment A A : E : F F 28* 2 I notice that my mind wanders frequently 3 Seeing ”a world in a grain of sand” is a quality of looking deeply I cultivate day by day A A : E : F F 33 A A : E : F F 30* 2 I notice things about myself I never knew before A A : E : F F 3* 1 notice things in nature that I never noticed before A A : E : F F 17* 1 teaches me to experience the world in an entirely new way A A : E : F F 25* 1 is harder than I first thought it would be A A : E : F F 7* 3 I often find great peace and joy in ordinary experiences A A : E : F F 26* 3 I observe experiences while I participate in them A A : E : F F 2* 2 I notice the causes of my emotions A A : E : F F 11* 3 I have more insights A A : E : F F 5* 1 feel thankful for things I usually take for granted A A : E : F F 16* 1 can be learned A A : E : F F 12* 2 I notice more control over my responses A A : E : F F 13* 2 I notice I feel more positive about the tasks I accomplish A A : E : F F 1* 2 I notice my emotions as they change during the day A A : E : F F 9* 2 I notice that other people seem to like it when I listen this way A A : E : F F 22* 1 makes me a more attentive listener |-----+-----+-----+-----+-----+-----+-----+-----+-----| NUM ITEM 10 20 30 40 50 60 70 80 90 100 122231443333312121111 11 1 1 5 1 3 11563548707525326162223097972678115 2 8 PERSONS T S M S T Illustrated by an observed category. Expected score: Mean. Each “:” indicates Rasch-half-point threshold. Number directly to the left of the statement denotes the researcher’s hypothesized level of mindfulness engagement based on novice mindfulness practitioner journal entries: 1 = Beginning, 2 = Intermediate, 3 = Advanced. Read vertical numbers of student distribution as two-digits; for example, the “M” (Mean) = 36. S = 1 Standard Deviation, T = 2 Standard Deviations. International Journal of Transpersonal Studies 67 Figure 3. Mindfulness Practice Wright Construct Map
  • 11. MAP OF PERSONS AND ITEMS MEASURE | BOTTOM P=50% | MEASURE | TOP P=50% MEASURE <more> ------PERSONS-+-ITEMS -+-ITEMS -+-ITEMS --- <rare> 100 .#### + + + 100 | | | | | | | | | .| | | | | | 90 + + + 90 | | | .### | | | .| | | .| | | ## | | | 80 .# + + + 80 .# | | | ### | | | .#### | | | .## | | |X .#### | | |X 70 .#### + + + XX 70 .## | | |X .### | | | .##### | |X |X ### | |X | XXX .##### | | XX | XX 60 #### + +X + XX 60 .####### | | | XXXX ######### | X |X | XX ######## | X | XXX | XXXX .######## | XX | XX | XXXXX .######## | X | XX | XX 50 .########## + + XXXX +X 50 .########### | X | XX |X .#### | XXX | XXXX |X .####### | XX | XXXXX | .###### | XX | XX | ####### | XXXX |X | 40 ###### + XX +X + 40 .### | XXXX |X | . | XXXXX | | .# | XX | | .# | X | | .|X | | 30 .+X + + 30 | | | .| | | | | | | | | | | | 20 + + + 20 .| | | | | | | | | | | | | | | 10 .# + + + 10 <less> ------PERSONS-+-ITEMS -+-ITEMS -+-ITEMS <frequ> EACH ‘#’ IN THE PERSON COLUMN IS 4 PERSONS: EACH ‘.’ IS 1 TO 3 Figure 4. Mindfulness Practice Wright Map 68 International Journal of Transpersonal Studies Solloway & Fisher
  • 12. Notice that item 8, at 55, is 17 units higher If then the student acknowledges that mind- up the scale than item 22, at 38. After taking the 4- fulness can be learned (item 16), and experiences some unit error of measurement into account, we see that the gratification in noticing what is usually taken for granted same unit difference distinguishing the T1 from the T2 (item 5), then she or he is ready and able to experience measures also distinguishes the differences between the the “taken for granted things” in the group 2 and 3 items two groups’ response likelihoods, respective to any pair right above these. When the student in due course breaks of items on the scale. These relationships constitute the through the next group of category 1 items, a new level substantive meaning of the quantitative comparisons of critical awareness or attunement is obtained, which facilitated by the scale. Any unit difference between supports receptivity to the following group of largely any two points on the scale will translate into substan- group 3 items. Sticking with that critical attunement then tively meaningful contrasts illustrated by the content leads to the next group 1 transition into reduced stress of the items and optimized rating scale. The constancy (item 8), and the associated group 2 and 3 new balance, of this relationship is itself substantiated by the fit to centering, and enhanced physical sensations. the measurement model, and the high correlations and linear plots of the items’ scale values across sub sample Discussion calibrations. Our replication of the first study offer further scientific evidence and theory supporting the substan- tive conjecture that the effects of mindfulness practice Theory-Data Convergence The numbers 1, 2, and 3 in the first column are teachable, learnable, and amenable to measure- of the item names in Figure 3 indicate the pre-experi- ment. Making “non-arbitrary measures” possible in mental theoretically predicted calibration ranges. These psychometrics was Rasch’s “outstanding contribution,” predicted calibration ranges correlate 0.03 to 0.10 with the according to Jane Loevinger (1965, p. 151). Loevinger multiple independent subsample recalibrations of the 30 further observed that, “When his (Rasch’s) model fits, items. The respondents’ ordering of the items thus differs the results are independent of the sample of persons and from the researcher’s original conceptualization of that of the particular items within some broad limits. Within hierarchy, offering an opportunity for rethinking theory these limits, generality is, one might say, complete” (p. and possibly establishing closer theory-data congruence. 151). This specific generality makes successful applica- The theoretical order was derived from several tions of science possible and is crucial to meaningful, years’ experience reading students’ mindfulness journals. linked conversations among the interested parties. It seemed evident that the empirical frequency with In this context, the historian of science, Bruno which students mentioned or described various effects Latour, remarked, “Every time you hear about a successful of mindfulness practice in their journals followed the application of science, look for the progressive extension pattern described by the three assigned categories, with 1 of a network” (Latour, 1987, p. 249). The extension emerging earliest, and 3, latest. of metrological networks in psychosocial science has But does the empirical order of emergence neces- been effectively blocked by instrument-dependent and sarily imply a hierarchy of effects? Perhaps the effects arbitrary numerical representations of its measured initially noticed are landmarks or a general structure constructs. The non-arbitrary measures calibrated in this within which the experience of later effects are catego- study begin the work of investigating the possibility that rized. The group 1 items in fact span the entire calibration mindfulness may be characterized by lawful regularities range, and seem to be marking out significantly different in its patterns of presence and absence. Insofar as those ranges in the items, with the content of the group 1 item lawful regularities are not found to be dependent on the signifying a theme common to the group 2 and 3 items particulars of this study, a common language for inter- falling in that range. preting and reading qualitatively-informed amounts of That is, if a student is experiencing enhanced mindfulness presence and absence will emerge. listening ability as an effect (item 22, at the bottom of The first requirement for any network of the scale), then it becomes possible to do the “noticing” relations is a medium or a common language. The (category 2) items right above it, each of which may be in mindfulness ruler calibrated in this study is a first step some degree entailed by the first item. in establishing a non-arbitrary common language and International Journal of Transpersonal Studies 69 Mindfulness in Measurement
  • 13. an invitation for further meaningfully linked conversa- program at one particular time? The population might tions. Such common languages are in various stages of be expanded to include college students in general, or emergence in different areas of psychology, education, adults in general, but this will be determined only by and health care (Dawson, 2002a, 2002b; Fisher, 1997a, additional research that focuses specifically on these 1997b; Stenner, 1994). issues. What these studies have in common is that Establishing a common language of mind- scatter plots illustrating the measured relationships fulness practice effects that researchers can think in are linear. A plot illustrating one-to-one relationships together requires more than having different samples of between amounts of length measured in centimeters and respondents reproduce the calibrations of the items from amounts of length measured in inches is linear because one instrument. It must also be possible for different amounts of length remain invariant across the numerical samples of items from the infinite universe of all possible representations of it. Measures exhibiting the properties mindfulness practice effects items—that is, different of conjoint additivity, invariance, sufficiency, parameter mindfulness practice effects instruments—to produce separation, and others which accordingly emerge from linearly comparable measures that could be expressed in data fitting a Rasch model, are linear in the same way. a common metric. Scientific research, properly under- A scatter plot illustrating a typical correlation stood, makes a fundamental priority of this kind of of about 0.91 between separate sample calibrations of collectively distributed care for the unity and sameness the mindfulness self-assessment is shown in Figure 1. of what is studied. The constant amounts of mindfulness practice’s effects Human beings, like any form of life, exist in across the samples measured are illustrated in the way ecological webs of relations. Physical, emotional, social, the pairs of item calibrations fall together in a consis- and spiritual forms of well-being are experienced as tently orderly pattern roughly along the identity line (an projected from networked webs of relations. Susser and imaginary line extending from the lower left corner to Susser (1996) called the future of epidemiology eco- the upper right). Though the item order is constant from epidemiology, acknowledging the necessity of mean- T1 to T2, the calibrations are somewhat skewed away ingful communication across molecular, individual, and from the identity line because, at T1, the students are societal levels of organization. inexperienced with the construct and unable to distin- Similarly, our findings point to the convergence guish among the effects of mindfulness practice as well of mindfulness effects across all three ecological levels as they can after training. This gain in construct defini- of relations in positive psychology (Figure 5), and so tion has been documented in other research, with the acknowledge and incorporate the ecological implica- suggestion that the items be anchored at their outcome tions of mindfulness practice. Substantial growth in values in practical applications (Bezruczko, 2005). psychological strengths was demonstrated with only The pattern is, in addition, not as narrow and one day a week of intentional practice. These effects linear as a plot of centimeter vs. inch measures of the converge simultaneously with several of The Five Basic same objects would be, but it still provides us with a Postulates of Humanistic Psychology (Greening, n.d.) precision of more than four statistically distinct ranges and are reflected as well in Figure 5. This strengthening (when reliability is greater than 0.94). These ranges are of emotional balance integrated itself positively across sections of the measurement continuum that have centers the subjective, individual, and social levels. That our three errors apart (Wright & Masters, 1982, p. 96), and calibrated ruler now offers non-arbitrary measures of so establish the precision of the calibrations that can be this growth opens the possibility for testing the efficacy expected to be reliably reproduced for this instrument of methods of mindfulness instruction in developing by samples of about these sizes from the population. psychological strengths within and between individ- The nature of the population remains an uals, ecologically. Might one future of the exploration issue for further investigation. Is it the population of of mindfulness practice be defined by developments in all possible students in preservice teacher education the direction of an eco-positive psychology facilitated by programs? Or is it only students in one particular preser- non-arbitrary measures? vice teacher education program? Or will the population Indeed, we have dedicated much space to the studied in this project turn out to be just students in one details of the quantitative aspects of the study. As the 70 International Journal of Transpersonal Studies Solloway & Fisher
  • 14. Positive Psychology/Subjective Level—Valued Subjective Experiences: Well-being, contentment, satisfaction, happiness • Notice I feel more positive about the tasks I accomplish (Postulates 3, 5) • Feel thankful for things I usually take for granted (Postulates 3, 4, 5) • I often find great peace and joy in ordinary experiences (Postulates 3, 5) • Notice that I experience a kind of happiness that’s different (Postulate 3) • Makes me feel peaceful (Postulate 3) Positive Psychology/Individual Level—Positive Individual Traits: Capacity for Vocation • Notice I feel more positive about the tasks I accomplish (Postulates 3, 5) • Reduces my stress (Postulate 3) Interpersonal skill • Makes me a more attentive listener (Postulates 3, 4) • Notice that other people like it when I listen to them this way (Postulates 3, 4, 5) • Notice more control over my responses (Postulates 3, 4, 5) • Notice the causes of my emotions (Postulate 3) Aesthetic Sensibility • Notice things in nature I never noticed before (Postulate 3) • Feel thankful for things I usually take for granted (Postulates 3, 4, 5) Wisdom • I have more insights (Postulate 3) • Increases my power to intensely examine my life (Postulates, 3, 5) • Can observe my thoughts without being caught up in them (Postulates 3, 4, 5) • Feel thankful for things I usually take for granted (Postulates 3, 4, 5) Positive Psychology/Group Level—Civic Virtues and the Institutions Toward Better Citizenship: Responsibility, Nurturance, Moderation, Tolerance, Civility, Work Ethic • Notice more control over my responses (Postulates 3, 4, 5) • Notice I feel more positive about the tasks I accomplish (Postulates 3, 5) Correlations between Seligman & Csikszentmihalyi’s (2000) Positive Psychology Definition, Five Postulates of Humanistic Psychology (Greening, n.d.), and Novice Practitioners’ Descriptions of Effects of Mindfulness Practice Figure 5. Positive Psychology and Five Basic Postulates of Humanistic Psychology Link to Effects of Mindfulness Practice for Novice Practitioners International Journal of Transpersonal Studies 71 Mindfulness in Measurement
  • 15. value of qualitative work in the history of mindfulness Conclusions practice is well established, it seemed more important The study is innovative in at least three ways. to deeply describe our quantitative process. As a quali- First, it demonstrates mindfulness practice as measurable, tative researcher, Solloway is well aware of the initial as teachable and learnable, and as an object of experi- prejudice she herself brought to Fisher’s early introduc- mental research. Second, it does so through a rich herme- tion of the idea that a quantitative corroboration could neutic integration of qualitative and quantitative processes enhance this work. It was her meditation practice in (Fisher, 2003a, 2003b, 2004). One of Rasch’s probabilistic support of her mindfulness practice that brought her conjoint models of fundamental measurement is shown to face to face with that prejudice. Solloway’s commitment entertain uncertainty and chance in conversation, in order to truly and openly entering the present moment with for what is known to converge with differences that make curiosity dismantled that prejudice in order to more a difference across ecological webs of relations. Third, the non-judgmentally investigate Rasch models as possibili- study is innovative in its qualitative evidence corrobo- ties for discovering the organic partnership between her rated by quantitative evidence of the value of mindful- qualitative data and the quantitative ruler that data were ness practice as an assignment in the university classroom. ready to construct with Fisher’s help. We have worked to Future research will seek to generalize these findings to make that process as transparent as possible. other mindfulness settings and measures. The way has never been more open for researchers to work back and forth between qualitative evidence and Issues for Future Research Several issues present themselves for further more fully mathematical, quantitative measures. To do so study. First, can the effects measured here be reproduced with integrity, care must be taken to retain the contempla- elsewhere by others? Second, can the revised substantive tive and compassionate in the best qualitative work while theory of the variable be used to improve the instrument? at the same time holding quantitative methodologies to Third, DIF analysis shows that items 25 and 28 differ the rigorous requirements of fundamental measurement. significantly by sex; this contrast is confounded a bit by Important obstacles to meaningful conversations have the repetition of the same people across two time points. been removed; the way has opened for the proliferation of This issue should be addressed in a later study. Fourth, invitations for meaningful conversations and the means for the participants’ overall growth in mindfulness practice sustaining those conversations is at hand. We suggest that as defined by the survey items demonstrates the growth this work supports not a “type of scientism [which] can be predicted in several sections of the operational defini- termed methodolatry, the undue elevation of a method to tion of mindfulness proposed by Bishop, Lau, Shapiro, a sacred artifact” (Friedman, 2003), but rather a research/ Anderson, Carmody, Segal, Abbey, Speca, Velting, & living stance of a curiosity open to the present moment. Devins (2004). Follow-up studies can further corrobo- rate this finding. Fifth, what is the nature of the gap Endnotes separating the five items at the top of the scale from those 1. Portions of this paper were presented at the International Objective Measurement Workshop, April, 2006, Berkeley, CA; American Asso- lower down? Sixth, the suggestive connections between ciation for the Advancement of Curriculum Studies, April, 2006, novice practitioners’ interest in positive and humanistic Berkeley, CA; and the American Educational Research Association Conference, April, 2006, San Francisco, CA. psychologies might be further investigated with other We thank the reviewers for their helpful insights. studies providing different mindfulness instructions but comparable with non-arbitrary measures. Seventh, the corroboration of the journal entries and the mindful- Appendix A: ness ruler to show growth by university students in their Journal Entry Samples with Instructor Responses and Pre/ ability to mediate the debilitating effects of emotional Post Measures for Students A, B, C imbalances, stress, and prejudicial orientations to present moment experience provides important validation for Week 1 the inclusion of mindfulness assignments at the univer- Student A— sity. Future research should address these corroborations Usually when I awake in the morning, my mind and analyze the differences using rigorous measurement is racing with thoughts of everything I need to get done. models. 72 International Journal of Transpersonal Studies Solloway & Fisher
  • 16. Taking deep breaths and trying to clear my mind proved a bit Good Morning, _____________! difficult. Lying in bed, trying to be in the now, I could hear Best wishes for your next mindfulness day. Be sure to my heart beating, and my ears ringing. I could feel that my put something close to your bed to remind you as soon as you eyes were itchy, my teeth were throbbing (I grind them in my awake that it is your mindfulness day. Take that first conscious sleep), and my throat was sore. I thought that I must be doing breath of the morning and begin your mindfulness day. Be this wrong, this wasn’t fun. Relax more, take another breath, gentle with yourself. Be happy at whatever number of times concentrate. Now I noticed that everything has a rhythm, you remember during the day to use your breath as an anchor and as I listened and felt that rhythm, I was soothed. Eating for your attention. In your journal entry, describe at least one my bowl of Kashi, I had to slow down, put my spoon down mindful moment and analyze how it was different from ordinary between bites, and concentrate on each mouthful. I could feel moments…I look forward to what you learn…ss and enjoy the coolness of the milk, the taste and texture of the cereal, the weight and smoothness of the spoon. This was chal- Student C— lenging and unnatural for me as I am usually not that aware of Today while trying to be mindful I realized it could eating breakfast. The day continued to be a challenge. Many be harder than I thought. It was hard at first because I usually times I had to stop, breathe, and pay attention to the rhythm daydream and aren’t very attentive to what is going on around to clear my mind. What stands out for me is how easily dis- me. As I paid closer attention to breathing and clearing my head tracted I am from the moment. Interruptions from my son, of the daydreaming, I was more attentive to what was actually my dogs, the phone, but mostly from my own mind, seem a going on around me. I noticed the bird’s chirping, I noticed huge obstacle. I need to incorporate all of these into “happen- other people talking as they walked by me, I noticed the con- ings of the now” instead of intrusions. Being in the moment struction worker’s noise, and in class I was more attentive to the seemed easier in the evening. Perhaps my mind was tired, or I professor and fellow classmates. I was more mindful of what was less distracted now that the day was near an end. Playing they said and of what I said when talking to them. When talking cards with my husband, it was simpler to enjoy just doing to my friends I paid more attention to what they were saying what I was doing, and not thinking about anything else. For instead of half listening and half daydreaming at the same time. some reason, this day seemed longer than most. Maybe it was It was a clear feeling being mindful all day. It was a nice feeling because I became disappointed with myself every time my to actually be in the present when I needed to be. mind wandered, which was often. I hope, as the mindful days progress, that “being in the now” will become more natural Good Evening, ________, for me. Yes, the practice of keeping attention focused in the present moment seems simple. But as you discovered, the mind Good Afternoon, ____________, constantly dashes out of the moment taking our thoughts You wrote: “Maybe it was because I became disap- elsewhere. Best wishes for your next mindfulness day…ss pointed with myself every time my mind wandered, which was often.” Remember that it is NORMAL for the mind to Week 4 wander. Mindfulness practice is about NOTICING that. If you notice it OFTEN, that means that you are practicing Student A— mindfulness…try to just notice without judging yourself or Thanks to your input from last week, and the revela- anything else in the moment…let me know what happens…… tion that what was really driving my busy mind was a need for Best wishes for your next mindfulness day…ss approval, I have found it much easier to focus on the now. It’s Student B— funny that once I was aware of this, I find being mindful, and my The first mindfulness day didn’t go as well as I would entire day, less stressful. I think I was just seeking exterior goals, have liked. I didn’t stop and pull myself back as much as I the shell as it were, when really, inside I was seeking control of would have liked. The one time I really did experience it was my day. But by keeping my mind on what I am presently doing, after work and classes. I came home and lay down to take a instead of what also needs to be done later, each undertaking has nap. As I lay there, I thought about being mindful and was become so much more enjoyable and freeing. Do you believe able to bring myself back into the moment. It was nice to just you can actually enjoy a task as mundane as folding laundry? lay there and hear myself breathe and feel the breeze come in When you’re in the moment, you can feel the warmth, feel the though my open window and fall asleep. textures, smell the fresh scents. Meals taste better, are more plea- International Journal of Transpersonal Studies 73 Mindfulness in Measurement
  • 17. surable, and I think you actually eat less because you realize Week 8 when you’ve had your fill. Listening during conversations is gratifying, because Student A— you are no longer obsessed with your own agendas, or what With the holidays approaching, I was afraid I might you’d rather be doing. It’s not that I no longer seek approval, but backslide, start to panic about what needs to be done before from my new viewpoint, I no longer need to chase after it. My family arrives. My need for approval, my old mental habit, might mind still wanders from the moment, but I can relax, cleanse rear its ugly head. But that hasn’t happened. This mindfulness my mind with a breath, and bring it back. Or, if I am thinking is like a natural tranquilizer. It’s not that I’m numb or blasé. I’m about something, I become aware and allow myself to think. I excited and looking forward to sharing the holidays. It’s more have to do this every day now, not just one day a week. It’s not like I am at ease, aware of my own mental connections with that this is a radical change, but my patterns of thinking are what’s around me. Life is touching me, and I’m allowing it. changing, and you can’t just turn that on once a week. With the “approval monster” banished, I am free to be sensitive to a whole new realm, and enjoy each experience and mindful Good Evening, _______, moment as it comes. From past experience, I had connected You wrote, “Do you believe you can actually enjoy family gatherings with a certain amount of stress; trying to a task as mundane as folding laundry? When you’re in the make sure everything was perfect (nothing is ever perfect, so moment, you can feel the warmth, feel the textures, smell that was unrealistic to begin with). And what for? Approval. the fresh scents.” YES! One of the most lovely benefits of And why was approval important? Because it made me feel mindfulness practice is the way it lets you experience the good, like I should be admired or something. Once I realized AWE and WONDER of ordinary tasks or experiences! how egotistical this really was, and how it was cutting me off, I This nourishes the soul and we feel more energy for our lives!... could clear my mind and end the pursuit. While I was chasing Best wishes for your next mindfulness day…ss self-satisfaction, life was passing by unnoticed. And like I said before, nothing in life is perfect--but that is okay. Something Student B— doesn’t have to be perfect to be enjoyed. You just have to I was actually very pleased with my mindfulness ignore your old impulse to fix everything, and instead become this week. Before leaving the house I caught myself at least comfortable with the reality. No matter what reality brings, it twice and was able to bring myself back into the moment. The can be beautiful. You don’t have to analyze it, manage it, or rest of the day I forgot to do it. improve upon it - just be part of it. This holiday season is going to be the best one since childhood. Good Morning, _________! In your next journal entry, try to describe one Good Morning, _______, mindful moment in your day and analyze how it was different Well, this is your last mindfulness journal entry. from ordinary moments….ss Thank you for letting me share in this journey with you. It has been a joy….Best wishes for your CONTINUED mindfulness Student C— practice…ss This week my mindfulness brought me back to the senses of walking around campus. Since being sick it is hard Student B— to keep focus but I have since recovered and while walking My last mindfulness day was very successful. I have to class this week I was happy that I was finally feeling better come such a long way since the first day of this project. On and therefore had a better outlook on things. I once again this day, I was able to successfully catch myself at least ten noticed the chatter of people talking and the leaves blowing times and bring myself back. It was an amazing feeling! and rustling and the clatter of high heels clicking along and Good Afternoon, _______! the construction going on. It is nice being able to walk and Yes, what we cannot change is that you can only listen with a clear head!! live ONE moment at a time AND that the mind constantly wanders! And mindfulness practice empowers you to Good Morning, ________, NOTICE that the mind has wandered, bring it back, and Glad you are feeling better. Best wishes for your then live that moment with crystal clear energy and wisdom! next mindfulness day…ss Best wishes for your continued use of mindfulness practice with ever more expertise beyond this assignment…ss 74 International Journal of Transpersonal Studies Solloway & Fisher