1. Development of health
measurement scales
If you cannot express in numbers something that you are describing,
you probably have little knowledge about it.
4. Why you need to worry about reliability and Validity ?
What happens with low reliability and validity ?
What is the relationship between reliability and validity ?
Do you need validity always ? Or reliability always ? Or both ?
What is the minimum reliability that is needed for a scale ?
6. No matter how well the
objectives are written,
or how clever the items,
the quality and usefulness
of an examination is
predicated on Validity
and Reliability
Validity & Reliability
7. Validity Reliability
We don’t say “an exam is valid and reliable”
We do say “the exam score is reliable and
Valid for a specified purpose”
KEY ELEMENT!
Validity & Reliability
10. Validity
• Two steps to determine usefulness of a scale
– Reliability – necessary but not sufficient
– Validity – next step
• Validity – is the test measuring what it is meant to measure?
• Two important issues
– The nature of the what is being measured
– Relationship of that variable to its purported cause
• Sr. creatinine is a measure of kidney func. because we know it is regulated
by the kidneys
• But whether students who do volunteer work will become better doctors?
• Since our understanding of human behaviour is far from
perfect, such predictions have to validated against actual
performance
11. Types of validity
• Three Cs (conventionally)
– Content
All types of validity are addressing the same
– Criterion issue of the degree of confidence we can place
in the inferences we can draw from the scales
• Concurrent
• Predictive
• Construct –
– Convergent, discriminant, trait etc.,
•Others (face validity)
12. Differing perspectives
• Previously validity was seen as demonstrating the properties
of the scale
• Current thinking - what inferences can be made about the
people that have given rise to the scores on these scales?
– Thus validation is a process of hypothesis testing (someone who scores
on test A, will do worse in test B, and will differ from people who do
better in test C and D)
– Researchers are only limited by their imagination to devise
experiments to test such hypothesis
14. • Face validity
– On the face of it the tool appears to be measuring what it is
supposed to measure
– Subjective judgment by one/more experts, rarely by any
empirical means
• Content validity
– Measures whether the tool includes all relevant domains or
not
– Closely related to face validity
– aka. ‘validity by assumption’ because an expert says so
• Certain situations where these may not be desired
15. Content validity
• Example – cardiology exam;
– Assume it contains all aspects of the circulatory
system (physiology, anatomy, pathology,
pharmacology etc., etc.,)
– If a person scores high on this test, we can say ‘infer’
that he knows much about the subject (i.e., our
inferences about the person will right across various
situations)
– In contrast, if the exam did not contain anything about
circulation, the inferences we make about a high scorer
may be wrong most of the time and vice versa
16. • Generally, a measure that includes a more representative
sample of the target behaviour will have more content validity
and hence lead to more accurate inferences
• Reliability places an upper limit on validity (the maximum
validity is the square root of reliability coeff.) the higher the
reliability the higher the maximum possible validity
– One exception is that between internal consistency and
validity (better to sacrifice IC to content validity)
– The ultimate aim of scale is inferential which depends
more on content validity than internal consistency
17. Criterion validity
• Correlation of a scale to an accepted ‘gold standard’
• Two types
– Concurrent (both the new scale and standard scale are given at the
same time)
– Predictive – the Gold Standard results will be available some time in
the future (eg. Entrance test for college admission to assess if a person
will graduate or not)
• Why develop a new scale when we already have a criterion scale?
– Diagnostic utility/substitutability(expensive, invasive, dangerous, time-
consuming)
– Predictive utility (no decision can be made on the basis of new scale)
• Criterion contamination
– If the result of the GS is in part determined in some way by the results
of the new test, it may lead to an artificially high correlation
18. Construct validity
• Height, weight – readily observable
• Psychological - anxiety, pain, intelligence are abstract
variables and can’t be directly observed
• For eg. Anxiety – we say that a person has anxiety if he has
sweaty palms, tachycardia, pacing back and forth, difficulty in
concentrating etc., (i.e., we have a hypothesize that these
symptoms are the result of anxiety)
• Such proposed underlying factors are called hypothetical
constructs/ constructs (eg. Anxiety, illness behaviour)
• Such constructs arise from larger theories/ clinical
observations
• Most psychological instruments tap some aspect of construct
19. Establishing construct validity
• IBS is a construct rather than a disease – it is a
diagnosis of exclusion
• A large vocabulary, wide knowledge and
problem solving skills – what is the underlying
construct?
• Many clinical syndromes are constructs rather
than actual entities (schizophrenia, SLE)
20. • Initial scales for IBS – ruling out other organic
diseases and some physical signs and symptoms
– These scales were inadequate because they lead to
many missed and wrong diagnoses
– New scales developed incorporating demographical
features and personality features
• Now how to assess the validity of this new scale
– Based on theory high scorers on this scale should
have
• Symptoms which will not clear with conventional therapy
• Lower prevalence of organic bowel disease on autopsy
21. Differences form other types
1. Content and criterion can be established in one or two
studies, but there is no single experiment that can prove a
construct
•Construct validation is an ongoing process, learning more
about the construct, making new predictions and then testing
them
•Each supportive study strengthens the construct but one
well designed negative study can question the entire
construct
2. We are assessing the theory as well as the measure at the
same time
22. IBS example
• We had predicted that IBS patients will not respond to
conventional therapy
• Assume that we gave the test to a sample of patients
with GI symptoms and treated them with conventional
therapy
• If high scoring patients responded in the same
proportion as low scorers then there are 3 possibilities
– Our scale is good but theory wrong
– Our theory is good but scale bad
– Both scale and theory are bad
• We can identify the reason only from further studies
23. • If an experimental design is used to test the
construct, then in addition to the above
possibilities our experiment may be flawed
• Ultimately, construct validity doesn’t differ
conceptually from other types of validity
– All validity is at its base some form of construct
validity… it is the basic meaning of validity –
(Guion)
25. Extreme groups
• Two groups – as decided by clinicians
– One IBS and the other some other GI disease
– Equivocal diagnosis eliminated
• Two problems
– That we are able to separate two extreme groups implies
that we already have a tool which meets our needs
(however we can do bootstrapping)
– This is not sufficient, the real use of a scale is making
much finer discriminations. But such studies can be a first
step, if the scale fails this it will be probably useless in
practical situations
26. Multitrait-multimethod matrix
• Two unrelated traits/constructs each measured by two different methods
• Eg. Two traits – anxiety, intelligence; two methods – a rater, exam
Anxiety Intelligence
Rater Exam Rater Exam
Rater 0.53
Anxiety
Exam 0.42 0.79
Rater 0.18 0.17 0.58
Intelligence
Exam 0.15 0.23 0.49 0.88
– Purple – reliabilities of the four instruments (sh be highest)
– Blue – homotrait heteromethod corr. (convergent validity)
– Yellow – heterotrait homomethod corr. (divergent validity)
– Red – heterotrait heteromethod corr. (sh be lowest)
• Very powerful method but very difficult to get such a combination
27. • Convergent validity - If there are two measures for
the same construct, then they should correlate with
each other but should not correlate too much.
E.g. Index of anxiety and ANS awareness index
• Divergent validity – the measure should not correlate
with a measure of a different construct, eg. Anxiety
index and intelligence index
28. Biases in validity assessment
• Restriction in range
• May be in new scale (MAO level)
• May be in criterion (depression score)
• A third variable correlated to both (severity)
• Eg. A high correlation was found between
MAO levels and depression score in
community based study, but on replicating the
study in hospital the correlation was low
30. The information we seek and our
best hope for obtaining it.
Content/
Action + Error
Our human frailty and inability to
write effective questions.
Validity & Reliability
32. Maximum validity of a test is the square root of reliability coefficient. Reliability places
an upper limit on validity so that higher the reliability, higher the maximum possible
validity
33. Variance = sum of (individual value – mean value) 2
----------------------------------------------------------------------------------
no. of values
34. Reliability
• Whether our tool is measuring the attribute in a
reproducible fashion or not
• A way to show the amount of error (random and
systematic) in any measurement
• Sources of error – observers, instruments, instability
of the attribute
• Day to day encounters
– Weighing machine, watch, thermometer
35. Assessing Reliability
• Internal Consistency
– The average correlation among all the items in the tool
• Item-total correlation
• Split half reliability
• Kuder-Richardson 20 & Cronbach’s alpha
• Multifactor inventories
• Stability
– Reproducibility of a measure on different occasions
• Inter-Observer reliability
• Test-Retest reliability (Intra-Observer reliability)
36. Internal consistency
• All items in a scale tap different aspects of the same
attribute and not different traits
• Items should be moderately corr. with each other and
each item with the total
• Two schools of thought
– If the aim is to describe a trait/behaviour/disorder
– If the aim is to discriminate people with the trait from those
without
• The trend is towards scales that are more internally
consistent
• IC doesn’t apply to multidimensional scales
37. Item-total correlation
• Oldest, still used
• Correlation of each item with the total score w/o that
item
• For k number of items, we have to calculate k number
of correlations, labourious
• Item should be discarded if r < 0.20(kline 1986)
• Best is Pearson’s R, in case of dichotomous items -
point-biserial correlation
38. Split half reliability
• Divide the items into two halves and calculate corr.
between them
• Underestimates the true reliability because we are
reducing the length of scale to half (r is directly related
to the no. of items)
– Corrected by Spearman-Brown formula
• Should not be used in
– Chained items
Difficulties-ways to divide a test
-doesn't point which item is contributing to
poor reliability
39. KR 20/Cronbach’s alfa
• KR-20 for dichotomous responses
• Cronbach’s alfa for more than two responses
• They give the average of all possible split half reliabilities of a
scale
• If removing an item increases the coeff. it should be discarded
• Problems
– Depends on the no. of items
– A scale with two different sub-scales will prob. yield high alfa
– Very high alfa denotes redundancy (asking the same question in
slightly different ways)
– Thus alfa should be more than 0.70 but not more than 0.90
40. • Cronbach’s basic equation for alpha
n ΣVi
α= 1 −
n − 1 Vtest
– n = number of questions
– Vi = variance of scores on each question
– Vtest = total variance of overall scores on the
entire test
41. Multifactor inventories
• More sophisticated techniques
• Item-total procedure – each item should correlate
with the total of its scale and the total of all the scales
• Factor analysis
– Determining the underlying factors
– For eg., if there are five tests
• Vocabulary, fluency, phonetics, reasoning and
arithmetic
• We can theorize that the first three would be correlated
under a factor called ‘verbal factor’ and the last two
under ‘logic factor’
42. Stability/ Measuring error
• A weighing machine shows weight in the range of
say 40-80 kg and thus an error of ±1kg is
meaningful
Reality we calculate the ratio
variability between subjects / total variability
(Total variability includes subjects and measurement error)
• So that a ratio of
–1 indicates no measurement error/perfect reliability
–0 indicates otherwise
43. • Reliability =
subj. variability / (subj. variability + measurement error)
• Statistically ‘variance’ is the measure of variability so,
• Reliability =
SD2 of subjects / (SD2 of subjects + SD2 of error)
• Thus reliability is the proportion of the total variance that
is due to the ‘true’ differences between the subjects
• Reliability has meaning only when applied to specific
populations
44. Calculation of reliability
• The statistical technique used is ANOVA and
since we have repeated measurements in
reliability, the method is
– repeated measures ANOVA
47. • Classical definition of reliability
• Interpretation is that 88% of the variance is
due to the true variance among patients (aka
Intraclass Correlation coefficient)
48. Fixed/random factor
• What happened to the variance due to observers?
• Are these the same observers going to be used or they
are a random sample?
• Other situations where observations may be treated as
fixed is subjects answering ‘same items on a scale’
49. Other types of reliability
• We have only examined the effect of different
observers on the same behaviour
• But there can be error due to ‘day to day’ differences,
if we measure the same behaviour a week or two
apart we can calculate ‘intra-observer reliability
coefficient’
• If there are no observers (self-rated tests) we can still
calculate ‘test-retest reliability’
50. • Usually high inter-observer is sufficient, but if it is
low then we may have to calculate intra-observer
reliability to determine the source of unreliability
• Mostly measures of internal consistency are reported
as ‘reliability’, because there are easily computed in a
single sitting.
– Hence caution is required as they may not measure
variability due to day to day differences
51. Diff. forms of reliability coefficient
• So far we have seen forms of ICC
• Others
– Pearson product-moment correlation
– Cohen’s kappa
– Bland – altman analysis
52. Pearson’s correlation
• Based on regression – the extent to which the relation
between two variables can be described by straight
line
53. Limitations of Pearson’s R
• A perfect fit of 1.0 may be obtained even if the intercept
is non-zero and the slope is not equal to one unlike with
ICC
• So, Pearson’s R will be higher than truth, but in practice it
is usually equal to ICC as the predominant source of error
is random variation
• If there are multiple observations then multiple pairwise
Rs are required, unlike the single ICC
• For eg. with 10 observers there will be 45 Pearson’s Rs
whereas only one ICC
54. Kappa coeff.
• Used when responses are dichotomous/categorical
• When the frequency of positive results is very low or high,
kappa will be very high
• Weighted kappa focuses on disagreement, cells are weighted
according to the distance from the diagonal of agreement
• Weighting can be arbitrary or using quadratic weights (based
on square of the amount of discrepancy)
• Quadratic scheme of weighted kappa is equivalent to ICC
58. Bland and Altman method
• A plot of difference between two observations
against the mean of the two observations
59. • Agreement is expressed as the ‘limits of agreement’. The
presentation of the 95% limits of agreement is for visual
judgement of how well two methods of measurement agree.
The smaller the range between these two limits the better the
agreement is.
• The question of how small is small depends on the clinical
context: would a difference between measurement methods as
extreme as that described by the 95% limits of agreement
meaningfully affect the interpretation of the results
• Limitation - the onus is placed on the reader to juxtapose the
calculated error against some implicit notion of true variability
60. Standards for magnitude of reliability coeff.
•How much reliability is good?
Kelly (0.94) Stewart (0.85)
•A test for individual judgment should be higher
than that for research in groups
•Research purposes –
– Mean score and the sample size will reduce the error
– Conclusions are usually made after a series of studies
– Acceptable reliability is dependent on the sample size
in research(in sample of 1000 reliablity may low
compared to sample size of 10)
61. Reliability and probability of misclassification
•Depends on the property of the instrument and the
decision of cut point
•Relation between reliability and likelihood of
misclassification
– Eg. A sample of 100, one person ranked 25th and another
50th
– If the R is 0, 50% chance that the two will reverse order on
retesting
– If R is 0.5, 37% chance, with R=0.8, 2.2% chance
•Hence R of 0.75 is minimum requirement for a useful
instrument
62. Improving reliability
• Increase the subject variance relative to the error
variance (by legitimate means and otherwise)
• Reducing error variance
– Observer/rater training
– Removing consistently extreme observers
– Designing better scales
• Increasing true variance
– In case of ‘floor’ or ‘ceiling’ effect, introduce items that
will bring the performance to the middle of the scale (thus
increasing true variance)
• Eg. Fair-good-very good-excellent
63. • Ways that are not legitimate
– Test the scale in a heterogeneous population
(normal and bedridden arthritics)
– A scale developed in homogeneous population will
have a larger reliability when used in a
heterogeneous population
• correct for attenuation
64. • Simplest way to increase R is to increase the no. of
items(statistical theory)
• True variance increases as the square of items
whereas error variance increases only as the no. of
items
• If the length of the test is triples
– Then Rspearman brown = 3R/ 1 + 2R
65. • In reality the equation overestimates the new
reliability
• We can also use this equation to determine the
length of a test for achieving a pre-decided
reliability
• To improve test-retest reliability – shorten the
interval between the tests
• An ideal approach is the examine all the sources
of variation and try to reduce the larger ones
(generalizability theory)
66. Summary for Reliability
• Pearson R is theoretically incorrect but in
practice fairly close
• Bland and Altman method is analogous to
error variance of ICC but doesn’t relate this to
the range of observations
• kappa and ICC are identical and most
appropriate
Even when a test is constructed on the basis of a specific criterion, it may ultimately be judged to have greater construct validity than the criterion .We start with a vague concept which we associate with certain observations. We then discover empirically that these observations co vary with some other observation which possesses greater reliability or is more intimately correlated with relevant experimental changes than is the original measure.