1. Measuring and Scaling of
Quantitative Data
Prof. Dr. Khalid Mahmood
University of the Punjab
Lahore-PAKISTAN

2. Agenda
 What are measuring and scaling?
 Levels of measurement
 Process of measurement
 Methods of scaling
 Types of scales
 Reliability and validity of scales

3. What are measuring and scaling?
 Measurement: The process of describing some
property of a phenomenon by assigning numbers.
 Scale: A type of composite measure composed of
several items that have a logical or empirical
structure among them. It allows to measure the
intensity or direction of a construct by aligning the
responses on a continuum.
“If a thing exists, it exists in some amount; and if
it exists in some amount, it can be measured.”
–E. L. Thorndike (1914)

4. Levels of measurement
 Nominal
 Ordinal
 Interval
 Ratio

5. Nominal
 A categorical variable, also called a nominal
variable, is for mutual exclusive, but not ordered,
categories.
 Nominal scales are mere codes assigned to objects
as labels, they are not measurements.
 Not a measure of quantity. Measures identity and
difference. People either belong to a group or they
do not.
 Sometimes numbers are used to designate
category membership.
 Examples: Gender, eye color, marital status

6. Ordinal
 This scale has the ability to rank the individual
attributes of two items in same group but unit
of measurement is not available in this scale,
like student A is taller than student B but their
actual heights are not available.
 Designates an ordering: greater than, less
than.
 Does not assume that the intervals between
numbers are equal.

7. Interval
 Classifies data into groups or categories
 Designates an equal-interval ordering
 The difference in temperature between 20 degrees
Fo and 25 degrees Fo is the same as the difference
between 76 degrees Fo and 81 degrees Fo
 Zero point on the interval scale is arbitrary zero, it
is not the true zero point
 Common IQ tests are assumed to be interval
measures

8. Ratio
 This is the highest level of measurement and has
the properties of other three levels; coupled with
fixed origin or zero point.
 Measurements of heights of students in a class
(zero means complete lack of height).
 Someone 6 ft tall is twice as tall as someone 3 feet
tall.
 Heart beats per minute has a very natural zero
point. Zero means no heart beats.

9. Process of measurement
 Define concepts to be measured
 Define attributes of the concepts
 Select level of measurement (data type)
 Generate items/questions
 Wording
 Response format
 Layout and design questionnaire
 Pretest and refine

10. Methods of scaling
 Rating scales
 Have several response categories and
are used to obtain responses with regard
to the object, event, or person studied.
 Ranking scales
 Make comparisons between or among
objects, events, persons and obtain the
preferred choices and ranking among
them.

11. Types of scales
 Likert scale
 Semantic differential scale
 Stapel scale
 Graphic rating scale
 Thurstone scale
 Guttman scale
 Paired comparison scale
 Forced choice
 Comparative scale

12. Likert scale
 Is designed to examine how strongly subjects agree or
disagree with statements on a 5-point scale.

13. Semantic differential scale
 Several bipolar attributes are identified at the
extremes of the scale, and respondents are
asked to indicate their attitudes.

14. Stapel scale
 This scale simultaneously measure both
the direction and intensity of the
attitude toward the items under study.
 It is a slight modification of semantic
differential scale.
 The scale consists of a single adjective
in the middle of positive and negative
numbers

15. Stapel scale

16. Graphic rating scale
 A graphical representation helps the
respondents to indicate their answers to
particular question by placing a mark at
the appropriate point on the line.

17. Thurstone scale
 This technique assesses the extent of agreement
among a group of judges about the proposed items
for a scale.
 For example, one might ask a group of persons to
judge how closely 25 different items come to
measuring self-esteem. Then, one might select
the 10 items that received the highest average
scores for having content validity with self-esteem.
 It can help find the best questions to ask to
measure an abstract concept.
 It does not specify how a question or set of
questions should be formatted on a questionnaire.

18. Guttman scale
 Who agrees with an item will also agree with all other
items expressing a less extreme position
 Using a series of statements to reflect the strength of
attitudes
“I think the following contains
SubjectC
pornographic materials.”
A B Scale
Adult movies rated [Yes] [Yes [Yes Value
XXX ] ] 4
Pla y bo y magazine [Yes] [Yes [No] 3
]
Lingerie ads [Yes] [No] [No] 2
N w Yo rk Tim e s
e [No] [No] [No] 1
-

19. Paired comparison scale
 The respondents are asked to
choose between two objects at a
time.

20. Forced choice
 Enables respondents to rank
objects relative to one another,
among the alternatives provided.

21. Comparative scale
 Provides a benchmark or a point of
reference to assess attitudes toward the
current object, event, or situation under
study.

22. Reliability of scale
 Indicates the extent to which it is
without bias (error free) and hence
ensures consistent measurement across
time and across the various items in the
instrument.

23. Types of reliability
 Stability of measures
 Test-retest reliability
 Parallel-form reliability
 Internal consistency of measures
 Inter-item consistency reliability
 Cronbach’s alpha
 Split-half reliability

24. Validity of scale
 Ensures the ability of a scale to indeed
measure the concept we want to
measure and not something else.
 Content validity
 Criterion related validity
 Construct validity

25. Content validity
 Ensures that the measure includes an
adequate and representative set of
items that tap the concept.
 A panel of judges

26. Criterion related validity
 Is established when the measure
differentiates individuals on a criterion
it is expected to predict.
 Concurrent validity: established when the
scale differentiates individuals who are
known to be different
 Predictive validity: indicates the ability of
measuring instrument to differentiate
among individuals with reference to
future criterion

27. Construct validity
 Testifies to how well the results obtained from
the use of the measure fit the theories around
which the test is designed.
 Convergent validity: established when the scores
obtained with two different instruments measuring
the same concept are highly correlated
 Discriminant validity: established when, based on
theory, two variables are predicted to be
uncorrelated, and the scores obtained by measuring
them are indeed empirically found to be so

28. THANKS A LOT