1. Scale Development –
Key concepts
Prof. Dr. Khalid Mahmood
University of the Punjab
Lahore-PAKISTAN

2. Acknowledgment
 My presentation on scale development
has been prepared with the help of:
 Textbook: DeVellis, R. F. (2003). Scale
development: Theory and applications .
Thousand Oakes, CA: Sage.
 Class lectures and presentations:
 Dr. Jamie DeCoster, University of Alabama,
USA
 Dr. Daniel Stahl, King’s College London, UK

3. Concepts/terms
 Measurement  Path diagram
 Scale  Correlation
 Variable  Significance
 Construct  Item
 Theory  Response category
 Latent vs. observed variable  Variance
 Psychometrics  Covariance
 Causal relationship  Levels of measurement
 Error  Reliability
 Validity

4. Measurement
 Stevens: measurement is the
“assignment of numerals to objects or
events according to rules”
 Duncan: “Measurement is also the
assignment of numerals in such a way
as to correspond to different degrees of
a quality…or property of some object or
event”

5. 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.

6. Variable
 An element, feature, or factor that is
liable to vary or change.
 Examples: Race, gender, student
attitude, parent satisfaction, etc.

7. Construct
 An abstract or general idea inferred or
derived from specific instances.
 Something that exists theoretically but is not
directly observable.
 A theoretical definition in which concepts are
defined in terms of other concepts. For
example, intelligence cannot be directly
observed or measured; it is a construct.

8. Theory
 A coherent group of tested general
propositions, commonly regarded
as correct, that can be used as
principles of explanation and
prediction for a class of
phenomena: Einstein‘s theory of
relativity.

9. Latent vs. observed variable
 A latent variable is not directly observable.
Instead, it is inferred from variables that can
be observed.
 Represented by total score on the scale
 Observed variables are the actual
measurements you make.
 Represented by the individual items in the scale
 Also called measured variables or indicator
variables

10. Psychometrics
 A field concerned with the theory and
technique of measurement of
psychological and social phenomenon.

11. Causal relationship
 Causality (also referred to as causation) is the
relationship between an event the cause) and a
second event (the effect), where the second event is
understood as a consequence of the first.
 Causality is also the relationship between a set of
factors (causes) and a phenomenon (the effect).
 A causal relationship between variables is when one
variable causes a change in another variable.

12. Error
 A measurement will never be exact, there will be
always some error in a measurement.
 The uncertainty of a measurement is usually
expressed as a standard error and we can only be
confident to a certain degree that the true score lies
within a certain range.
 Observed value = true value + measurement error
 The error of the measurements should be a small
fraction of the true range of observations.

13. Path diagram
Observed 1 Error 1
b
b Observed 2 Error 2
b
Latent Observed 3 Error 3
b
b Observed 4 Error 4
Observed 5 Error 5

14. Correlation
 Correlation is a statistical measurement of the relationship
between two variables.
 Possible correlations range from +1 to –1.
 A zero correlation indicates that there is no relationship between
the variables.
 A correlation of –1 indicates a perfect negative correlation,
meaning that as one variable goes up, the other goes down.
 A correlation of +1 indicates a perfect positive correlation,
meaning that both variables move in the same direction
together.
 Examples are Pearson’s and Spearman’s coefficients

15. Significance
 In normal English, "significant" means
important.
 In statistics "significant" means probably true
(not due to chance).
 A research finding may be true without being
important. When statisticians say a result is
"highly significant" they mean it is very
probably true. They do not (necessarily)
mean it is highly important.

16. Item
 A general term referring to a single
statement, question, exercise, problem,
or task on a test or evaluative
instrument for which the test taker is to
select or construct a response, or to
perform a task.

17. Response category
 An answer provided for a closed-ended
question to be ticked or circled on the form.
 Response categories for Likert scale:
 Strongly agree
 Agree
 Undecided
 Disagree
 Strongly disagree

18. Variance
 A measure of how far a set of numbers
is spread out.
 The average of the squared differences
from the Mean.

19. Covariance
 A measure of how much two random
variables change together.
 If the greater values of one variable mainly
correspond with the greater values of the other
variable, and the same holds for the smaller values,
i.e. the variables tend to show similar behavior, the
covariance is a positive number.
 In the opposite case, when the greater values of one
variable mainly correspond to the smaller values of
the other, i.e. the variables tend to show opposite
behavior, the covariance is negative.

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

21. 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.

22. Validity of scale
 Ensures the ability of a scale to indeed
measure the concept we want to measure
and not something else.