Scale Development – Key concepts

Prof. Dr. Khalid MahmoodUniversity of the Punjab

Lahore-PAKISTAN

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

Concepts/terms

Measurement Scale Variable Construct Theory Latent vs. observed

variable Psychometrics Causal relationship Error

Path diagram Correlation Significance Item Response category Variance Covariance Levels of measurement Reliability Validity

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”

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.

Variable

An element, feature, or factor that is liable to vary or change.

Examples: Race, gender, student attitude, parent satisfaction, etc.

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.

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.

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

Psychometrics

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

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.

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.

Path diagramObserved 1

Observed 2

Observed 3

Observed 4

Observed 5

Error 1

Error 2

Error 3

Error 4

Error 5

bb

b

b

b

Latent

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

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.

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.

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

Variance

A measure of how far a set of numbers is spread out.

The average of the squared differences from the Mean.

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.

Levels of measurement

NominalOrdinalIntervalRatio

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.

Validity of scale

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