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Why is factor analysis central to psychometrics but not to most other statistical methods?

Because psychometrics focuses on latent variables, which cannot be observed directly and must be inferred from patterns among observed variables.

Why is factor analysis described as a data reduction technique?

It reduces a large number of observed variables into a smaller number of underlying factors without losing essential information.

Why is factor analysis particularly suited to psychology?

Because psychological constructs (e.g., depression, intelligence) are theoretical and inferred rather than directly measurable.

Why can’t a single item adequately measure most psychological constructs?

Because complex constructs involve multiple facets and require multiple indicators to achieve reliability and validity.

Observable variable:

directly measured (e.g., questionnaire item)

Latent variable:

inferred construct explaining covariance among observed variables

Why are symptoms or behaviors considered indicators rather than the construct itself?

Because they are manifestations caused by the latent construct, not the construct itself.

Why does factor analysis assume causality from latent variables to observed variables?

The model assumes that the latent construct gives rise to patterns in item responses.

What is a factor loading?

A regression coefficient representing the strength of the relationship between an observed variable and a latent factor.

shows how strongly a question reflects the underlying construct and how much it helps us approximate the true score instead of adding noise

Why are factor loadings regression coefficients rather than correlations?

Because factor analysis assumes directional influence from the latent variable to the observed variable.

How should factor loadings be interpreted conceptually?

As indicators of how well an item represents the latent construct.

What does a factor loading of .80 mean in terms of variance explained?

64% of the variance in the item is attributable to the latent factor.

Why are high factor loadings desirable?

They indicate that most variance in the item reflects the construct rather than measurement error.

What loading values are typically considered acceptable or good?

• ≥ .30–.40: acceptable

• ≥ .60: desirable

• ≥ .70: excellent

What might a negative factor loading indicate?

• Item should have been reverse-scored

• Poor item quality

• Misfit with the factor

What is a Heywood case and why is it problematic?

A factor loading > 1, often indicating model misspecification, small samples, or multicollinearity.

What are the two primary purposes of factor analysis in psychometrics?

1. Scale development (EFA)

2. Scale validation (CFA)

Why is EFA used before CFA?

Because the underlying factor structure is unknown in early stages of scale development.

Why is CFA considered a stricter test than EFA?

CFA tests a hypothesized structure rather than exploring patterns freely.

What is the core goal of exploratory factor analysis?

To identify the number and nature of latent factors underlying a set of items.

Why is EFA described as “exploratory”?

Because it allows the data to inform the factor structure without strong prior constraints.

What does it mean when items form a “cluster” in EFA?

They share variance and likely reflect the same latent construct.

Why does EFA require correlations among items?

Without shared variance, there is no latent structure to extract.

Why is factor analysis inappropriate when items are uncorrelated?

Because latent variables explain shared variance among items.

Why is simplification a key principle in factor analysis?

Because the goal is to represent complex data using the smallest meaningful number of factors.

Why is parsimony important in psychometric models?

Simpler models are more interpretable, stable, and generalizable.

How does factor analysis help deal with measurement error?

By isolating variance attributable to the latent construct from random and systematic error.

Why do multiple indicators improve construct measurement?

They average out item-specific error and strengthen construct representation.

Why might a scale show high reliability but poor factor structure?

Items may be redundant or reflect multiple constructs inconsistently.

Why is a statistically “clean” factor solution not always theoretically acceptable?

Because factors must make conceptual sense, not just statistical sense.

Why should factor analysis results always be interpreted alongside theory?

Because factor analysis does not define constructs—it only reveals statistical patterns.

Why is factor analysis not a test of validity by itself?

It examines structure, not whether the construct itself is meaningful or correct.

Why is EFA inappropriate for testing predefined models?

Because CFA is designed for hypothesis testing, while EFA is not.

Why does factor analysis not prove causality in the real world?

The causal direction is theoretical, not empirically demonstrated.

What is the single most important contribution of factor analysis to psychometrics?

It provides a statistical bridge between observable responses and theoretical constructs.

What should you always remember for the exam about factor analysis?

Factor analysis helps you understand structure—not truth.