Glossary

Factor Analysis

Factor analysis is a statistical method used to describe variability among observed variables in terms of a potentially lower number of unobserved variables called factors. Exploratory factor analysis (EFA) discovers the underlying factor structure, while confirmatory factor a...

Definition

Factor analysis is a statistical method used to describe variability among observed variables in terms of a potentially lower number of unobserved variables called factors. Exploratory factor analysis (EFA) discovers the underlying factor structure, while confirmatory factor analysis (CFA) tests whether a hypothesised structure fits the observed data.

Why It Matters

Researchers often measure constructs — such as intelligence, personality, or organisational culture — through multiple questionnaire items. Factor analysis reveals which items cluster together, indicating whether they tap into the same underlying dimension. This is essential for scale development, construct validation, and reducing data complexity without losing meaningful information.

Example

A psychologist develops a 20-item questionnaire to measure job satisfaction. After collecting responses from 500 employees, she conducts an exploratory factor analysis with oblique rotation. The analysis reveals three clear factors: remuneration (items 1-7), work-life balance (items 8-13), and career growth (items 14-20). She now has evidence that job satisfaction is multi-dimensional and can report subscale scores rather than a single total score.

Related Terms

Software Notes

  • SPSS: Analyze > Dimension Reduction > Factor. Select extraction method (Principal Axis Factoring or Maximum Likelihood) and rotation (Varimax for orthogonal, Promax for oblique). Request factor loadings, scree plot, and KMO measure of sampling adequacy.
  • R: psych::fa(data, nfactors = 3, rotate = "promax") for EFA. lavaan::cfa() for CFA. psych::alpha() computes Cronbach's alpha after factor structure is confirmed.
  • Stata: factor var1-var20, pcf for principal-component factor analysis. rotate, promax for oblique rotation. alpha var1-var7 computes Cronbach's alpha for a subscale. sem for CFA.