ILLUSTRATIVE EXAMPLE
Exploratory Factor Analysis for a
Scale Development Study
Polychoric correlations, parallel analysis and an oblique rotation to find the structure of a new 30-item questionnaire, reported to APA 7 with a plan for confirmatory testing.
This example does not describe a real client or project. Every engagement is confidential, during the project and after it ends.
RESEARCH QUESTION
What the Study Set Out to Test
This exploratory factor analysis example follows an industrial-organizational psychology research team that has drafted a 30-item workplace resilience questionnaire. Before refining the instrument, they need to learn how many dimensions the items form and which items belong to which dimension.
The question is exploratory by design: the team has expectations but no confirmed structure. The analysis is therefore planned to propose a structure with its supporting evidence, and to leave confirmation to a later, separate sample.
STUDY DESIGN AND DATA
A Pilot Survey With Ordinal Items
A cross-sectional pilot with around 450 respondents, roughly 15 per item. Each of the 30 items is rated on a five-point agreement scale, so the data are ordinal. The dataset holds the item responses, basic demographics and a record of missing responses per item, with the analysis plan written before the pilot data were examined.
- Design: cross-sectional pilot of a 30-item questionnaire
- Data: five-point ordinal items, with the analysis plan fixed in advance
- Software requested: R, with scripts and a session log
METHOD AND ASSUMPTIONS
Why Polychoric Correlations, and What Must Hold
Five-point items are ordinal, and Pearson correlations between them can understate the underlying associations and distort the factor solution. The plan therefore uses polychoric correlations, which treat each item as a coarse measure of a continuous latent response, with principal axis factoring and an oblique rotation, because the dimensions of resilience are expected to correlate. This is run in R, since SPSS has no built-in polychoric option.
The number of factors is set by parallel analysis computed on the polychoric matrix, together with interpretability, and the eigenvalue-greater-than-one rule is reported only for comparison. Against criteria fixed in the plan (a primary loading of at least .40 and no secondary loading above .30), several items cross-load and two have low communalities, so they are reviewed for wording and content with the team, not dropped on loadings alone. Sampling adequacy is checked as a screen, not as a gate, and the missing-response pattern is examined before the correlations are estimated.
OUTPUT AND INTERPRETATION
What the Results Showed
The output has the pattern matrix of loadings, communalities, the factor correlations and a parallel analysis plot showing where the observed eigenvalues fall against the simulated ones. A table of flagged items lists each cross-loading or weak item with a note on its wording, so the revision is a judgment about content supported by the numbers.
Reliability of each proposed subscale is reported with omega alongside the factor results, and the structure is framed as a proposal. Because the same respondents were used to find the structure, the loadings are not evidence that it holds, which is why a confirmatory factor analysis in a new sample is set out as the next step.
REPORTING
What the Researcher Received
A written report formatted to APA 7, with statistical wording for the methods, matched to the output, for the team to check and incorporate, and the decisions on the number of factors and on flagged items explained. The research question, substantive interpretation and conclusions remain with the research team.