EFA is a multivariate technique that uncovers the latent factors generating the correlations among observed variables. Use it when you do not yet have a confirmed structure for a measurement instrument — for example, when developing a personality scale, a customer-satisfaction questionnaire, or grouping ecological habitat variables into broader constructs. EFA tells you how many underlying factors exist and which variables belong to each.

Principal Component Analysis (PCA) explains total variance using uncorrelated linear combinations and is purely a data-reduction tool. EFA explains shared (common) variance and assumes latent factors generate the correlations. PCA is appropriate when the goal is dimensionality reduction; EFA is appropriate when you want to identify or interpret underlying constructs.

The Kaiser–Meyer–Olkin (KMO) statistic compares squared partial correlations to squared correlations. It ranges from 0 to 1. Kaiser's interpretive guide: ≥ .90 marvelous, .80–.89 meritorious, .70–.79 middling, .60–.69 mediocre, .50–.59 miserable, < .50 unacceptable. A KMO below .60 suggests the data are not factorable and EFA should not proceed.

Bartlett's test checks whether the observed correlation matrix is significantly different from an identity matrix (a matrix in which all variables are uncorrelated). A significant result (p < .05) means there are meaningful correlations among variables, and factor analysis is justified. A non-significant result is a red flag — there is nothing to factor.

The scree plot displays eigenvalues in descending order. The "elbow" — the point where the curve flattens — is often used to choose the number of factors. Combined with Kaiser's rule (retain factors with eigenvalue > 1), it provides a practical guide. Modern best practice also uses parallel analysis as a more accurate criterion.

Varimax is an orthogonal rotation that maximizes the variance of squared loadings within each factor, producing a "simple structure" where each variable loads strongly on one factor and weakly on the others. This dramatically improves interpretability while keeping factors uncorrelated. If you expect factors to be correlated (e.g., aspects of psychological wellbeing), use an oblique rotation such as Promax instead.

A factor loading is the correlation between a variable and a factor. Conventional benchmarks: |.32| poor, |.45| fair, |.55| good, |.63| very good, |.71| excellent (Comrey & Lee, 1992). In practice, |λ| ≥ .40 is the most common threshold for declaring a loading "salient". Negative loadings indicate the variable is inversely related to the factor.

Communality (h²) is the proportion of a variable's variance explained by the retained factors together. It is the sum of squared loadings across factors. Values above .50 indicate the variable is well represented by the factor solution; values below .30 suggest the variable is largely unique and may need to be dropped.

Use multiple criteria together: Kaiser's rule (eigenvalue > 1), the scree plot elbow, parallel analysis, theoretical interpretability, and total variance explained (typically ≥ 60% for social-science data). When criteria disagree, prefer the most interpretable solution. Always report the rationale for the retained number of factors.

Common rules: at least 5–10 cases per variable, with a minimum of 100–200 cases. Higher communalities (≥ .60) and over-determined factors (≥ 4 strong loadings per factor) allow smaller samples (n ≈ 100). Low communalities or weakly defined factors require n ≥ 300. Cases-to-variables ratios below 5:1 should be avoided.