How do you run a factor analysis in SPSS?

Open Analyze, then Dimension Reduction, then Factor, and move your scale items into the Variables box. Under Descriptives request KMO and Bartlett's test, under Extraction choose Principal Axis Factoring and a scree plot, and under Rotation choose Direct Oblimin or Varimax. Click OK, confirm the data are factorable, decide how many factors to keep, and read the pattern matrix to see which items load on each factor.

What is a good KMO value for factor analysis?

The Kaiser-Meyer-Olkin measure runs from 0 to 1, and you generally want the overall value above 0.70, with anything below 0.50 considered unacceptable for factoring. Values in the 0.80s are good and the 0.90s excellent. Also check the anti-image correlation matrix, where the KMO for each individual item sits on the diagonal, and consider removing any item below 0.50.

Should you use Varimax or Oblimin rotation?

Use an oblique rotation such as Direct Oblimin or Promax when you expect the factors to correlate, which is usual for psychological and social constructs, and read the pattern matrix. Use an orthogonal rotation such as Varimax only when the factors are genuinely independent. You can run oblique first and inspect the factor correlation matrix: if the inter-factor correlations are all trivially small, an orthogonal solution was adequate.

How many factors should you retain in SPSS?

Do not rely on the default Kaiser rule of eigenvalues over 1, which tends to overestimate the number of factors. Read the scree plot for the elbow, use parallel analysis to compare your eigenvalues against random data, and weigh interpretability. Decide the number from these together, then rerun forcing that exact number of factors rather than accepting the eigenvalue default.

How to run a factor analysis in SPSS

To run a factor analysis in SPSS, you open Analyze > Dimension Reduction > Factor, enter your scale items, confirm the data are factorable with the KMO measure and Bartlett's test, choose an extraction method and the number of factors to keep, apply a rotation, and read the rotated solution to see which items load on which factor. The solution that holds up depends on the judgement at each of those steps, especially how many factors you retain and whether you rotate orthogonally or obliquely. This guide covers the procedure, the decisions, and the reporting.

Exploratory factor analysis versus principal components

The first decision is made before you touch the menu, and it is the one most often got wrong. Principal component analysis summarises the total variance of your items into composite components, while exploratory factor analysis models only the shared (common) variance to recover the latent factors thought to cause the items. For a dissertation that aims to validate a construct, common factor analysis is the conceptually correct choice, which in SPSS means selecting Principal Axis Factoring or Maximum Likelihood as the extraction method rather than the SPSS default of Principal Components. The distinction and the wider validation logic are unpacked in factor analysis and Cronbach's alpha. Choose Maximum Likelihood when your items are roughly normal and you want a significance test of fit; choose Principal Axis Factoring when normality is doubtful, because it makes no distributional assumption.

Checking the data are factorable before you extract

Two diagnostics decide whether factoring is even appropriate. The Kaiser-Meyer-Olkin measure of sampling adequacy compares the size of the observed correlations against the partial correlations; it runs from 0 to 1, and you want the overall value above about 0.70, treating anything below 0.50 as unacceptable. The anti-image correlation matrix carries the KMO for each individual item on its diagonal, and an item below 0.50 there is a candidate for removal. Bartlett's test of sphericity must be significant, because it tests whether the correlation matrix differs from an identity matrix; a non-significant result means your items are essentially uncorrelated and there is nothing to factor. You also need an adequate sample size, with common guidance of at least ten cases per item and a floor near 150 to 200 cases for a stable solution.

Running the analysis and the syntax to keep

Open Analyze > Dimension Reduction > Factor and move every scale item into the Variables box. Under Descriptives, tick KMO and Bartlett's test of sphericity and the anti-image matrix. Under Extraction, set the method to Principal Axis Factoring, base the analysis on the correlation matrix, and request the scree plot. Under Rotation, choose Direct Oblimin (oblique) or Varimax (orthogonal). Under Options, sort the loadings by size and suppress small coefficients below about 0.30 to declutter the matrix. The reproducible syntax is:

FACTOR
  /VARIABLES q1 q2 q3 q4 q5 q6 q7 q8 q9 q10
  /MISSING LISTWISE
  /ANALYSIS q1 q2 q3 q4 q5 q6 q7 q8 q9 q10
  /PRINT INITIAL KMO AIC EXTRACTION ROTATION
  /FORMAT SORT BLANK(.30)
  /PLOT EIGEN
  /CRITERIA MINEIGEN(1) ITERATE(25)
  /EXTRACTION PAF
  /CRITERIA ITERATE(25) DELTA(0)
  /ROTATION OBLIMIN
  /METHOD=CORRELATION.

The MINEIGEN(1) line is only your starting point for the number of factors. Once you have decided on a number by the criteria below, rerun with /CRITERIA FACTORS(k) to force exactly k factors rather than letting the eigenvalue rule choose.

Deciding how many factors to retain

This is the decision that most shapes the result, and the default Kaiser criterion of keeping every factor with an eigenvalue over 1 is the weakest of the available rules: it routinely overestimates the number of factors. Read it alongside three better guides. The scree plot shows eigenvalues in descending order, and you retain the factors above the elbow where the curve levels into rubble. Parallel analysis, the method most recommended in current methodological writing, compares your eigenvalues against those from random data of the same size and keeps only factors whose eigenvalue exceeds the random benchmark; SPSS does not offer it in the menus, so you run it through a published syntax macro (O'Connor's) or compute it alongside. Finally, interpretability is a legitimate criterion: a factor you cannot name or that holds only one or two items is usually not worth keeping. Decide the number using these together, then fix it explicitly rather than accepting the eigenvalue default.

Rotation: orthogonal against oblique

Rotation does not change how much variance the factors explain; it redistributes the loadings to make the structure readable. The real choice is between orthogonal rotation, chiefly Varimax, which forces the factors to be uncorrelated, and oblique rotation, chiefly Direct Oblimin or Promax, which allows them to correlate. In social science the underlying constructs almost always do correlate, so an oblique rotation is the more defensible default, and you can inspect the Factor Correlation Matrix it produces: if the inter-factor correlations are all trivially small (below about 0.30), the orthogonal solution was adequate after all and is simpler to report. The important consequence is which table you read. After an oblique rotation SPSS prints both a Pattern Matrix and a Structure Matrix, and you interpret the Pattern Matrix, whose coefficients are the unique contribution of each factor to an item, analogous to regression weights.

Reading the factor output in order

Several tables matter and the order helps. KMO and Bartlett's Test confirms factorability. The Communalities table reports how much of each item's variance the retained factors explain; an extracted communality below about 0.30 flags an item the solution barely accounts for. The Total Variance Explained table gives the eigenvalues and the cumulative percentage of variance, where a solution explaining at least roughly 50 to 60 percent is generally considered adequate. The scree plot supports the retention decision. The Pattern Matrix (oblique) or Rotated Factor Matrix (orthogonal) is where the findings live: you read it row by row, keeping items that load at about 0.40 or higher on one factor and weakly elsewhere, and flagging any cross-loading item that loads on two factors at once. That skill sits within reading SPSS output table by table.

From a clean structure to a usable scale

A clean solution is the start, not the end. You refine iteratively: drop the worst cross-loading or lowest-loading item, rerun, and re-examine, changing one item at a time so you can see each effect. Once the structure is stable, name each factor from the items that define it, then test whether the items within each factor are reliable enough to combine, which is the job of Cronbach's alpha or, better, McDonald's omega. Reverse-coded items must be recoded before that reliability step or alpha will look artificially poor. This factor-then-reliability sequence, and the per-item diagnostics behind it, is set out in factor analysis and Cronbach's alpha, and for ordinal questionnaire items it connects to the wider choices in analysing Likert scale data.

Confirming the structure you found

Exploratory factor analysis lets the data suggest a structure; it cannot prove it. When theory or a previous study already proposes a specific structure, or once your exploratory work has produced one, the rigorous next step is confirmatory factor analysis, which tests a hypothesised pattern of loadings and reports fit indices such as the comparative fit index and the root mean square error of approximation rather than eigenvalues. Confirmatory work belongs to the structural equation modelling family and is not available through the basic Factor dialog. A strong dissertation often explores on one half of the sample and confirms on the other, so the exploratory run you have just done becomes the foundation for a confirmatory model rather than the whole measurement story.

Reporting factor analysis in APA style

Report the suitability checks, the extraction and rotation methods, the retention rationale, the variance explained, and a table of loadings. A clean passage reads: an exploratory factor analysis with principal axis factoring and oblique (direct oblimin) rotation was conducted on the ten items; the Kaiser-Meyer-Olkin measure was .84 and Bartlett's test was significant, chi-square(45) = 612.4, p < .001, confirming the data were suitable. Parallel analysis and the scree plot supported a two-factor solution explaining 58 percent of the variance, and all items loaded above .45 on their intended factor with no substantial cross-loadings. Present the full pattern matrix as a table with small loadings suppressed. The decimal and italics rules are part of the APA write-up conventions.