Exploratory Factor Analysis in SPSS

Imagine that you have collected a large amount of survey data with 30 questions about different psychological attitudes. You suspect that these are underpinned by only a few basic constructs, such as ‘achievement motivation’ or ‘social desirability’. This is where exploratory factor analysis (EFA) comes in: It helps you identify a smaller number of latent dimensions from a large set of observed variables. Here, we will look at how to implement it in SPSS.

Definition: Exploratory Factor Analysis Exploratory factor analysis (EFA) is a statistical procedure used to reduce the relationships among many observed variables to a smaller number of latent factors. It is used when there is not yet a clear theoretical structure.

Prerequisites for Factor Analysis

Before you get started, check whether your data are suitable for an EFA. There are a few basic rules to keep in mind:

1. Sample Size

A rule of thumb is: at least 5 to 10 cases per variable. If you have 20 items, you should therefore have surveyed at least 100 to 200 people.

2. Correlation Matrix

EFA is based on relationships among variables. So, check whether your variables are sufficiently correlated in the first place:

• Bartlett’s test of sphericity should be significant ($p < 0{,}05$).
• Kaiser-Meyer-Olkin (KMO) measure should ideally be > 0{,}6.

Definition: KMO measure The KMO measure assesses whether the items share sufficient common variance to be suitable for factor analysis.

Conducting exploratory factor analysis in SPSS

Here you will find a step-by-step guide on how to conduct the analysis in SPSS:

Step 1: Use the SPSS menu

Go to:

Analysieren → Dimensionen reduzieren → Faktoren...

Select all variables you want to examine here (e.g., all scale items from a questionnaire).

Step 2: Check descriptive statistics

Click the “Descriptives” button and activate:

• Correlations
• Anti-image matrix (for KMO)
• KMO and Bartlett’s test

Step 3: Choose the extraction method

Under “Extraction”, you can select:

• Principal component analysis (default)
• Principal axis factoring (particularly suitable when examining latent constructs)

Definition: Eigenvalue An eigenvalue indicates how much variance a factor explains. Factors with an eigenvalue > 1 are generally considered significant.

Also activate the scree plot to check where an “elbow” occurs, which provides clues about the number of meaningful factors.

Step 4: Rotate for better interpretability

Go to “Rotation” and select:

• Varimax: If you expect independent factors.
• Oblimin: If you expect the factors to overlap.

Definition: Rotation Rotation in factor analysis is a mathematical transformation used to make the factor structure clearer and easier to interpret.

Step 5: Interpreting the results

Communalities

They show how much of an item’s variance is explained by the extracted factors. Values < 0.4 are critical.

Factor loadings

The heart of the matter: They tell you which item “loads” on which factor.

Definition: Factor loading A factor loading describes the correlation between an item and a factor. High loadings (> 0.4) indicate a strong association with the respective factor.

Rotated component matrix

This table shows how the items are distributed across the factors. Ideally, each item should load strongly on exactly one factor.

An example from psychology (fictional)

Imagine that you collect 12 questions on self-efficacy, locus of control, and test anxiety. The EFA yields 3 factors:

• Factor 1: Items measuring self-efficacy load here > 0.6
• Factor 2: Items measuring locus of control > 0.7
• Factor 3: Items measuring test anxiety > 0.5

This would reveal a clear structure. You could then create a scale for each factor (the mean of the corresponding items).

Tips for interpretation

• Check whether the items belonging to a factor are also similar in terms of content
• You may want to exclude items with very low loadings (< 0.3)
• Communalities should be > 0.4
• Watch out for cross-loadings (items with high values on several factors)

Conclusion

Exploratory factor analysis is an indispensable tool when you want to discover hidden structures in questionnaires or psychological tests. With SPSS, you can also carry it out effectively without any programming knowledge. It is important to check the prerequisites and interpret the results critically.

Q&A for review

1. What does Bartlett’s test of sphericity test?

Example answer: Whether the correlations between the variables are significantly different from zero. If it is significant ($p < 0{,}05$), factor analysis can be conducted.

2. What does a factor loading of 0.65 mean?

Example answer: The item correlates 0.65 with the respective factor, which indicates a