What is The Exploratory Factor Analysis?

Using Exploratory Factor Analysis (EFA) Test in Research

This easy tutorial will show you how to run the exploratory factor analysis test in SPSS, and how to interpret the result.

The purpose of an EFA is to describe a multidimensional data set using fewer variables. Once a questionnaire has been validated, another process called Confirmatory Factor Analysis can be used. This is supported by AMOS, a ‘sister’ package to SPSS. (Source)

EFA has two goals:

  • Identification and understanding of the basic idea
  • Reducing the number of variables in an analysis when there are too many, some of which overlap because they have similar meanings and behavior.

Assumptions of exploratory factor analysis:

  • Sample size (N > 150)
  • Eligibility of correlation matrix for factorization
  • Linearity
  • No outliers

An Example: How to run exploratory factor analysis test in SPSS

We collected data from students about their feeling before the exam. The students were asked to rate the following feelings on the scale from 1 to 5. We wanted to reduce the number of variables and group them into factors, so we used the factor analysis.

Before starting the Analysis: The Approach

  1. Before carrying out an EFA the values of the bivariate correlation matrix of all items should be analyzed. It is easier to do this in Excel or SPSS. High values are an indication of multicollinearity, although they are not a necessary condition. Suggests removing one of a pair of items with bivariate correlation scores greater than 0.8.
  2. Decide on the appropriate method and rotation (probably varimax to start with) and run the analysis.
  3. Remove any items with communalities less than 0.2 and re-run.
  4. Optimize the number of factors – the default number in SPSS is given by Kaiser’s criterion (eigenvalue >1) which often tends to be too high. You are looking for as many factors as possible with at least 3 items with a loading greater than 0.4 and a low cross-loading as a result fix the number of factors to extract and re-run.
  5. Clear away any items with no factor loadings > 0.3 and you need to perform the test again.
  6. Remove any items with cross-loadings > 75% starting with the one with the lowest absolute maximum loading on all the factors.
  7. Once the solution has stabilized, check the average within and between factor correlations. To obtain the factors, use a PCA with the identified items and save the regression scores Hence, If there is not an acceptable difference between the within and between factor average correlations,  for the reason that you should try an oblique rotation instead.

A number of final checks;

8. Provided the average within factor correlation is now higher than the average between factor correlation, a number of final checks should be made:

  • Check that the proportion of the total variance explained by the retained factors is at least 50%.
  • Control the adequacy of the sample size using the KMO statistic  and a minimum acceptable score for this test is 0.5
  • If the sample size is less than 300 check the average commonality of the retained items. Therefore an average value above 0.6 is acceptable for samples less than 100 likewise an average value between 0.5 and 0.6 is acceptable for sample sizes between 100 and 200.
  • The determinant of the correlation matrix should be greater than 0.00001 due to a lower score might indicate that groups of three or more questions have high intercorrelations, so the threshold for item removal should be reduced until this condition is satisfied.
  • Cronbach’s alpha coefficient for each scale can also be calculated.
  1. If the goal of the analysis is to create scales of unique items then the meaning of the group of unique items that load on each factor should be interpreted to give each factor a meaningful name. (Source)

This guide will explain, step by step, how to run the exploratory factor analysis test in SPSS statistical software by using an example.

How to Run Exploratory Factor Analysis Test in SPSS: Explanation Step by Step

From the SPSS menu, choose to Analyze – Dimension Reduction – Factor

EFA Step by step approach

From the left box transfer variables happy, inspired, proud, attentive, excited, nervous, ashamed, scared, irritable, upset into the Variables box.

How to run exploratory factor analysis test in SPSS

Click the Descriptives button, and a new window will open. In the Statistics box choose Initial Solution

How to run exploratory factor analysis test in SPSS

Click the Extraction button. In the Method, the box chooses Principal components. In the Analyze box, choose the Correlation matrix.

Click the Rotation button. Choose Direct Oblimin in the Method box and Rotated solution in the Display box.

ecide on the appropriate method and rotation (probably varimax to start with) and run the analysis.

Click the Options button. In the Missing value box, choose Exclude cases pairwise.

In the Coefficient Display Format box, choose Sorted by size and Suppress absolute values less than. Please write down 0.30 in the box Suppress.

how to run exploratory factor analysis test in SPSS statistical software by using an example

Exploratory factor analysis results will appear in the output window.

Exploratory Factor Analysis Output Results: Explanation Step by Step

How to Report KMO and Bartlett’s test Table in SPSS Output?

If Kaiser-Meyer-Olkin Measure of Sampling Adequacy is equal or greater than 0.60 then we should proceed with Exploratory Factor Analysis; the sample used was adequate. If Bartlett’s test of sphericity is significant (p < 0.05), we should proceed with the Exploratory Factor Analysis.

kmo and barlett test table

How to Report Total Variance explained Table in SPSS Output?

The table shows the Initial Eigenvalues. We should look at only components that have Total Initial Eigenvalues greater than 1. In our case, only two components have Total Initial Eigenvalues greater than 1. Those two components explain 63.41% of the variance. Therefore, we conclude that there are two factors. But, we should also look at the Scree plot.

Total Variance explained output

How to Report Scree Plot in SPSS Output?

Scree plot shows that we have two factors.

scree plot output spss

How to Report Pattern Matrix Table in SPSS output?

The table shows factor weights. The first component is nervous, ashamed, scared, upset, and irritable – all negative feelings. The second component is happy, inspired, attentive, excited, proud – all positive feelings.

pattern matrix output spss

How to report Component Correlation Matrix in SPSS Output?

Table Component Correlation Matrix shows that there is no strong correlation between factors which is good for our analysis.

Component Correlation Matrix spss output

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