# Interpreting a Factor Analysis

Interpreting a Factor Analysis

Factor analysis is a powerful statistical technique that is frequently used in test construction. When performing factor analysis, researchers look at correlations between test items or variables and, in doing so, seek to discover underlying dimensions. It may be discovered that groups of items measure the same dimension, which may in turn lead to the discovery of subscales. Exploratory factor analysis is used to discover how items group together; confirmatory factor analysis is used to see if the items group together in a way that is consistent with theory or expectation. For this assignment, you interpret an exploratory factor analysis on the provided dataset. Because factor analysis is so important in test construction, the steps on how to perform a factor analysis are presented below. You may wish to work through these steps on your own in SPSS since familiarity with this process may benefit you in the future; however, you are not required to do so.
To perform a factor analysis on the provided MoneyData dataset, click on ANALYZEDIMENSION REDUCTIONFACTOR. Move the 18 test items into the VARIABLES box, L1 to L5, L6R, D1 to D6, and R1 to R6. Click on the EXTRACTION button. For METHOD, select Principle Axis Factoring. For DISPLAY, uncheck Unrotated factor solution, and check Scree Plot. Under Extract, select Fixed number of factors, and enter 3 in the Factors to extract box. Click on Continue. Click on the ROTATION button, and select Direct Oblimin as the rotation method. Click on Continue, and then click on OK.
Notice the Scree Plot. This shows how many distinct factors are present in your data. The number of factors above the plot elbow is the number you should retain. In this case, three factors should be retained.

Now look at the Pattern Matrix. It shows, for the most part, that each item loads on only one factor. Each item has a high loading in only one column and negligible loadings on the other two factors. The factor analysis shows that there are three distinct scales with 6 items each.
The factor analysis for the Final Project dataset is provided to you. Consider how you would interpret the results of this factor analysis.
The Assignment
Interpret the results of the factor analysis.