Deck 15: Factor Analysis and Reliability Analysis: Data Reduction Techniques

Question 1

What is the purpose of conducting an exploratory factor analysis (EFA)?

Answer 1

The purpose of exploratory factor analysis is to determine which items in a dataset are most strongly correlated with each other so that they can be grouped into a smaller number of factors. It is a method of data reduction and organization so that multiple items, or indicators, of underlying factors can get grouped together.

Question 2

How does an EFA differ from a confirmatory factor analysis (CFA)?

Answer 2

Whereas the EFA organizes measured items together based on the strength of their correlations with each other, in a confirmatory factor analysis (CFA) the researcher specifies, prior to the analysis, which items belong in which factors, and then performs the analysis to see how well the data "fit" the hypothesized factor model. EFA is a method that is used to discover which items should be grouped together, and CFA is a method to test hypotheses about which items belong on each factor and how many factors should be used to model the data.

Question 3

What are three of the criteria that researchers can use to determine how many factors should be retained from an EFA?

Answer 3

Eigenvalues, percentage of variance explained, and theory. A general rule of thumb is that factors should have eigenvalues over 1.0 and explain at least 10% of the variance of all of the items in the factor analysis in order to be retained. In addition, the factors should make sense conceptually and theoretically. Just because items load together onto a factor, if it does not make sense for the items to be combined into a single factor then the factor should perhaps not be retained.

Question 4

What kinds of variables are appropriate to use in a factor analysis?

Question 5

What does it mean to say that an item is "cross-loaded" on two factors?

Question 6

Suppose that I performed a reliability analysis to determine whether high school students' grades in four different subjects (English, Math, Science, Social Studies) formed a reliable scale with a high Cronbach's alpha. I performed the analysis and got the results presented in the two tables below.
a. What is the reliability of this scale, as indicated by the Cronbach's alpha. Is this a high or low level of reliability?
b. Which item seems to be contributing the least to the overall Cronbach's alpha?
c. Which item, if any, would you recommend removing from this scale?