Discuss the roles of confirmatory and exploratory factor analysis in establishing construct validity. Give an example of a study using each type of factor analysis.

Question

What will be an ideal response?

Answer 1

• Factor analysis is a statistical procedure that can be used to identify whether the pattern of correlations among all the questions on a test can be more simply explained by a smaller number of underlying constructs, or factors.

• If we had a test that contained both reading and arithmetic questions, we might expect it to produce two factors—one for the verbal factor (as represented by the reading questions) and one for the mathematical factor (as represented by the arithmetic questions). This is because we would expect that each person’s answers to the arithmetic questions would be more correlated with their answers to other arithmetic questions than with their answers to the reading questions. As the test questions group together, they form factors—underlying dimensions that measure the same trait or attribute.

• In an exploratory factor analysis, researchers do not propose a formal hypothesis about the factors that underlie a set of test scores, but instead use the procedure broadly to help identify underlying components.

• In confirmatory factor analysis, the researcher specifies in advance what he believes the factor structure of his data should look like and then statistically tests how well that model actually fits the data. The researcher relies on either existing theoretical or empirical knowledge to design the model that will be tested. As with exploratory factor analysis, the researcher can specify the number of factors that he expects to be able to extract from the data. But unlike exploratory factor analysis, he can also specify in advance a large number of other characteristics he believes will be present in the data, such as which variables are most strongly associated with each factor and even whether the factors themselves are correlated.