Using the data in Table 16.1, the Project Talent test score data:
a. What kinds of preliminary data screening would you need to run to evaluate whether assumptions for factor analysis are reasonably well met? Run these analyses.
b. Using PAF as the method of extraction, do a factor analysis of this set of test scores: English, reading, mechanic, abstract, and math; the default criterion to retain factors with eigenvalues >1; varimax rotation; and the option to sort the factor loadings by size; also request that factor scores be computed using the regression method, and saved. Report and discuss your results. Do your results suggest more than one kind of mental ability? Do your results convince you that mental ability is “one-dimensional” and that there is no need to have theories about separate math and verbal dimensions of ability?
c. Compute unit-weighted scores to summarize scores on the variables that have high loadings on your first factor in the preceding analysis. Do this in two different ways: using raw scores on the measured variables and using z scores. (Recall that you can save the z scores for quantitative variables by checking a box to save standardized scores in the descriptive statistics procedure.) Run a Pearson correlation to assess how closely these three scores agree (the saved factor score from the factor analysis you ran in 2b, the sum of the raw scores, and the sum of the z scores). In future analyses, do you think it will make much difference which of these three different scores you use as a summary variable (the saved factor score, sum of raw scores, or sum of z scores)?