Date of Award
Doctor of Philosophy
The purpose of this research was to study the number of principal components problem. In order to accomplish this objective the problems associated with principal components analysis were presented, an exposition of principal components analysis was given, the literature on the number of factors problem was reviewed, and three new distribution free sphericity tests proposed by Harshman and Reddon (1983) were presented. The empirical research focused on the evaluation of these new tests and the comparison of these new tests with four other commonly used test procedures.;The evaluation of the three distribution free sphericity tests focused on the evaluation of the equivalence of the marginal distributions with the marginal distributions under the null hypothesis. Of the three tests only the residual observation permutation test was found to be sufficiently distribution free. In the next stage of the research a series of matrices, with correlational scaling, were constructed and the power and type one error rates in determining the dimensionality of a principal components solution was assessed. The power and type one error rates for the three distribution free sphericity tests were compared with Bartlett's test, two of Guttman's lower bounds, and Velicer's test. All these tests were also applied to eight representative research applications. The results suggested that the residual observation permutation test is superior to the other test procedures considered.
Reddon, John Robert, "The Number Of Principal Components Problem: A Monte Carlo Study" (1984). Digitized Theses. 1379.