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UBC Theses and Dissertations

A comprehensive examination of procedures for testing the significance of a correlation matrix and its elements Fouladi, Rachel Tanya


Correlational techniques are important tools in multivariate behavioural and social science exploratory research. A wide array of procedures have been proposed for testing (a) whether any of the variables are related, and (b) which variables are related. In the current study, the performance of the procedures currently available for testing these distinct questions is assessed on the primary Neyman-Pearson criterion for an optimal test. According to this criterion, an optimal procedure is the most powerful procedure that controls experimentwise Type I error rate at or below the nominal level. The findings of the first part of this study addressing how to test complete multivariate independence suggest that the statistic traditionally used (QBA) is not the optimal test, and that one of several recently derived statistics (QSE> QSA> QF) should be used. Computational efficiency of the procedures is also considered with the resulting recommendation of the use of QSA- The second part of this study addresses how to test which variables are correlated; the findings suggest the use of a multi-stage order statistics approach with z-tests (CF). The conditions necessary to ensure maximal power when addressing these questions are also considered.

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