| Summary: | A wide array of procedures have been proposed for testing correlation pattern. Many, but
not all, of the statistical techniques available for testing correlation pattern are derived under the
distributional condition of multivariate normality which does not always hold in the behavioral,
educational and social sciences. Though a number of studies have explored the performance of
structure analysis techniques under conditions of multivariate nonnormality, very little is known
about the actual performance of many correlation structure analysis techniques under conditions
of multivariate nonnormality. In addition, very little is known about the actual concurrent
performance of tests of multivariate normality.
The present investigation ascertains how tests of correlation pattern hypotheses and
indicators of multivariate normality perform when data are from multivariate normal or nonnormal
parent populations. This paper reviews and examines, using a Monte Carlo simulation study, the
concurrent performance of different approaches to testing (1) correlation pattern hypotheses,
including, (i) normal theory (NT) and asymptotically distribution free (ADF) covariance structure
analysis techniques, (ii) NT and ADF correlation structure analysis techniques, (iii) correlation
pattern specific techniques; (2) the distributional assumption of multivariate normality using
statistics based on Mardia's measures of multivariate skewness and kurtosis. This paper also
examines the performance characteristics of test procedures based on joint consideration of tests
of multivariate normality and structure analysis techniques. Performance of the covariance and
correlation structure analysis techniques, tests of multivariate normality, and joint test procedures
was assessed across different types of correlation pattern models, numbers of variables, levels of
skew and kurtosis, sample sizes, and nominal alpha levels, on the primary Neyman-Pearson
criterion for an optimal test, according to which an optimal procedure (1) controls
experimentwise Type I error rate at or below the nominal level, (2) maximizes power.
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