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Multivariate Randomization Tests for Small-N Behavioral Research: A Web-Based Application

Behavioral research involving statistical analyses of small group data is frequently compromised by conventional parametric statistical procedures. As an alternative, we have developed and deployed several web-based applications that allow behavioral researchers to easily input data on-line and to calculate levels of significance for small-n studies. Previously, our web-based applications were restricted to parametric and randomization tests involving only one dependent variable. We now have expanded our algorithms such that multivariate analyses may be conducted on sample sizes as small as 6 while employing several dependent measures. This paper provides details for on-line input and interpretation of randomized multivariate statistical tests for small-n studies. Also, to test the power and reliability of our applications, we have compared our multivariate randomization algorithms against a traditional multivariate statistic with two dependent variables. Using Monte Carlo methods, we have assessed the statistical advantages and accuracy of applied multivariate analyses when calculated in both randomized and traditional/parametric formats. Specifically, we have compared probability values for both traditional and randomized MANOVA models by way of Hotelling’s T2 and the Randomized multivariate/composite z scores. We discuss the reliability problems associated with using traditional multivariate statistics with small-n studies, and we describe the statistical advantages and some limitations of using our on-line, small-n, multivariate randomization tests.