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Abstract:
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We’ve developed a global hypothesis test intended for early stage studies, when the number of measures, m, of interest is large and the sample size is small, a situation in which many tests perform poorly. Our test statistic uses researcher provided predictions about the directionality of the measures but does not require homogeneous responses across the measures. In addition, we weight the individual measures using the sample correlation matrix in order to account for the potential of dependent measures. The test statistic has an exact distribution which can easily be calculated for small samples and a normal approximation that adequately approximates the true distribution for m ? 15. We’ve shown that the test has good power and error control under a variety of possible situations. Due to intense interest in the area of global tests for many measures there are a plethora of options to choose from. We compare our approach to other common global tests such as O’Brien’s test via simulations of power, family wise error control and analyses of edge cases were the different tests can fail.
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