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Abstract:
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Early biomedical research is often interested in whether or not a researcher understands a process, for example does a researcher understand the biological mechanisms of a drug in an experimental unit. At this stage in the research process there are typically many, often one-sided, hypotheses of interest with a relatively small overall sample size. To deal with this set of hypotheses a typical, if flawed, process is for researchers to choose a primary hypothesis and treat all others as secondary even if this does not accurately represent the underlying scientific questions. In this way power can be specified for one test rather than many, and FWER is either controlled through a multiplicity adjustment or not at all. We present a test statistics and associated testing procedure which addresses the hypothesis of whether or not the researcher understands the process, i.e. is their theory plausibly correct given the outcomes of all the individual hypothesis tests. Our method is essentially a weighted sum of the results of the hypothesis tests, with the weights based on the correlations between tests.
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