Publication Date:
2020-07-23
Description:
In randomized experiments, Fisher-exactPvalues are available and should be used to help evaluate results rather than the more commonly reported asymptoticPvalues. One reason is that using the latter can effectively alter the question being addressed by including irrelevant distributional assumptions. The Fisherian statistical framework, proposed in 1925, calculates aPvalue in a randomized experiment by using the actual randomization procedure that led to the observed data. Here, we illustrate this Fisherian framework in a crossover randomized experiment. First, we consider the first period of the experiment and analyze its data as a completely randomized experiment, ignoring the second period; then, we consider both periods. For each analysis, we focus on 10 outcomes that illustrate important differences between the asymptotic and Fisher tests for the null hypothesis of no ozone effect. For some outcomes, the traditionalPvalue based on the approximating asymptotic Student’stdistribution substantially subceeded the minimum attainable Fisher-exactPvalue. For the other outcomes, the Fisher-exact null randomization distribution substantially differed from the bell-shaped one assumed by the asymptoticttest. Our conclusions: When researchers choose to reportPvalues in randomized experiments, 1) Fisher-exactPvalues should be used, especially in studies with small sample sizes, and 2) the shape of the actual null randomization distribution should be examined for the recondite scientific insights it may reveal.
Print ISSN:
0027-8424
Electronic ISSN:
1091-6490
Topics:
Biology
,
Medicine
,
Natural Sciences in General
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