Many articles in Stroke have considered good statistical practice for adequate planning and high-power analysis for stroke trials. They have discussed which test may be adequate and powerful, proposals for an effect size measure, and proposals for defining number needed to treat (NNT) based on an ordinal scale (see online-only Data Supplement for citations).The clinical problem is straightforward. We read results of trials that fall into 3 categories: unequivocally neutral or even negative; overwhelmingly positive; or encouraging but open to various interpretations according to the approach taken to statistical analysis and presentation of findings. This dependence on methodology for the third group undermines our confidence in effective treatments and can prompt unjustified repetition of trials of ineffective treatments. A robust, powerful, and universal statistical approach is required.The statistical problem is more complex. From dozens of available statistical tests, each may be uniquely powerful in certain circumstances. However, trials intended as confirmatory for regulatory approval or for the use in clinical guidelines demand that the analysis plan be prespecified so that the test of choice should minimize assumptions yet maximize power for the anticipated difference between treatment groups. Furthermore, it is not sufficient to indicate that 1 treatment is significantly different from another: clinical research guidelines require that the magnitude of the treatment effect should be declared using the so-called effect size measure accompanied by its measure of precision, the confidence interval.Thus, there is need for a robust test, preferably for all data types-binary, ordinal, or continuous-and a test-related effect size measure, with a confidence interval that matches the test-related P value. This requirement for an adequate analysis of study data fortunately restricts the plethora of available tests to a small number of useful candidates.Here, we describe and explain the relationships between 2 tests, of which 1 is well-known and the other is less familiar. Both are suitable for the analysis of binary, ordinal, and continuous data, and both offer associated confidence intervals. Using intravenous thrombolysis trial data, we can illustrate the relative merits of these tests when compared with other approaches. We will demonstrate why dichotomizing ordinal scales are undesirable. Finally, we can show that in principle each well-known effect size measure can be reexpressed as the popular NNT. Family of Mann-Whitney MeasuresOne family of effect size measures fulfills both desirable criteria: robustness, that is minimizing assumptions, and relevance for clinical research in which medicinal products are tested against a reference treatment. This family is based on the concept of proversions. Two groups are contrasted by comparing each patient of 1 group with each member of the other and counting the number of cases for which there is superiority for 1 or the other group. The number of proversions for the ...

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The standardized mean difference is a well‐known effect size measure for continuous, normally distributed data. In this paper we present a general basis for important other distribution families. As a general concept, usable for every distribution family, we introduce the relative effect, also called Mann–Whitney effect size measure of stochastic superiority. This measure is a truly robust measure, needing no assumptions about a distribution family. It is thus the preferred tool for assumption‐free, confirmatory studies. For normal distribution shift, proportional odds, and proportional hazards, we show how to derive many global values such as risk difference average, risk difference extremum, and odds ratio extremum. We demonstrate that the well‐known benchmark values of Cohen with respect to group differences—small, medium, large—can be translated easily into corresponding Mann–Whitney values. From these, we get benchmarks for parameters of other distribution families. Furthermore, it is shown that local measures based on binary data (2 × 2 tables) can be associated with the Mann–Whitney measure: The concept of stochastic superiority can always be used. It is a general statistical value in every distribution family. It therefore yields a procedure for standardizing the assessment of effect size measures. We look at the aspect of relevance of an effect size and—introducing confidence intervals—present some examples for use in statistical practice.

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