'Parallel Universe' or 'Proven Future'? The Language of Dependent Means t-Test Interpretations

Abstract

Of the three kinds of two-mean comparisons which judge a test statistic against a critical value taken from a Student t-distribution, one -the repeated measures or dependent-means application -is distinctive because it is meant to assess the value of a parameter which is not part of the natural order. This absence forces a choice between two interpretations of a significant test result and the meaning of the test hypothesis. The parallel universe view advances a conditional, backward-looking conclusion. The more practical proven future interpretation is a non-conditional proposition about what will happen if an intervention is (now) applied to each population element. Proven future conclusions are subject to the corrupting influence of time-displacement, which include the effects of learning, development, and history. These two interpretations are explored, and a proposal for new conceptual categories and nomenclature is given to distinguish them, applicable to other repeated measures procedures derived from the general linear model including ANOVA.

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