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Full-Text Articles in Physical Sciences and Mathematics
'Parallel Universe' Or 'Proven Future'? The Language Of Dependent Means T-Test Interpretations, Anthony M. Gould, Jean-Etienne Joullié
'Parallel Universe' Or 'Proven Future'? The Language Of Dependent Means T-Test Interpretations, Anthony M. Gould, Jean-Etienne Joullié
Journal of Modern Applied Statistical Methods
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 …
An Empirical Demonstration Of The Need For Exact Tests, Vance W. Berger
An Empirical Demonstration Of The Need For Exact Tests, Vance W. Berger
Journal of Modern Applied Statistical Methods
The robustness of parametric analyses is rarely questioned or qualified. Robustness, generally understood, means the exact and approximate p-values will lie on the same side of alpha for any reasonable data set; and 1) any data set would qualify as reasonable and 2) robustness holds universally, for all alpha levels and approximations. For this to be true, the approximation would need to be perfect all of the time. Any discrepancy between the approximation and the exact p-value, for any combination of alpha level and data set, would constitute a violation. Clearly, this is not true, and when confronted with this …