Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Statistical Significance Revisited

Version 1 : Received: 11 March 2021 / Approved: 15 March 2021 / Online: 15 March 2021 (15:55:33 CET)

A peer-reviewed article of this Preprint also exists.

Tormählen, M.; Klinkova, G.; Grabinski, M. Statistical Significance Revisited. Mathematics 2021, 9, 958. Tormählen, M.; Klinkova, G.; Grabinski, M. Statistical Significance Revisited. Mathematics 2021, 9, 958.

Journal reference: Mathematics 2021, 9, 958
DOI: 10.3390/math9090958

Abstract

Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider binomially distributed variables in the example of medication testing with fixed placebo efficacy, asking how many experiments are needed in order to achieve a significance of 95 %. In the next step, we take the probability distribution of the placebo efficacy into account, which to the best of our knowledge has not been done so far. Depending on the specifics, we show that in order to obtain identical significance, it may be necessary to perform twice as many experiments than in a setting where the placebo distribution is neglected. We proceed by considering more general probability distributions and close with comments on some erroneous assumptions on probability distributions which lead, for instance, to a trivial explanation of the fat tail.

Subject Areas

statistical significance; confidence; medication tests; central limit theorem; fat tail

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