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Statistical significance revisited

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  • Maike Tormahlen
  • Galiya Klinkova
  • Michael Grabinski

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.

Suggested Citation

  • Maike Tormahlen & Galiya Klinkova & Michael Grabinski, 2021. "Statistical significance revisited," Papers 2104.00262, arXiv.org, revised Apr 2021.
    • Handle: RePEc:arx:papers:2104.00262
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    References listed on IDEAS

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    1. Jae H. Kim, 2020. "Decision-Theoretic Hypothesis Testing: A Primer With R Package OptSig," The American Statistician, Taylor & Francis Journals, vol. 74(4), pages 370-379, October.
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