Simple Methods for Estimating Confidence Levels, or Tentative Probabilities, for Hypotheses Instead of P Values

Abstract: In many fields of research null hypothesis significance tests and p values are the accepted way of assessing the degree of certainty with which research results can be extrapolated beyond the sample studied. However, there are very serious concerns about the suitability of p values for this purpose. An alternative approach is to cite confidence intervals for a statistic of interest, but this does not directly tell readers how certain a hypothesis is. Here, I suggest how the framework used for confidence intervals could easily be extended to derive confidence levels, or "tentative probabilities", for hypotheses. I also outline four quick methods for estimating these. This allows researchers to state their confidence in a hypothesis as a direct probability, instead of circuitously by p values referring to an unstated, hypothetical null hypothesis. The inevitable difficulties of statistical inference mean that these probabilities can only be tentative, but probabilities are the natural way to express uncertainties, so, arguably, researchers using statistical methods have an obligation to estimate how probable their hypotheses are by the best available method. Otherwise misinterpretations will fill the void. Key words: Confidence, Null hypothesis significance test, p value, Statistical inference