P-value’s historical background put to a simulation test

Abstract

Background and Aim : Fisher’s “tea experiment”, among other important aspects, may be considered the cradle of the modern usage of p-value equal to 0.05 as a resourceful estimation of statistical significance. We aim to shed light on the matter by presenting its historical background as well as a computer simulation of the estimated probabilities.

Methods : The main concepts concerning the p-value and its interpretation are discussed. We also present a statistical simulation of a “modified tea experiment”. A binomial distribution probability test is applied in two different strategies. We estimate the probabilities of guessing the correct answer under different scenarios. The commands as well as the results are presented in two mainstream statistical computer packages: R and Stata. We compare the simulation with the “standard” threshold of statistical significance, generally accepted in clinical research as a p-value equal to 0.05 or below.

Conclusion : The presentation of a historical background on a par with the computer simulations are helpful to shed light on Fisher’s tea experiment. The combination of understandable information within a short statistical expression took eventually the allure of simplicity and, to some extent, may explain the prestige and overall usage of the p-value.

Key-words : Statistics, binomial distribution, statistical programs.