On Judging the Significance of a Difference Obtained by Averaging Essentially Different Series
Hermann Joseph Muller · The American Naturalist · 1941
It is supposed that data on the frequency (p) of events of a given type have been obtained in the form of a number of series (1-k), which may differ determinately from one another, and that each series consists of two lots, representing the contrasting conditions A and B, while the total numbers observed (n) vary irregularly from series to series as well as from lot to lot. Formulae (1, 3) are given for calculating the best weighted average frequencies (p) in the two sets of lots, obtained under the two conditions, for the purpose of comparison of the results under the two conditions with one another. The error of the difference between these averages is given (2) and formula (7) is developed for ascertaining the minimum chance of the sets of lots showing as bad a fit as they do to one another, if the difference in conditions A and B had no real influence on the frequency (p). The purpose of these formulae, then, is to determine to what extent the results indicate that a difference in these conditions influences the frequency.