A Significance Test for Simultaneous Quanta1 and Quantitative Responses

A significance test is designed for a situation where a discrete variate r, representing the number of successes in a sample of size n, is observed together with a continuous variate , representing the arithmetic mean of a measure concerning only the r successes (or the n – r failures). The aim is to test the null-hypothesis H 0 : ω = ω0, μ = μ0 against an alternative (say) H 1 : ω<ω0 and/or μ<μ0, where ω is the proportion of successes of the whole population, estimated by r/n, and μ is the mean, estimated by , of the above mentioned measure concerning the r successes alone. The parameters ω0, μ0. are either given or unknown parameters associated with a second sample to be compared with the first. Although the two variates r and are usually not independent, the above problems can be solved by combination of probabilities. Moreover, it is shown that, quite generally, Fisher's method of combining probabilities of continuous variates and its generalization for discrete variates can be extended to variates that are not stochastically independent.