Using a Normal Approximation to Test for the Binomial Distribution
Ping Sun, Laurence V. Madden · Biometrical Journal · 1997
Abstract The commonly used method to test for the binomial distribution is thex2‐test. In this paper, we introduce an alternative method to test for the binomial distribution. SupposeNis the number of sample groups withnindividuals each,xijis thejth sample inith group, a Bernoulli variable with parameter and VVI=s2/[m(1 ‐m)/n]. Then it is well know that the asymptotic distribution of the statistic (N‐ 1) VVI isx2(N‐ 1) under the hypothesisp1= p2= … = pN.Here we find that VVI has an asymptotic normal distributionN(1, 2(1 ‐ 1/n)/(N‐ 1)). Unlike thex2‐statistic, the variance of the normal test statistic is a function ofn.This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples.