Abstract: | The commonly used method to test for the binomial distribution is the x2-test. In this paper, we introduce an alternative method to test for the binomial distribution. Suppose N is the number of sample groups with n individuals each, xij is the jth sample in ith 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 is x2(N - 1) under the hypothesis p1 = p2 = … = pN. Here we find that VVI has an asymptotic normal distribution N(1, 2(1 - 1/n)/(N - 1)). Unlike the x2-statistic, the variance of the normal test statistic is a function of n. This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples. |