A New Method of Testing Hypotheses and Estimating Parameters for the Logistic Model

Publisher Website
Google Scholar
Abstract
A method of analyzing the results of an experiment in which several treatments have been applied at several levels and the data consist of the proportion of observations at each treatment combination that have a specified attribute is developed. It is assumed that the observations taken at each combination of treatments follow a binomial distribution with parameters P and n, where P is the expected proportion that has the attribute and n is the sample size. The transformation loge (P/l-P) is assumed to provide a scale on which the treatment effects are linearly related to the transformation. In contrast to the usual techniques for testing hypotheses when using this model, the method developed in this paper does not require fitting the full model to the data if one is confident that the model is correct. Also, in many cases, the goodness of fit of the model can be tested without actually fitting the model to the data. Roots of certain equations arising in making this test can be used to compute maximum likelihood estimates of the parameters in the model without iteration other than that required to obtain roots of the equations. The test statistics all follow the X2-distribution if the hypothesis being tested is true and the sample size at each treatment combination is large.

This publication has 1 reference indexed in Scilit: