Least-Squares Analysis of Discrete Data

Abstract

There are two important advantages of using general least-squares procedures to analyze discrete data. First is the ready availability of general least-squares computer programs. Second is the greater flexibility in the models which may be used when analyzed under least-squares procedures rather than by other methods. For example, one can easily complete covariance and even multiple covariance analyses under the least-squares procedures. Also, analyses may be completed under complex mixed models, and estimates of variance components for discrete characters, as well as covariance components between discrete and continuous traits, may be obtained. However, this summary would not be complete without a word of caution regarding tests of significance. Clearly, estimates of “treatment” effects and least-squares means obtained from an analysis of discrete data by least-squares procedures are unbiased. The accuracy of tests of significance depends largely on whether adequate numbers are available for the estimation of treatment or subclass means. In general, for binomial data, if nµ and n(l—µ) are greater than or equal to 5 the tests of significance from a least-squares analysis will be accurate enough for practical purposes, where µ is the probability of “success” and n is the sample size.