Sample Size Requirements of a Mixture Analysis Method with Applications in Systematic Biology

The available information on sample size requirements of mixture analysis methods is insufficient to permit a precise evaluation of the potential problems facing practical applications of mixture analysis. We use results from Monte Carlo simulation to assess the sample size requirements of a simple mixture analysis method under conditions relevant to biological applications of mixture analysis. The mixture model used includes two univariate normal components with equal variances but assumes that the researcher is ignorant as to the equality of the variances. The method used relies on the EM algorithm to compute the maximum likelihood estimates of the mixture parameters, and the likelihood ratio test to assess the number of components in the mixtures. Our results suggest that sample sizes close to 500 or 1000 data may be required to adequately solve mixtures commonly found in biology. Sample sizes of 500 or 1000 are difficult to achieve. However, use of this MA method may be a reasonable option when the researcher deals with problems which are intractable by other means.