| The goal of this study was to provide minimum sample size recommendations for performing a two-group discriminant analysis under a variety of conditions. Sample size recommendations were determined by conducting a series of Monte Carlo simulations. For each simulation, data were generated from two multivariate normal distributions and an estimate of the OER was calculated. This process was repeated 5000 times resulting in the production of 5000 different estimates of the OER For each sample size considered, a sample size was determined to be the minimum necessary sample size when 95% of the estimates fell within a specified range of the OER. This range was determined by a tolerance level. Three tolerance levels were used in this study; .02, .03, and .05. It was discovered that sample size is a function of the optimum error rate (OER), also known as the total probability of misclassification. Based upon the relationship between sample size and OER, three conclusions regarding sample size were drawn from the data: (1) as the value of the OER increases the sample size increases; (2) as the value of k (the number of variates) increases the sample size increases; (3) and as the tolerance level increases the sample size decreases. Sample size recommendations for this study are presented based upon the value of the OER, the number of variates, where k = 2, 3, 5, and 8, and each tolerance level. Findings of this study will enable researchers to use appropriate sample sizes, thereby ensuring resources are not wasted by taking a sample that is larger than necessary, or, that inaccurate results are obtained by taking a sample that is too small. |
