Factors affecting a lower-bound estimate of internal consistency reliability, Cronbach's coefficient alpha, are explored. Theoretically, coefficient alpha is an estimate of the correlation between two tests drawn at random from a pool of items like the items in the test under consideration. As a practical matter, coefficient alpha can be an index of internal consistency (i.e., an index of the degree to which item response scores correlate with total test scores). Cronbach's procedure is a method of calculating coefficient alpha. Three factors affecting coefficient alpha--total test variance, sum of item variances, and homogeneity of item difficulty--were examined using a mini Monte Carlo model. Small data sets generated by a computer program were used to make the discussion concrete. By considering bivariate correlation, multiple R correlation, beta-weight, and structure coefficients, total test variance was shown to account for the most variance of coefficient alpha, followed by the standard deviation of item difficulties, and the sum of item variances. Seven tables and three figures illustrate the discussion. (SLD)