An Investigation of the Restraints with Respect to Sample Size Commonly Imposed on the Use of the Chi-Square Statistic

Abstract

This empirical study of the chi-square approximations as commonly encountered in behavioral research involved: (1) both tests of goodness-of-fit and of independence, (2) uniform distributions and two levels of departure from uniform, (3) sample sizes ranging from 10 to 100. Excellent approximations were obtained with average expected frequencies of one or two in tests of goodness-of-fit to uniform; slightly higher expected frequencies were required with the non-uniform cases. Tests of independence were strikingly robust with respect to Type I errors; in almost all cases the errors were in the conservative direction.