Chance Expectancy,Sample Size,Replacement and Non-Replacement Sampling

Abstract

This study investigates the influence of sample size, non-replacement and replacement sampling on the number of MMPI items which will reach significance levels of .05, .01, and .001 purely by chance. The results show that replacement sampling of a VA NP population gives a more stable sampling distribution than non-replacement sampling. Larger sized samples seem to have a somewhat greater number of mean chance occurrences than smaller sized samples. The common procedure of requiring that more than 19 items of a 373-item MMPI have to reach significance at the .05 level before a non-chance occurrence is accepted is a definite underestimation according to the upper range limits of chance significances found in this study for samples of size 30, 40, 50, 100, 150, and 200. The best solution for a decision whether or not findings are non-chance occurrences would be to use a more stringent level of significance than the .05 level and co use the upper range limits of chance significances found in this study for the appropriate sample size. It is likely that different populations have associated with them different numbers of items which will reach chance significance.