The Central Limit Effect for a Variety of Populations and the Influence of Population Moments

Abstract

From each of two dozen populations varying widely in shape and skewness, empirical distributions of Z = (X̄ - μ)/σN^−1/2 were obtained for several sample sizes to investigate the approach of the sampling distribution of Z to a normal distribution. For many populations the approach to normality is very slow as N increases. Unequally long or unequally thick opposite tails appear to be the population features most deleterious to the Central Limit Effect.