Understanding the Sampling Distribution: Why We Divide by n-1 To Estimate the Population Variance.

This paper explains the underlying assumptions of the sampling distribution and its role in significance testing. To compute statistical significance, estimates of population parameters must be obtained so that only one sampling distribution is defined. A sampling distribution is the underlying distribution of a statistic. Sampling distributions are theoretical distributions that comprise an infinite number of sample statistics from an infinite number of randomly selected samples of a specified sample size. The influence that a large sample size has on statistical significance is demonstrated through some "what if" analyses. A "what if" analysis is simply an analysis of variance summary table in which the sample size is changed to see how statistical significance is affected. A large enough sample size invariably leads to statistical significance. Researchers with large sample sizes should look for other ways to interpret their results. One such way is effect size, which is a variance accounted for statistic that can tell how much of the variability in a dependent variable can be explained by the independent variables. (Contains 2 tables, 4 figures, and 12 references.) (SLD)