What statistical test determines if a distribution of scores differs significantly from a normal distribution?

The Kolmogorov-Smirnov test is a non-parametric test that is specifically designed to compare the distribution of a sample with a reference probability distribution, such as the normal distribution. This test quantifies the difference between the empirical distribution function of the sample and the cumulative distribution function of the normal distribution. It assesses whether the sample data deviates significantly from what would be expected if it followed a normal distribution.

When using the Kolmogorov-Smirnov test, a significant result indicates that the sample's distribution is different from the normal distribution, which has implications for selecting appropriate statistical methods for further analysis. This test can be especially useful in research settings where the assumption of normality is critical for the validity of parametric tests.

In contrast, other options do not directly assess the normality of a distribution. The Shapiro-Wilk test is also used to test for normality, but the Kolmogorov-Smirnov test is often favored for its broader application in comparing distributions. Levene's test is intended to assess the equality of variances across groups, and the Kruskal-Wallis test is used for comparing median differences across three or more groups rather than testing for normality directly.