The Absolute Normal Scores Test for Symmetry.

Behavioral scientists often wish to determine if a sample has been taken from a symmetric population. Similarly, classroom teachers are interested in symmetry if they wish to grade on a "curve." Previously, the sign test, the Wilcoxon test and the t-test have been used to test a hypothesis concerning the symmetry of a distribution of scores about a location parameter. Another test, which is more powerful than either the sign test (S) or the Wilcoxon test (W), and as powerful as the t-test, when the assumptions under the t are met, is the absolute normal scores test (K). The test utilizes the expected order statistics for a sample of absolute values from the standardized normal distribution. The procedure for utilizing the absolute normal scores test is carefully outlined. Two hypothetical examples are presented and analyzed by each of the three tests, S, W, and K. The power of the three nonparametric tests when used with various types of frequency distributions is discussed. (CK)