Named after the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that k population distribution functions are equal.
The average of the normal scores for each sample can then be computed as The variance of the normal scores can be computed as The Van der Waerden test can then be defined as follows: The test statistic is For significance level α, the critical region is where Χα,k − 12 is the α-quantile of the chi-squared distribution with k − 1 degrees of freedom.
If the hypothesis of identical distributions is rejected, one can perform a multiple comparisons procedure to determine which pairs of populations tend to differ.
The advantage of the Van Der Waerden test is that it provides the high efficiency of the standard ANOVA analysis when the normality assumptions are in fact satisfied, but it also provides the robustness of the Kruskal-Wallis test when the normality assumptions are not satisfied.
This article incorporates public domain material from the National Institute of Standards and Technology