  Although several nonparametric tests are available for testing population
identical distributions or equal means in multiple groups problem, the Van der
Waerden test has asymptotically the same efficiency as the classical one-way
analysis of variance test under normality assumption where it depends on
inverse normal score. In this study the Waerden test statistic is used to
create a form that assists in deriving adjusted p values chart in terms of
Bonferroni and Benjamini-Hochberg methods. The sampling distribution of the
proposed form is derived as a gamma distribution that utilized to acquire
initial p values. The proposed method will provide well recognition and deep
knowledge where the changes occur. Simulation study is executed to study the
characteristic of the proposed method in terms of size and power of the test
and compared with original Waerden test and one-way analysis of variance test.
The results are of great practical values since the proposed method stretches
visible shape to decision maker to gives complete picture and deep insight
where the differences happen, keep size and power of the test almost similar to
original Waerden test and gives a glimpse of various information that completes
the pairwise comparisons. To show the benefits of the proposed method, two
applications are presented.
