e-Statistics

## Nonparametric Test

The sample data from Group 1'' and Group 2'' must be shown separately in two different columns:

Group 1:

Group 2:

Here it is assumed that the distribution of Group 1 and that of Group 2 share the same shape with possible shift, but not necessarily normally distributed. The Wilcoxon rank sum test is based on ranks--the rank 1 is assigned to the smallest measurement in both groups, and 2 to the second smallest, and so on. Recall that the validity of t-test is based on the normality of population distributions,'' and that it requires that either sample distributions are approximately normal, or the sample sizes are appropriately large ( ). Since a normal distribution is parametric,'' the rank sum test procedure is referred as nonparametric,'' free from the assumption of normal distribution.

The null hypothesis is stated as the distributions from two groups are identical,'' and the test will determine whether it is rejected in favor of the following alternative hypothesis.

The distribution of Group 1 that of Group 2

It produces the estimate estimate.shift'' and the confidence interval (lower.bound,upper.bound)'' for the shift (the difference of locations) with confidence interval. The value p.value indicates the significance of the test: If p-value < , it suggest evidence against the null hypothesis in favor of the alternative hypothesis.

Here the estimate estimate.shift'' is calculated from the sample median of the difference  between in Group 1 and in Group 2. It is called the Hodges-Lehmann estimator.