# Tests for Several Independent Samples Test Types

Three tests are available to determine if several
independent samples come from the same population. The Kruskal-Wallis *H* test, the median test, and the Jonckheere-Terpstra
test all test whether several independent samples are from the same
population.

The **Kruskal-Wallis H
test**, an extension of the Mann-Whitney *U* test, is the nonparametric analog of one-way
analysis of variance and detects differences in distribution location.
The **median test**, which is
a more general test (but not as powerful), detects distributional
differences in location and shape. The Kruskal-Wallis *H* test and the median test assume that there
is no *a priori* ordering of the *k* populations from which the samples are
drawn.

When there *is* a
natural *a priori* ordering (ascending
or descending) of the* k* populations,
the **Jonckheere-Terpstra test** is more powerful. For example, the *k* populations might represent *k* increasing temperatures. The hypothesis that different temperatures
produce the same response distribution is tested against the alternative
that as the temperature increases, the magnitude of the response increases.
Here, the alternative hypothesis is ordered; therefore, Jonckheere-Terpstra
is the most appropriate test to use. The Jonckheere-Terpstra test
is available only if you have installed the Exact Tests add-on module.