# Tests for Two Independent Samples

There are four non-parametric tests for cases involving two independent samples. These tests are:

- The Mann-Whitney U test
- The Wald-Wolfowitz Runs test
- The Kolmogorov-Smirnov Z test
- The Moses Extreme Reactions test

**The Mann-Whitney U test** in the tests for two independent samples is an alternative form of the *t*-test. It is widely used to test whether or not two independent samples are significantly different. In SPSS, the Mann-Whitney U test in the tests for two independent samples is done by selecting “analyze” from the menu, then clicking on “Nonparametric Tests.” After this, select “legacy dialogs” and then “2 Independent Samples” and select the “Mann-Whitney U” option from the Test Type option.

**The Wald-Wolfowitz Runs test** in the tests for two independent samples is used for testing the significant difference between two independent samples of an ordinal variable. In SPSS, Wald-Wolfowitz Runs in the tests for two independent samples is done by selecting “Nonparametric Tests” from the analyze menu, and then selecting “legacy dialogs” and then “2 Independent Samples.” Finally, select the “Wald-Wolfowitz runs” option from the Test Type option.

**The Kolmogorov-Smirnov Z test** in the tests for two independent samples is used to test whether or not the maximum absolute difference in the overall distribution of the two groups is significant. In SPSS, Kolmogorov-Smirnov Z test in the tests for two independent samples is done by selecting “Nonparametric Tests” from the analyze menu, and then clicking on “legacy dialogs” and then “2 Independent Samples.” Finally, select the “Kolmogorov-Smirnov Z” option from the Test Type option.

**The Moses Extreme Reactions test **in the tests for two independent samples is used to test if the treatment variables will affect the subjects in a positive manner or in a negative manner. In SPSS, the Moses Extreme Reactions in the tests for two independent samples is done by selecting “Nonparametric Tests” from the analyze menu, and then clicking on “legacy dialogs” and then “2 Independent Samples.” Finally, choose the “Moses Extreme Reactions” option from the Test Type option.

**Assumptions:**

In all the tests for two independent samples, sampling is done randomly. The four tests in the tests for two independent samples are non-parametric tests that do not assume normal distribution. The four tests in the tests for two independent samples are based on ordinal data or higher.

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**Related Pages:**

Conduct and Interpret a Mann-Whitney U-Test

Conduct and Interpret an Independent Sample T-Test

**To Reference this Page: **Statistics Solutions. (2013). Test for Two Independent Samples [WWW Document]. Retrieved from http://www.statisticssolutions.com/academic-solutions/resources/directory-of-statistical-analyses/tests-for-two-independent-samples/