STATISTICA Blogs

STATISTICA offers several nonparametric hypothesis tests that are very useful when assumptions of traditional statistical tests (such as t-tests and ANOVA) fail. These nonparametric tests do not make distributional assumptions such as normality of the data that other tests make.

The one sample t-test from the Basic Statistics module tests the population mean against a hypothesized value. This test assumes a normal distribution of the data. If this assumption is not met, a nonparametric test can be used. The Nonparametric module does not offer a specific one-sample test. This example illustrates how the one-sample nonparametric test is performed.

A Wilcoxon Signed-Rank Test can be used for the one-sample case by keeping in mind that you are comparing the center of your data to a specific hypothesized value, d0. Thus, adding a variable in which all values equal d0 enables you to use the Wilcoxon Signed Rank test for this task.
 
For example, say you have the data from one sample as shown below:

Suppose you want to test that the average length for the population is 3. Add a variable to the spreadsheet in which all cases equal the hypothesized value of 3. The data should now look like this:

Now you can perform the Wilcoxon Signed-Rank Test using Length as the first variable and d0 as the second. To do this, select Nonparametrics from the Statistics menu. In the Nonparametric Statistics Startup Panel, choose Comparing two dependent samples (variables). In the Comparing two variables dialog, click the Variables button and select Length in the First variable list and d0 in the Second variable list, and click OK. Then, perform a Wilcoxon matched pairs test:

Performing the Wilcoxon matched pairs test using a variable containing the hypothesized value is equivalent to performing a large sample approximation Wilcoxon Signed Rank test without a continuity correction.