# Statistics > Nonparametrics > 2-Sample Matched-Pair Sign Test

This utility performs calculations for testing claims about two population means for the case when the type of population distribution cannot be assumed, except that the population of the pairwise differences is symmetric. The null hypothesis H0 of a claim is μ1= μ2. The alternative hypothesis H1 can be one of the following: μ1 < μ2, μ1 > μ2, or μ1 ≠ μ2.

A positive difference is assigned a positive (+) sign. A negative difference is assigned a negative (-) sign. The test statistic is computed as follows:

- Left-tailed (H1: μ1 < μ2): s = the number of positive (+) signs
- Right-tailed (H1: μ1 > μ2): s = the number of negative (-) signs
- Two-tailed (H1: μ1 ≠ μ2): s = the minimum of the number of (+) signs and the number of (-) signs

The p-value for a one-tailed test (left-tailed or right-tailed) is P(X ≤ s) where X is a random variable representing the number of positive signs. The-value for a two-tailed test is 2P(X ≤ s).

If the sample size n (excluding values that are equal to the hypothesized mean) is not more than 50, exact binomial probability calculations are used to compute the p-value. If the sample size is greater than 50, the normal distribution is used as an approximation to binomial:

To use the utility, follow these steps:

- If individual samples are entered in two columns of the Datasheet, select the Samples in column: radio button, and select the column names in the drop-down menu.
- To use summary statistics of the sample data, select the Summarized sample data: radio button, and input the number of positive signs and the number of negative signs in the provided text fields.
- Select the form of the alternative hypothesis in the Alternative Hypothesis: drop-down menu.
- Click the OK button to perform the computation. The results will be displayed in the log window.