# 17.3.3 Pair-Sample T-Test

## Introduction

The Paired-Sample t-Test is a parametric hypothesis test that enables you to test whether the means of paired (or related, matched) samples are equal or whether they differ by a given value. The term paired means that there are two measurements taken on the same subject or there is one measurement taken on a pair of subjects.

The test can be either one-tailed or two-tailed. The test statistic and p-value will be calculated so that you can decide whether or not to reject the null hypothesis. A small P-value, which less than a significance level $\sigma$, indicates that you can reject the null hypothesis.

To estimate the difference between two population means, the sample mean difference with confidence interval is also computed for each confidence level.

Power is the chance of correctly rejecting the null hypothesis. A power that is too low suggests that rejecting the null hypothesis is dangerous. However, power should not be too high. An excessively high power would lead to a rejection of the hypothesis even with trivial fluctuations of the samples.

## Handling Missing Values

If there are missing values in the data range, the whole pair will be excluded in the analysis

## Performing Pair-Sample t-test

To perform a pair-sample t-test:

1. Select Statistics: Hypothesis Testing: Pair-Sample t-Test. This opens the PairSampletTest dialog, in which you first specify the Input Data Form (Indexed or Raw), then specify the Input Data, the Test Mean, and the Alternate Hypothesis.
2. Upon clicking OK, an analysis report sheet is generated that shows the degrees of freedom, t statistic, the associated p-value, and the test conclusion. In addition, you can produce the confidence intervals for the difference of sample means, histogram and box chart, and the power analysis.
 Topics covered in this section: Tutorial