The two-sample paired t test is used to test the null hypothesis that the population mean of the paired differences of the two samples is 0.

### Assumptions:

- The paired differences are independent.
- The paired differences are all identically normally distributed (same mean and variance).

Note that it is *not* assumed that the two samples are independent of each other. In fact, they *should* be related to each other such that they create pairs of data points, such as the measurements on two matched people in a case/control study, or before- and after-treatment measurements on the same person.

The two-sample paired t test is equivalent to performing a one-sample t test on the paired differences.

### Guidance:

Ways to detectbefore performing the paired t test whether your data violate any assumptions.Ways to examinepaired t test results to detect assumption violations.Possible alternativesif your data or paired t test results indicate assumption violations.

To properly analyze and interpret results of the *two-sample paired t test*, you should be familiar with the following terms and concepts:

If you are not familiar with these terms and concepts, you are advised to consult with a statistician. Failure to understand and properly apply the* two-sample paired t test* may result in drawing erroneous conclusions from your data. Additionally, you may want to consult the following references:

- Brownlee, K. A. 1965.
Statistical Theory and Methodology in Science and Engineering.New York: John Wiley & Sons.- Daniel, Wayne W. 1995.
Biostatistics.6th ed. New York: John Wiley & Sons.- Miller, Rupert G. Jr. 1996.
Beyond ANOVA, Basics of Applied Statistics.2nd. ed. London: Chapman & Hall.- Rosner, Bernard. 1995.
Fundamentals of Biostatistics.4th ed. Belmont, California: Duxbury Press.- Sokal, Robert R. and Rohlf, F. James. 1995.
Biometry.3rd. ed. New York: W. H. Freeman and Co.- Zar, Jerrold H. 1996.
Biostatistical Analysis.3rd ed. Upper Saddle River, NJ: Prentice-Hall.

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