Two-sample paired t test

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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.


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.


  • Ways to detect before performing the paired t test whether your data violate any assumptions.
  • Ways to examine paired t test results to detect assumption violations.
  • Possible alternatives if 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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