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Sample size calculation: Paired samples t-test


Calculates the required sample size for the paired samples t-test. The sample size takes into account the required significance level and power of the test (see Sample size calculation: Introduction).

Required input

  • Type I error - alpha: the probability of making a Type I error (α-level, two-sided), i.e. the probability of rejecting the null hypothesis when in fact it is true.
  • Type II error - beta: the probability of making a Type II error (β-level), i.e. the probability of accepting the null hypothesis when in fact it is false.
  • Mean difference: the hypothesized mean difference (considered to be biologically significantly different from the null hypothesis value 0).
  • Standard deviation: hypothesized standard deviation of differences (known for example from a Paired samples t-test from previous studies, or from the literature).


You consider an average difference between two paired observations before and after a study, of at least 8 to be meaningful. From a previous study you expect the standard deviation of the differences to be 12.

For α-level you select 0.05 and for β-level you select 0.20 (power is 80%). For mean difference, you enter 8 and for standard deviation enter 12.

Sample size calculation for paired samples t-test.


After you click Calculate the program displays the required number of data pairs (20 in the example).

A table shows the required sample size for different Type I and Type II Error levels.


  • Machin D, Campbell MJ, Tan SB, Tan SH (2009) Sample size tables for clinical studies. 3rd ed. Chichester: Wiley-Blackwell.

See also