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Sample size calculation: Paired samples t-test

Command: Sample size
Next selectPaired 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. Buy from Amazon

See also

Recommended book

Sample Size Tables for Clinical Studies
David Machin, Michael J. Campbell, Say-Beng Tan, Sze-Huey Tan

Buy from Amazon US - CA - UK - DE - FR - ES - IT

Sample Sizes for Clinical, Laboratory and Epidemiology Studies includes the sample size software (SSS) and formulae and numerical tables needed to design valid clinical studies. The text covers clinical as well as laboratory and epidemiology studies and contains the information needed to ensure a study will form a valid contribution to medical research.

The authors, noted experts in the field, explain step by step and explore the wide range of considerations necessary to assist investigational teams when deriving an appropriate sample size for their when planned study. The book contains sets of sample size tables with companion explanations and clear worked out examples based on real data. In addition, the text offers bibliography and references sections that are designed to be helpful with guidance on the principles discussed.

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