Sample size: Single mean


Calculates the required sample size for the comparison of a sample mean with a given value. The sample size takes into account the required significance level and power of the test.

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: the hypothesized mean (considered to be biologically significantly different from the null hypothesis value).
  • Standard deviation: hypothesized standard deviation (known from previous studies or from the literature).
  • Null hypothesis value: the null hypothesis value.


If the null hypothesis value is 50, and you consider a value of at least 60 to be significantly different, then you will enter these numbers for Null hypothesis value and Mean. If from a previous study, you expect the standard deviation of the sample to be 14, you enter 14 for the Standard deviation. For α-level you select 0.05 and for β-level you select 0.20 (power is 80%).


After you click the OK button, the program will display the required sample size.

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.


Go to Sample size: Single mean.