Sample size: Single proportion


Calculates the required sample size for the comparison of a proportion with a given proportion. 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.
  • Proportion (%): the hypothesized proportion (considered to be biologically significantly different from the null hypothesis value), expressed as a percentage.
  • Null hypothesis value (%): the null hypothesis value (a proportion, expressed as a percentage).


If the null hypothesis value is 50%, and you consider a proportion of at least 70% to be significantly different, then you enter the numbers 70 and 50 in the dialog box. 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 (47 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.


Go to Sample size: Single proportion.