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Sample size calculation: McNemar test

Command:Sample size
Next selectMcNemar test


Calculates the required sample size for the comparison of two related proportions as analysed with the McNemar test. 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 (%) of total expected to shift from Positive to Negative: hypothesized proportion of cases that will shift from positive to negative result or outcome.
  • Proportion (%) of total expected to shift from Negative to Positive: hypothesized proportion of cases that will shift in the other direction, from negative to positive result or outcome.


In a cross-over trial you expect that 20% of the total number of cases will shift from a positive to a negative response, and that 10% will shift from negative to positive. In the dialog box you enter 20 and 10 for the percentages.

For α-level you select 0.05 and for β-level you select 0.20 (power is 80%).

Sample size calculation for McNemar test - comparison of paired proportions.


After you click Calculate the program displays the required total number of cases in the study. For the example the minimum required total sample size is 234.

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

Book cover

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

Buy from Amazon

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.