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Sample size: Confidence Interval for a mean difference between paired samples

Command:Sample size
Next selectConfidence Interval estimation & Precision
Next selectMean difference between paired samples


Calculates the required minimum sample size for the estimation of a confidence interval with a required width for an average difference between paired observations (Machin et al., 2009).

Note that the calculation does not include a null hypothesis value or a factor for power (1−β). Therefore the estimated sample size does not give a certainty that a particular value will fall inside or outside the confidence interval. The number of cases is only the number required to attain a specified confidence interval width.

Required input

  • Confidence level (%): select the confidence level: 90, 95 or 99%. A 95% confidence level (the value for a 95% Confidence Interval) is the most common selection. You can enter a different confidence level if required.
  • Standard deviation of differences: the expected standard deviation of the differences between the paired observations (known for example from a Paired samples t-test in previous studies, or from the literature).
  • Confidence interval width (2-sided): this is the required total width of the confidence interval. For example when a mean difference is 35 with 95% Confidence Interval 30 to 40, then the confidence interval width is 10.


Sample size for the confidence interval of a mean difference between paired samples


  • 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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