C.4 Sample size estimation

The following formulas compute the approximate minimum (i.e., conservative) sample size needed to produce a 95% CI with a specified margin of error (i.e., the 'give-or-take' amount).

  • To estimate the sample size needed for estimating a proportion (Sect. 32.3), use:
    n=1(Margin of error)2.

  • To estimate the sample size needed for estimating a mean (Sect. 32.4) use:
    n=(2×sMargin of error)2 for some estimate s of the standard deviation of the data.

  • To estimate the sample size needed for estimating a mean difference (Sect. 32.5) use:
    n=(2×sdMargin of error)2 for some estimate sd of the standard deviation of the differences.

  • To estimate the sample size needed for estimating the difference between two means (Sect. 32.6) use:
    n=2×(2×sMargin of error)2 for each group being compared, where s is an estimate of the common standard deviation in the population for both groups. This formula assumes:

    • the sample size for each group will be the same; and
    • the standard deviation in each group is the same.
  • To estimate the sample size needed for estimating the difference between two proportions (Sect. 32.7) use:
    n=2(Margin of error)2 for each group being compared. This formula assumes the sample size in each group will be the same.

Notes:

  • In sample size calculations, round up the sample size found from the above formulas.