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:
\[ n = \frac{1}{(\text{Margin of error})^2}. \]To estimate the sample size needed for estimating a mean (Sect. 32.4) use:
\[ n = \left( \frac{2\times s}{\text{Margin of error}}\right)^2 \] 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:
\[ n = \left( \frac{2 \times s_d}{\text{Margin of error}}\right)^2 \] for some estimate \(s_d\) of the standard deviation of the differences.To estimate the sample size needed for estimating the difference between two means (Sect. 32.6) use:
\[ n = 2\times \left( \frac{2 \times s}{\text{Margin of error}}\right)^2 \] 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:
\[ n = \frac{2}{(\text{Margin of error})^2} \] 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.