16.2 General Principles of design (proportions)
Sample size to achieve a specified standard error:
- Standard error: \(\sqrt{p(1-p)/n} \approx 0.5/\sqrt{n}\)
- So \(n \approx (0.5/\text{s.e.})^2\)
Sample size to achieve specified probability (power) of statistical significance:
- For 80% probabilty of 95% statistical significance, the true effect must be 2.8 standard errors from zero
- \(n = p(1-p)(2.8/(p-p_0))^2\)
For comparisons of proportions, you need approximately 4 times the samples.