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.