Sample size required to test proportion

Use this calculator to find the minimum sample size required to test hypothesis about proportion $p$.

Sample size required to test proportion

The $ES$ is defined as $$ ES=\frac{|p_1-p_0|}{\sqrt{p_0*(1-p_0)}} $$

where

  • $p_0$ is the proportion under null hypothesis,
  • $p_1$ is the proportion under alternative hypothesis.

The formula for determining the sample size required to ensure that the test has a specified power is

$$ n =\bigg(\frac{Z_{1-\alpha/2}+Z_{1-\beta}}{ES}\bigg)^2 $$

where

  • $\alpha$ is the selected level of significance,
  • $1-\beta$ is the selected power and
  • $ES$ is the effect size.

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