Documentation

Test 1 Mean

Compare 2 Means

Compare k Means

Test 1 Proportion

Compare 2 Proportions

Compare Paired Proportions

Compare k Proportions

Test Time-To-Event Data

Test Odds Ratio

Test Relative Incidence in Self Controlled Case Series Studies

This calculator is useful for tests concerning whether a proportion, $p$, is equal to a reference value, $p_0$. The Null and Alternative hypotheses are

$H_1:p\neq p_0$

This calculator uses the following formulas to compute sample size and power, respectively:
$$n=p(1-p)\left(\frac{z_{1-\alpha/2}+z_{1-\beta}}{p-p_0}\right)^2$$

$$1-\beta=
\Phi\left(z-z_{1-\alpha/2}\right)+\Phi\left(-z-z_{1-\alpha/2}\right)
\quad ,\quad z=\frac{p-p_0}{\sqrt{\frac{p(1-p)}{n}}}$$
where

- $n$ is sample size
- $p_0$ is the comparison value
- $\Phi$ is the standard Normal distribution function
- $\Phi^{-1}$ is the standard Normal quantile function
- $\alpha$ is Type I error
- $\beta$ is Type II error, meaning $1-\beta$ is power

R code to implement these functions:

p=0.5 p0=0.3 alpha=0.05 beta=0.20 (n=p*(1-p)*((qnorm(1-alpha/2)+qnorm(1-beta))/(p-p0))^2) ceiling(n) # 50 z=(p-p0)/sqrt(p*(1-p)/n) (Power=pnorm(z-qnorm(1-alpha/2))+pnorm(-z-qnorm(1-alpha/2)))

Chow S, Shao J, Wang H. 2008.Sample Size Calculations in Clinical Research. 2nd Ed. Chapman & Hall/CRC Biostatistics Series.page 85.

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