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Test 1 Mean

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Test 1 Proportion

Compare 2 Proportions

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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 the means of two groups are different.
Suppose the two groups are 'A' and 'B', and we collect a sample from both groups -- i.e. we have two samples.
We perform a two-sample test to determine whether the mean in group A, $\mu_A$, is different from the mean in group B, $\mu_B$.
The hypotheses are

$H_1:\mu_A-\mu_B\neq0$

where the ratio between the sample sizes of the two groups is

This calculator uses the following formulas to compute sample size and power, respectively:
$$
n_A=\kappa n_B \;\text{ and }\;
n_B=\left(1+\frac{1}{\kappa}\right)
\left(\sigma\frac{z_{1-\alpha/2}+z_{1-\beta}}{\mu_A-\mu_B}\right)^2$$

$$1-\beta=
\Phi\left(z-z_{1-\alpha/2}\right)+\Phi\left(-z-z_{1-\alpha/2}\right)
\quad ,\quad z=\frac{\mu_A-\mu_B}{\sigma\sqrt{\frac{1}{n_A}+\frac{1}{n_B}}}$$
where

- $\kappa=n_A/n_B$ is the matching ratio
- $\sigma$ is standard deviation
- $\Phi$ 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:

muA=5 muB=10 kappa=1 sd=10 alpha=0.05 beta=0.20 (nB=(1+1/kappa)*(sd*(qnorm(1-alpha/2)+qnorm(1-beta))/(muA-muB))^2) ceiling(nB) # 63 z=(muA-muB)/(sd*sqrt((1+1/kappa)/nB)) (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 58.

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