Power Analysis

Definition

Power analysis can be used to calculate the minimum sample size required so that one can be reasonably likely to detect an effect of a given size.

Power values range from 0 to 1, and a common power value is 0.8

Example

for two groups A and B:

d = \frac{μ_{a} - μ_{b}}{S D_{a} b}

where d is the effect size, $μ$ is the mean of each group, and SD is the pooled estimated SD.
Then you can Google with the combination of effect size, power, and desired significance threshold.

Rule of thumb

n = \frac{2 σ^{2} (z_{α / 2} + z_{β})^{2}}{δ^{2}}

where

$σ^{2}$ : variance
$α$ : significance level, Type I error (false positive)
$β$ : Type II error (false negative)
$δ$ : difference between the two groups
Therefore, more samples are needed when
large variance in historical tests and data
high confidence level (smaller alpha and beta)
small difference between groups