Power Analysis

• What is Power? - StatQuest
• To get the effect size, which is the requested sample size of a experiment
• StatQuest

Formula

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

Sample size on non-normal data

• Rules of Thumb for Web Site Experimenters: $355 \times s^2$, where $s=\frac{E[(y_i-\mu)^3]}{sigma^2}$
• Neither the t-test nor the permutation test have much power to identify a difference in means between two such extraordinarily skewed distributions.

Readings

• Using Effect Size—or Why the P Value Is Not Enough
• Nonparametric Cohen’s d-consistent effect size