What is power analysis and how do you use it?

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Answer

$\mathrm{Power}\; = \;P(\mathrm{reject}\;\mathrm{H0}\; \mid \;\mathrm{H1}\;\mathrm{true})\; = \;1\; - \;{\beta}$
$Power analysis: given effect size, α, and power (typically 0.8), solve for required sample size.$
$Or: given n, α, effect size, solve for achieved power.$
$Uses: (1) plan A/B tests (how many users do we need?); (2) diagnose 'no significant effect' — was the study under-powered?$
$Free tools: G*Power, statsmodels.power.$
$Always do this before running an experiment.$

Check yourself — multiple choice

Not needed
Given effect size + α + target power (0.8), solve for n; also: n + effect + α → achieved power for post-hoc diagnostics
Same as p-value
Only for regression

Power analysis: n needed for target power (0.8) given effect size and α.

#hypothesis-testing#power

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