Type I and Type II Errors, Power of a Test

Hypothesis tests can make two kinds of errors. Understanding these errors and the power of a test is essential for designing studies and interpreting results.

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Types of Errors

	$H_0$H0​ is true	$H_0$H0​ is false
Do not reject $H_0$H0​	Correct decision	Type II error ($\beta$β)
Reject $H_0$H0​	Type I error ($\alpha$α)	Correct decision (power)

Type I Error

A Type I error occurs when $H_0$H0​ is rejected even though it is true (a "false positive").

$P(\text{Type I error}) = \alpha = \text{significance level}$P(Type I error)=α=significance level

Choosing $\alpha = 0.05$α=0.05 means we accept a 5% chance of rejecting a true $H_0$H0​.

Type II Error

A Type II error occurs when $H_0$H0​ is not rejected even though it is false (a "false negative").

$P(\text{Type II error}) = \beta$P(Type II error)=β

$\beta$β depends on the true value of the parameter, the sample size, and the significance level.