# Type I and Type II Errors ![[typeItypeII_statpower.png]] Suppose the following: $H_0$: Defendent is innocent $H_1$: Defendent is guilty Type I and Type II errors are summarised as follows: ![[type1type2summary.png]] **Type I Error: False Positive** - You wrongly say the person has cancer **Type II Error: False Negative** - You wrongly say the person is healthy ![[type1type2_distr.png]] [[Power Analysis|Power]] is the ability of the test to correctly reject a false null hypothesis. $n = \frac{2\sigma^2(z_{\alpha /2} + z_\beta)^2}{\delta^2}$ Where: - $\alpha$ is the significance level or Type I error (false positive) - $\sigma^2$ is the *variance* - $\beta$ is Type II error (false negative) which is 1 - *power* - $\delta$ is the difference between the two groups - If the standard deviation increases, the power decreases - If $n$ increases, the power increases - If $\delta$ increases, the power increases (? -- not sure about this one 2023-01-21) ## Source - [HYPOTHESIS TESTING BASICS: Type 1/Type 2 errors | Statistical power](https://www.youtube.com/watch?v=CJvmp2gx7DQ) - [[Power Analysis|Statistical Power]] - [[AB Testing|AB Testing]]