STAT 302 - 502 - Week 11 - 11/4 P(type I error) = α P(type II error) = β -as α decreases, β increases -as β decreases, α increases -α and β are inversely related P(reject H0|H0 is true) = P(Type I error) = α P(fail to reject H0|H0 is false) = P(Type II error) = β power of test: -probability of getting a sample that will result in you rejecting H0 at a given significance level α -probability of a correct decision -the higher the power, the better P(reject H0|H0 is false) = 1 - β -as α decreases, β increases and Power decreases -P(type I error) decreases -P(type II error) increases -power to make correct decision decreases -to reduce β, you want to shift the distribution over so that |p0 - p| gets larger -increase sample size n -variability decreases -spread becomes narrower -overlapped parts of two sampling models are reduced -α and β are reduced -power of test is increased ● If α increases, power _____increases_____. ● If increases, power _______decreases____. ● If n increases, power ______increases_____. ● If the effect size increases, power ______increases_______. -if p > α and your p-value was super small, then these results are very significant -the smaller our significance level is, the stronger the evidence must be to reject the null hypothesis -if your sample mean is close to the mean in this distribution, then it wasn’t that extreme of a value and we fail to reject H0 -if your sample mean is far from the mean, then we reject H0 bc it's very rare for the value to
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