POWER OF A TEST Power and Type 2 Error Power and Type 2 Error Type 1 error is rejecting H0 when you shouldn't have, and the probability of doing so is α (significance level) Power and Type 2 Error Type 1 error is rejecting H0 when you shouldn't have, and the probability of doing so is α (significance level). Power and Type 2 Error ▶ Type 1 error is rejecting H0 when you shouldn't have, and the probability of doing so is α (significance level) ▶ Type 2 error is failing to reject H0 when you should have, and the probability of doing so is β (a little more complicated to calculate) Power and Type 2 Error ▶ Type 1 error is rejecting H0 when you shouldn't have, and the probability is α (significance level). ▶ Type 2 error is failing to reject H0 when you should have, and the probability is β. Power of a test is 1 – β, and is the probability of correctly rejecting H0 Keep α and β low, but there are inherent trade-offs. Example: Given: Explain its meaning. What is the power of the test? Explain. Example: Given: Explain its meaning. This is the probability of failing to reject the null hypothesis when it is false. What is the power of the test? Explain. The power of the test is The probability of correctly rejecting the false null hypothesis is .85. The probability of Type I error: The probability of Type II error: The power of the test (probability of correctly rejecting null): To increase the power of a test ▶ Increase sample size ▶ Increase alpha (but,Type 1 error more likely) ▶ Decrease standard deviation Putting it all together True value Hypothesized 132 The End
