October 29, 2009 #2: Setting criteria for rejection Directional test ? One tailed test ? ? rejection region (the whole rejection region is in one tail only) if we calculate x? and it loads in the rejection region, we can reject null. Zcv = 1.65 Nondirectional test ? just difference Two-tailed test Just difference Zcv = ± 1.96 The larger ? is, the larger the rejection region When you use the test statistic formula (), you are in essence calculating a z score (and when you are engages in hypothesis testing) comparing it to the zcv (zcv depends on how you?ve set alpha). This z score is give the name of test statistic. Hypothesis Testing State hypothesis Ho and Ha Set your rejection criteria (?) You actually perform test Calculate test statistic (zobs) Interpret your results Reject the Ho Fail to reject the Ho Reality Flipside of ? is power ? is the probability of making a type two error Power is the probability of rejecting Ho when indeed the Ho is false. Seeing an effect that?s truly there Power = 1- ? Several Factors affect Power (Power is the probability of rejecting Ho when indeed Ho is false ? i.e., the probability of seeing a true effect/ of picking up on the fact that your variable/treatment makes a difference) Effect size More overlap between the two true distributions = smaller effect size Harder to pick up on the fact that there are two distributions Thus, the power here is fairly low. Decision Ho true (no effect, treatment/ variable doesn?t matter Ho false (effect really exists, treatment works, variable makes a difference) Reject Ho Type I error (?) true Fail to reject Ho (you are saying Ho is true) true Type II error (?) Factor What its affect on power is controllable Effect size (just how much ?Ho and ?Ha deviate in terms of raw magnitude) The larger effect size is, the greater power is no