Introduction to Statistics in Psychology PSY 201 Professor Greg Francis Lecture 33 ANalysis Of VAriance Error is sneaky HYPOTHESIS TESTING MULTIPLE t TESTS we know how to test the difference of two means if we have K 5 population means we might want to compare each mean to all the others H 0 1 2 0 Ha 1 2 0 by using the t distribution and estimates of standard error what if you have more populations and want to know if they are all equal requires K K 1 c 10 2 different t tests suppose each test is with 0 05 What is the Type I error 2 3 MULTIPLE t TESTS DEMONSTRATION DEMONSTRATION we have a risk of making a type I error for each t test count off by fours and split into four groups now go get X k sk and nk from the other three groups since we have c 10 different t tests with 0 05 the Type I error rate becomes 1 1 c 0 40 bigger risk of error than you might expect would need to set much smaller to insure that Type I error rate is below 0 05 kind of messy to do these are four populations k 1 k 2 k 3 k 4 within each group do the following 1 Go through your backpacks and count the total number of books textbooks novels notebooks in the group nk 2 Across the entire group compute the average number of pages across the books X k and the standard deviation sk n k Xki a X k i 1 n b sk k 2 2 i Xki i Xki nk nk 1 Run 3 hypothesis tests to test if any of the means are different from the mean of your group s sample we ll assume homogeneity of variance 1 State the hypothesis H 0 k j Ha k j 0 05 2 Find the critical value df nk nj 2 tcv 4 5 6 DEMONSTRATION DEMONSTRATION 3 Compute test statistic Now let s see how often you reject H0 n 1 s2k nj 1 s2j s2 k nk nj 2 1 1 sX X j s2 k nk nj X k X j 0 t sX X j k 4 Interpret your results t tcv R H0 was rejected N H0 was not rejected 1 2 3 4 1 2 3 4 Not only is it a pain to make multiple comparisions of means but it tends to lead to more Type I error than indicates we could simply decrease to a smaller value so that the overall Type I error is how we want it but there is a better method any rejections are probably Type I errors people were randomly assigned to samples so there should be no difference across populations 7 8 CONCLUSIONS NEXT TIME testing multiple means ANOVA loss of control of Type I error two measures of variance Measure twice cut once 10 WHAT DO WE MAKE OF THIS 11 9
View Full Document
Unlocking...