Psych 311 1nd Edition Lecture 22 Outline of Last Lecture I F Test II Logic of ANOVA III Reference Distribution for ANOVA Outline of Current Lecture I II Review of ANOVA One Way ANOVA Example Current Lecture I Review of ANOVA F between group variance within group variance F systematic variance unsystematic variance systematic variance IV unsystematic variance SE The larger the F the more likely we are to reject Ho The closer F is to 1 00 the more likely we are to FTR Ho II One Way ANOVA Example We are interested in knowing whether job satisfaction is influenced by work place setting Samples 20 people who work in cubicles 20 people who work in offices and 20 people who work at home DV ratings in job satisfaction on a 1 5 scale in which higher scores represent greater satisfaction Data Mc cubical 3 00 SSc 19 00 Tc 60 Mo office 3 20 SSo 17 10 To 64 Mh home 4 00 SSh 22 80 Th 80 T X sum of scores X 2 sum of all data 763 7 N 60 G T grand total 204 K of groups 3 These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Two possible explanations for the differences seen Ho Due to SE and not workplace setting H1 Due to workplace setting and not SE Step 1 State hypothesis and set Ho c o h H1 c o h 0 05 Note We don t specify a one tail or two tailed test when we do ANOVA essentially there is only one tail in an ANOVA test Step 2 Find our critical region Find df recall we are dealing with two sources of variance between and within each source of variance has its own df dfwi within variance df1 df2 df3 dfwi 19 19 19 dfbt between variance k 1 dfbt 3 1 dfwi 57 dfbt 2 Then consult the F distribution table to find critical region CR 3 17 Step 3 Collect data and compute F test statistic SSbt T 2 n G 2 N SSbt 60 2 20 64 2 20 80 2 20 204 2 60 SSbt 180 204 8 320 693 6 SSwi SS inside each condition SSbt 11 2 SSwi 19 17 1 22 8 SSwi 58 9 SStotal SSbt SSwi or x 2 G 2 N SStotal 11 2 58 9 dftotal dfbt dwi or N 1 SStotal 70 1 dftotal 57 2 dftotal 59 MS measure of variability used to compute ANOVA mean squared MSbt SSbt dfbt MSbt 11 2 2 MSbt 5 6 MSwi SSwi dfwi MSwi 58 9 57MSwi 1 03 F ratio MSbt MSwi F 5 6 1 03 Step 4 Make a decision F 5 44 Since our value for F 5 44 which is within our critical region we reject our Ho in favor of H1 and state that workplace setting does influence job satisfaction Step 5 Calculate effecet size Eta 2 2 2 SSbt SStotal 2 11 2 70 1 2 0 16 large effect size Effect Size Chart for F tests Small 0 01 2 0 06 Moderate 0 06 2 0 14 Large 2 0 14 Step 6 Post hoc test F test tells you if there is a significant difference but not where The post hoc test allows you to compare pairs of means to determine which pairs are significantly different Tukey s HSD honestly significant difference provides us with a single value that determines the minimum difference between means that is required if there is to be a significant difference between the means 3 compairisons Mc Mo Mc Mh Mo Mh If the difference between the means exceeds our value for HSD then the groups are significantly different HSD q MSwi n n of scores in each group groups must have same sample size Use dfwi 57 the number of groups k 3 and to find q in the table HSD 3 44 1 03 20 HSD 3 44 0 23 HSD 0 78 Mc Mo l3 0 3 2l 0 2 0 2 0 78 not significant difference Mo Mh l3 2 4 0l 0 8 0 8 0 78 there is a significant difference Mc Mh l3 0 4 0l 1 0 1 0 0 78 there is a significant difference