Question

5. A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below. Diet 30% fat 30% - 60% fat >60% fat Exercise <60 minutes 60 minutes or more a. Perform a Two-way analysis of variance (ANOVA) and report the results using correct APA style; report whether significance was found for Factor A, Factor B, and/or an interaction between Factors A and B was found. b. If the test statistic is significant, run a post hoc test to determine between what groups significance was found. c. Report an effect size for all significant results.

Answer 1

EXCEL (Data Analysis) output: ANOVA Source of Variation Exercise Diet Interaction Within Total SS 90.13333 6.2 18.46667 16 130.8 df MSF 1 90.13333 23.1 2 9.233333 24 0.666667 29 -value Fcrit 135.2 2.39E-11 4.259677 4.65 0.019643 3.402826 13.85 0.0001 3.402826 Since F(=135.2) > Fort (= 4.2597), then Factor A is significant. Since F(= 4.65) > Ferit (= 3.4028), then Factor B is significant.

(= 3.4028). then interaction between Factor A and Factor B is Since F(=13.85) > F significant (b) Post hoc analysis P-values for pairwise t-tests for Factor 2 >60% fat <30% fat 4.1 30%-60% fat 4.8 3.7 >60% fat <30% fat 30%-60% fat 3.7 4.1 4.8 2842 .0060 0672 Tukey simultaneous comparison t-values (d.f. = 24) >60% fat <30% fat 4.1 30%-60% fat 4.8 3.7 >60% fat <30% fat 30%-60% fat 3.7 4.1 1 .10 3.01 4.8 1.92 critical values for experimentwise error rate: 0.05 0.01 2.50 3.21

Group"30%-60% fat and >60% fat" is significant. Effect Size = $S Excercis SS sro 90.1333 16 = 5.6333 Effect Size = SSDiet SS970 6.2 16 = 0.3875