Izabel conducted an experiment to determine if the location of a 10-minute walk [on a treadmill in the lab (considered control group), in a forest, in a city center] and the presence of others (alone, with a partner, with a group of three) had an effect on the amount of vitality [on a 1(no vitality at all) to 10(bursting with energy and joie de vie) scale] that a person reported at the end of the walk. She recruited 20 participants and had each participant go through all of the experimental treatment conditions. Then, Izabel conducted a 3x3 repeated measures factorial ANOVA on her data. Below are the results of her analysis.

1. Should we report the main effects? Why or why not?

2. Which simple effect(s) is/are non-significant?

3. What would a a full APA report on the results of Izabel's analysis look like?

Tests of Within-Subjects Effects Measure: Vitality Type Ill Sum Partial Eta Source of Squares di Mean Square Sig Squared Location Sphericity Assumed 140.400 2 70.200 78.871 .000 806 Greenhouse-Geisser 140.400 1.466 95.743 78.871 000 806 Huynh-Feldt 140.400 1.559 90.079 78.871 000 806 Lower-bound 140.400 1.000 140.400 78.871 000 806 Error(Location) Sphericity Assumed 33.822 38 890 Greenhouse-Geisser 33.822 27.862 1.214 Huynh-Feldt 33.822 29.614 1.142 Lower-bound 33.822 19.000 1.780 Group Sphericity Assumed 18.300 9.150 8.566 .001 311 Greenhouse-Geisser 18.300 1.649 11.097 8.566 002 311 Huynh-Feldt 18.300 1.786 10.249 3.566 001 .311 Lower-bound 18.300 1.000 18.300 8.566 .009 .311 Error(Group) Sphericity Assumed 40.589 38 1.068 Greenhouse-Geisser 40.589 31.332 1.295 Huynh-Feldt 40.589 33.926 1.196 Lower-bound 40.589 19.000 2.136 Location * Group Sphericity Assumed 396.200 99.050 82.804 000 813 Greenhouse-Geisser 396.200 3.092 128.117 82.804 .000 813 Huynh-Feldt 396.200 3.762 105.306 82.804 000 813 Lower-bound 396.200 1.000 396.200 82.804 .000 .813 Error(Location*Group) Sphericity Assumed 90.911 76 1.196 Greenhouse-Geisser 90.911 58.757 1.547 Huynh-Feldt 90.911 71.485 1.272 Lower-bound 90.911 19.000 4.785 Simple Effects of Group at Each Level of Location: Multivariate Tests Partial Eta Location Value F Hypothesis df Error df Sig. Squared Pillai's trace 057 .541 2.000 18.000 591 057 Wilks' lambda .943 541 a 2.000 18.000 591 .057 Hotelling's trace .060 .541 2.000 18.000 591 057 Roy's largest root .060 541 2.000 18.000 591 057 2 Pillai's trace 868 59.319a 2.000 18.000 000 868 Wilks' lambda 132 59.319 2.000 18.000 000 .868 Hotelling's trace 5.591 59.319a 2.000 18.000 .000 868 Roy's largest root 6.591 59.319a 2.000 18.000 000 868 3 Pillai's trace 938 135.407 2.000 18.000 000 938 Wilks' lambda 062 135.407 2.000 18.000 000 938 Hotelling's trace 15.045 135.407 2.000 18.000 000 938 Roy's largest root 15.045 135.407 2.000 8.000 000 938 Each F tests the multivariate simple effects of Group within each level combination of the other effects shown. These tests are based on the linearly independent pairwise comparisons among the estimated marginal means.a. Exact statistic *Location 1 = Control, Location 2 = Forest, Location 3 = City Pairwise Comparisons Measure: Vitality 95% Confidence Interval for Mean Difference Difference (1- Location (1) Group (J) Group J) Std. Error Sig b Lower Bound Upper Bound 1 2 .250 354 1.000 1.181 681 3 100 452 1.000 -1.088 1.288 2 250 354 1.000 -.681 1.181 w - 350 372 1.000 ..626 1.326 3 -.100 452 1.000 -1.288 1.088 N - -.350 372 1.000 -1.326 626 2 1e IN 2.250 .280 .000 1.515 2.985 3.150 .327 .000 2.292 4.008 2 W - w -2.250 280 000 2.985 -1.515 900 369 074 .069 1.869 3 -3.150 327 .000 4.008 -2.292 -.900 369 074 -1.869 069 3 1e -3.950 .235 000 -4.566 -3.334 W N -5.350 372 000 -6.326 4.374 2 3.950 235 000 3.334 4.566 - W - -1.400 234 .000 -2.014 -.786 3 5.350 372 000 4.374 6.326 2 1.400 234 000 786 2.014 Based on estimated marginal means *. The mean difference is significant at the .05 level. b. Adjustment for multiple comparisons: Bonferroni c. Location 1 = Control, Location 2 = Forest, Location 3 = City e. Group 1 = Alone, Group 2 = Partners, Group 3 = GroupSimple Effect of Location for Each Isolated Level of Group: Multivariate Tests Partial Eta Group Value F Hypothesis of Error of Sig. Squared 1 Pillai's trace 960 215.494 2.000 18.000 000 960 Wilks' lambda 040 215.494 2.000 18.000 000 960 Hotelling's trace 23.944 215.494 2.000 18.000 000 960 Roy's largest root 23.944 215.494 2.000 18.000 000 960 2 Pillai's trace 495 8.813 2.000 18.000 .002 495 Wilks' lambda 505 8.813 2.000 18.000 002 495 Hotelling's trace 979 8.8132 2.000 18.000 .002 495 Roy's largest root 979 8.813 2.000 18.000 .002 495 3 Pillai's trace .770 30.143 2.000 18.000 000 770 Wilks' lambda 230 30.143a 2.000 18.000 000 770 Hotelling's trace 3.349 30.143 2.000 18.000 000 770 Roy's largest root 3.349 30.143a 2.000 18.000 000 770 Each F tests the multivariate simple effects of Location within each level combination of the other effects shown. These tests are based on the linearly independent pairwise comparisons among the estimated marginal means. a. Exact statistic *Group 1 = Alone, Group 2 = Partner, Group 3 = GroupPairwise Comparisons Measure: Vitality 95% Confidence Interval for Mean Difference" Difference (1- Group (1) Location (J) Location J) Std. Error Sig b Lower Bound Upper Bound 1 0 1 d 2 -3.950 366 000 4.911 2.989 3 2.450 373 000 1.470 3.430 2 3.950 .366 000 2.989 4.911 W 6.400 303 000 5.606 7.194 3 -2.450 373 000 -3.430 -1.470 2 -6.400 .303 .000 -7.194 5.606 1 d -1.450 344 001 -2.353 .547 -1.250 .347 006 -2.161 -.339 N 1.450 .344 .001 .547 2.353 .200 .268 1.000 -.502 902 UN - W - w 3 1.250 .347 006 .339 2.161 -.200 .268 1.000 -.902 502 3 1 d .900 261 .008 1.584 .216 w -3.000 .384 .000 -4.008 1.992 2 900 261 008 .216 1.584 W - -2.100 .307 000 -2.906 -1.294 3 1 3.000 384 000 1.992 4.008 2.100 .307 000 1.294 2.906 Based on estimated marginal means *. The mean difference is significant at the .05 level. b. Adjustment for multiple comparisons: Bonferroni c. Group 1 = Alone, Group 2 = Partners, Group 3 = Group d. Location 1 = Control, Location 2 = Forest, Location 3 = CityWithin-Subjects Factors Measure: Vitality Dependent Location Group Variable 1 Control_Alon e 2 Control_Partn er 3 Control_Grou p 2 1 Forest_Alone 2 Forest_Partn er 3 Forest_Group 3 City_Alone W N - City_Partner City_Group Descriptive Statistics Mean Std. Deviation N Control, Alone 4.9500 1.27630 20 Control, Partners 5.2000 1.15166 20 Control, Group 4.8500 1.22582 20 Forest, Alone 8.9000 1.02084 20 Forest, Partners 6.6500 1.08942 20 Forest, Group 5.7500 91047 20 City, Alone 2.5000 88852 20 City, Partners 6.4500 88704 20 City, Group 7.8500 98809 20 Mauchly's Test of Sphericity Measure: Vitality Epsilon Approx. Chi- Greenhouse- Within Subjects Effect Mauchly's W Square dt Sig Geisser Huynh-Feldt Lower-bound Location 636 8.142 2 017 733 779 500 Group .787 4.307 2 116 825 893 500 Location * Group 444 14.145 119 773 941 250 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a. Design: Intercept Within Subjects Design: Location + Group + Location * Group b. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table