Analysis of Three-Way ANOVA Data Given to Neuman, Alfred E.

The GLM Procedure

Class Level Information /
Class / Levels / Values /
Attractiveness / 2 / Attractive Unattractive
Crime / 2 / Burglary Swindle
Culture / 2 / American Chinese
Number of Observations Read / 320
Number of Observations Used / 320

The GLM Procedure

Dependent Variable: SENTENCE

Source / DF / Sum of Squares / Mean Square / F Value / PrF /
Model / 7 / 234.250000 / 33.464286 / 8.18 / <.0001
Error / 312 / 1276.950000 / 4.092788
Corrected Total / 319 / 1511.200000
Source / DF / Type I SS / Mean Square / F Value / PrF / Total Variation Accounted For /
Semipartial Eta-Square / Semipartial Omega-Square / Conservative
90% Confidence Limits /
Attractiveness / 1 / 51.20000000 / 51.20000000 / 12.51 / 0.0005 / 0.0339 / 0.0311 / 0.0087 / 0.0724
Crime / 1 / 36.45000000 / 36.45000000 / 8.91 / 0.0031 / 0.0241 / 0.0214 / 0.0041 / 0.0584
Attractiveness*Crime / 1 / 18.05000000 / 18.05000000 / 4.41 / 0.0365 / 0.0119 / 0.0092 / 0.0000 / 0.0391
Culture / 1 / 17.11250000 / 17.11250000 / 4.18 / 0.0417 / 0.0113 / 0.0086 / 0.0000 / 0.0380
Attractivene*Culture / 1 / 7.81250000 / 7.81250000 / 1.91 / 0.1681 / 0.0052 / 0.0025 / 0.0000 / 0.0262
Crime*Culture / 1 / 40.61250000 / 40.61250000 / 9.92 / 0.0018 / 0.0269 / 0.0241 / 0.0053 / 0.0625
Attrac*Crime*Culture / 1 / 63.01250000 / 63.01250000 / 15.40 / 0.0001 / 0.0417 / 0.0389 / 0.0130 / 0.0829

Do not forget to get the marginal means. You will need to report them when interpreting any significant main effect.

The GLM Procedure

Culture=American

Class Level Information /
Class / Levels / Values /
Attractiveness / 2 / Attractive Unattractive
Crime / 2 / Burglary Swindle
Number of Observations Read / 160
Number of Observations Used / 160

Dependent Variable: SENTENCE

Culture=American

Source / DF / Sum of Squares / Mean Square / F Value / PrF /
Model / 3 / 160.7687500 / 53.5895833 / 13.85 / <.0001
Error / 156 / 603.5750000 / 3.8690705
Corrected Total / 159 / 764.3437500
Source / DF / Type I SS / Mean Square / F Value / PrF / Total Variation Accounted For /
Semipartial Eta-Square / Semipartial Omega-Square / Conservative
90% Confidence Limits /
Attractiveness / 1 / 9.50625000 / 9.50625000 / 2.46 / 0.1190 / 0.0124 / 0.0073 / 0.0000 / 0.0552
Crime / 1 / 77.00625000 / 77.00625000 / 19.90 / <.0001 / 0.1007 / 0.0952 / 0.0379 / 0.1782
Attractiveness*Crime / 1 / 74.25625000 / 74.25625000 / 19.19 / <.0001 / 0.0972 / 0.0916 / 0.0355 / 0.1740

The GLM Procedure

Culture=Chinese

Class Level Information /
Class / Levels / Values /
Attractiveness / 2 / Attractive Unattractive
Crime / 2 / Burglary Swindle
Number of Observations Read / 160
Number of Observations Used / 160

Dependent Variable: SENTENCE

Culture=Chinese

Source / DF / Sum of Squares / Mean Square / F Value / PrF /
Model / 3 / 56.3687500 / 18.7895833 / 4.35 / 0.0056
Error / 156 / 673.3750000 / 4.3165064
Corrected Total / 159 / 729.7437500
Source / DF / Type I SS / Mean Square / F Value / PrF / Total Variation Accounted For /
Semipartial Eta-Square / Semipartial Omega-Square / Conservative
90% Confidence Limits /
Attractiveness / 1 / 49.50625000 / 49.50625000 / 11.47 / 0.0009 / 0.0678 / 0.0616 / 0.0180 / 0.1380
Crime / 1 / 0.05625000 / 0.05625000 / 0.01 / 0.9093 / 0.0001 / -0.0058 / 0.0000 / 0.0070
Attractiveness*Crime / 1 / 6.80625000 / 6.80625000 / 1.58 / 0.2111 / 0.0093 / 0.0034 / 0.0000 / 0.0488

Notice that the Attractiveness x Crime interaction is not significant for the Chinese participants. Accordingly, it would be useful to report and describe the significant effect of attractiveness among the Chinese.

Now for the Simple, Simple Main Effects

The GLM Procedure

Culture=American Crime=Burglary

Class Level Information /
Class / Levels / Values /
Attractiveness / 2 / Attractive Unattractive
Number of Observations Read / 80
Number of Observations Used / 80

Dependent Variable: SENTENCE

Culture=American Crime=Burglary

Source / DF / Sum of Squares / Mean Square / F Value / PrF /
Model / 1 / 68.4500000 / 68.4500000 / 15.36 / 0.0002
Error / 78 / 347.5000000 / 4.4551282
Corrected Total / 79 / 415.9500000
Proportion of Variation Accounted for /
Eta-Square / 0.16
Omega-Square / 0.15
90% Confidence Limits / (0.06,0.28)

When reporting and describing these simple, simple, main effects, do report the relevant cell means. For this effect, the mean sentencing recommendation from American mock jurors was significantly higher for the unattractive burglar than for the attractive burglar.

The GLM Procedure

Culture=American Crime=Swindle

Class Level Information /
Class / Levels / Values /
Attractiveness / 2 / Attractive Unattractive
Number of Observations Read / 80
Number of Observations Used / 80

Dependent Variable: SENTENCE

Culture=American Crime=Swindle

Source / DF / Sum of Squares / Mean Square / F Value / PrF /
Model / 1 / 15.3125000 / 15.3125000 / 4.66 / 0.0339
Error / 78 / 256.0750000 / 3.2830128
Corrected Total / 79 / 271.3875000
Proportion of Variation Accounted for /
Eta-Square / 0.06
Omega-Square / 0.04
90% Confidence Limits / (0.00,0.15)

The GLM Procedure

Culture=Chinese Crime=Burglary

Class Level Information /
Class / Levels / Values /
Attractiveness / 2 / Attractive Unattractive
Number of Observations Read / 80
Number of Observations Used / 80

Since the Attractiveness x Crime interaction was not significant among the Chinese participants, one would not normally look at the simple, simple main effects that follow, but, for pedagogical purposes, you report them in this assignment.

Dependent Variable: SENTENCE

Culture=Chinese Crime=Burglary

Source / DF / Sum of Squares / Mean Square / F Value / PrF /
Model / 1 / 9.8000000 / 9.8000000 / 1.94 / 0.1681
Error / 78 / 395.0000000 / 5.0641026
Corrected Total / 79 / 404.8000000
Proportion of Variation Accounted for /
Eta-Square / 0.02
Omega-Square / 0.01
90% Confidence Limits / (0.00,0.10)

Culture=Chinese Crime=Swindle

Class Level Information /
Class / Levels / Values /
Attractiveness / 2 / Attractive Unattractive
Number of Observations Read / 80
Number of Observations Used / 80

Dependent Variable: SENTENCE

Culture=Chinese Crime=Swindle

Source / DF / Sum of Squares / Mean Square / F Value / PrF /
Model / 1 / 46.5125000 / 46.5125000 / 13.03 / 0.0005
Error / 78 / 278.3750000 / 3.5689103
Corrected Total / 79 / 324.8875000
Proportion of Variation Accounted for /
Eta-Square / 0.14
Omega-Square / 0.13
90% Confidence Limits / (0.04,0.26)