# [[EDUC 7215 ]]Assignment 5 Jethro Jones Also available online at drjethro.com/7215ass5 # Assignment Research Question: “Is pro-environmental behavior (PEB) different across levels of race and gender in the Missouri area?” ## Methods Methods for 2-Way ANOVA: I used Tasks and Utilities, then Tasks, then Linear Models, then N-Way ANOVA. I selected the PEB dataset from library. Under Roles, I selected PEB for the Dependent variable and gender and race for the Factors. Under the Model tab, I built a Full Factorial model with both factors. Under the Options tab, I selected Default and Selected Statistics. I checked the box for Perform multiple comparisons, for Main Effects, the Tukey method, and Significance level at 0.05. I checked only the Adjusted sum of squares (Type 3) box. For Plots, I selected only the Interaction plot, the LS Means plot and the Diagnostic plots to display as Individual plots. I set the Maximum Number of Plot Points to defaults since the sample was small. After I clicked the Run icon, I saved the Results in a new window and took screenshots. I used an AI Program to rename the screenshots based on what the AI saw they indicated. Two assumptions of ANOVA, normality and homogeneity of variances, through the appropriate visual assessments. I can see that these results are not normal from the more sensitive QQ plot, as seen below. Even though the bell curve looks normal, the QQ is more sensitive and so I can see that it is not normal. ![[2025-03-05 Fit Diagnostics for PEB.png]] Hypotheses with the two-way ANOVA at the Type 1 error rate of 0.05 or 5%. My Hypotheses are as follows: - H_o1: PEB is equal among combinations of race and gender. - H_a1: PEB is not equal among combinations of race and gender. - H_o2: PEB is equal across the two race groups. - H_a2: PEB is not equal across the two race groups. - H_o3: PEB is equal across the two gender groups. - H_a3: PEB is not equal across the two gender groups. Decision Rule: If the p-value < 0.05, then reject Ho. As seen from the table below, the F value is 4.22 and the p-value is 0.7953. Since p >0.05 we fail to reject the H₀ and conclude that there is no significant interaction between gender and race in predicting PEB. Since the interaction effect is not significant, we proceed with the test of the two main effects (race and gender separately). - H_o2: PEB is equal across the two race groups. - H_a2: PEB is not equal across the two race groups. a = Type 1 error = 0.05 Decision rule: If the p-value is <0.05 then reject H₀2. Conclusion: When looking at race, p=0.0181, which means p <0.05, so we reject H_o2 and conclude PEB is NOT equal across the two race groups. - H_o3: PEB is equal across the two gender groups. - H_a3: PEB is not equal across the two gender groups. a = Type 1 error = 0.05 Decision rule: If the p-value is <0.05 then reject H₀2. Conclusion: When looking at gender, p=0.0420, which means p<0.05, so we reject H_o3 and conclude PEB is NOT equal across the two gender groups. I also tested the hypothesis for Equality or Homogeneity of Variances with Levene's test to assess the equal variances assumption: - H_o1: PEB is equal among combinations of race and gender. - H_a1: PEB is not equal among combinations of race and gender. a = Type 1 error = 0.05 Decision Rule: If calculated p-value < 0.05, then reject Ho. Conclusion: Since p<.0060 < 0.05, I reject H₀ and conclude the variances for the PEB among race and gender are not equal. So, the equal variance assumption is also violated. This means that we should use the p-value for Welch's ANOVA (p<.0060). ![[2025-03-05 Dependent Variable PEB Analysis.jpg]] We Don't need to look at the Tukey test to see which specific groups differ, but I will anyway. We can see from the Least Square means test the largest difference is between white females and black males (LSMEAN Numbers 4 vs 1 below) ![[2025-03-05 Least Squares Means Analysis.jpg]] Next, we will look at the Least Square Means for effect ```gender*race``` and this chart (second chart above) also confirms that the only significant difference (p <0.05) is black males vs white females. Finally, we will look at the 95% confidence limits for LSMEANS, the third chart above. White females have the highest PEB scores (2.99, with a confidence interval of 2.89-3.08). Black males have the lowest PEB scores with 2.66 (confidence interval of 2.47-2.84). Looking at the chart below, the results seem even more astounding, with the lowest PEB score for white females higher than the mean of each other group (white males, black females and black males.) What the chart below also makes intersting is the idea that the females in both black and white cohorts have a smaller range than the males. I take that to mean that the variance is females is less than the variance in PEB in males. ![[2025-03-05 LS-Means Gender Race Chart.png]] This idea is supported also by the interaction plot for PEB as shown below. Females tend to have higher PEB scores than males. And whites tend to have higher PEB scores than blacks. Since the lines are parallel, it suggests there are not strong interaction effect between gender and race on PEB. If the lines crossed or had a large slope between them it would indicate a stronger interaction. ![[2025-03-05 Interaction Plot for PEB.png]] ## Fit statistics I need to report the fit statistics for the two-way ANOVA: ![[2025-03-05 R-Square Coeff Var Root MSE PEB Mean.jpg]] Race and gender explain .037484 or about 3.7% of the variability in PEB scores, which is quite low. the coefficient of variation is moderate (20.5%) and the Root MSE is low at .588, so the model is fairly accurate. The mean PEB among gender and race groups is 2.87. ## Conclusion There is not a significant interaction effect between race and gender on PEB (p=0.7953). The biggest difference is between black males and white females where p = 0.0110. Since the interaction effect is not significant, we do interpret the main effects separately, race and gender alone. White females exhibit the highest PEB and black males exhibit the lowest PEB. The ANOVA test did not show a significant interaction effect, because the lines are nearly parallel, it affirms that the interaction effect is small.