# [[EDUC 7215]] Assignment 4 Jethro Jones can also be viewed at drjethro.com/7215ass4 # Assignment Compare PEB and the four education groups in the Missouri area. Research Question: Is pro-environmental behavior (PEB) the same across levels of education in the Missouri area? ## Methods ANOVA: I used Tasks and Utilities, then tasks, then Linear Models, then One-Way ANOVA. I selected my dataset from VBN Theory-based survey. Under Roles, I selected PEB as the dependent variable and education as the categorical variable. Under the options tab, I selected the Levene test for Homogeneity of variance, and I checked the welch's variance-weighted ANOVA box. I selected Tukey for the comparisons method and I kept the significance level at 0.05. For Plot I selected only the box plot and diagnostic plot to display as individual plots. I kept the default 5,000 for the max number of plot points. After I clicked the Run icon, I saved individual images and screenshotted others. I used an AI tool to rename my screenshots based on it detected. Methods for Kruskal Wallis test: I used Tasks and Utilities, Tasks, Linear Models, Nonparametric One-Way ANOVA. I selected the VBN data from our assignment library. I included a filter to select only education levels 2,3,4 and 5 ( 2=HS grad or GED, 3=Associate degree or certificate/license, 4=Four-year degree, 5=Masters, doctoral or professional degree.) . Under Roles, I selected PEB for the Dependent variable and education for the Categorical variable. Under the Options tab, I selected Plots then checked the box to Suppress plots. Under Tests, I selected Asymptotic tests and checked the Wilcoxon scores box. Under Additional Test, I checked the Pairwise multiple comparison analysis box. After I clicked the Run icon, I saved individual images and screenshotted others. I used an AI tool to rename my screenshots based on it detected. ## Results Analysis with One-way ANOVA: Assumption of Normality. I used the Distribution of Residuals and QQ Plot to determine that this data is not normal. The graph does not follow the normal curve nor do the plots align to the straight line on QQ plot. ![[20250303 DistributionOfResidualsForPEB.png]] ![[20250303_211643_QQPlotResidualsPEB.png]] Assumption of equal variances. I also tested the hypothesis for Equality or Homogeneity of Variances with Levene’s test to assess the equal variances assumption: Levene’s Test Results:  p = 0.0786. Since  p > 0.05 , we fail to reject the null hypothesis of equal variances. Welch's ANOVA P<.0001 and since p<.05, we can reject H₀. I used the Tukey test to determine where differences occurred among the mean scores for the four education levels. The LSMEAN numbers for the education levels are 2=1, 3=2, 4=3, and 5=4, which is what we would expect which aligns with the mean scores of 2 being the lowest and 5 being the highest. This part was confusing, because the comparison changes numbers from what we are used to, but you can see in the bottom chart below, that there is significant difference (<.0001) in four boxes (1,4; 2,4; 4,1 and 4,2) and a larger but still less than p<0.05 in 3,1 and 1,3 (.0320). ![[20250303-211728-statistical-analysis-results.jpg]] The Box Chart clearly shows that as education level increases, so does PEB. It appears that education level 4, bachelor's degree has the greatest variance. We can also see the F-value and p-value for ANOVA in the box at the upper left of the graph. ![[20250303T211709DistributionOfPEB 1.png]] Type 1 error rate of 0.05 H₀: PEB is equal across the four education groups. H_a: At least one inequality exists in PEB between the four education groups. We can reject the H₀ and clearly state that at least one inequality exists between the four education groups. Fit Statistics: I need to report the fit statistics for the ANOVA: ![[20250303-211555-education-statistics-table.jpg]] Only .097 or almost 10% of the variability with PEB is explained by education, which is very low. The Coefficient of Variation is about 20% and the root mSE is .58 (on a scale of 1-5). The mean score is 2.89. The ANOVA for this data shows there is variation in the data. Parametric one-way ANOVA (Kruskal Wallis test). The parametric one-way ANOVA confirms the findings from above. p<.0001 and if p<.05, we can reject the H₀. There is a statistically signifianct difference in PEB scores across education levels. ![[20250303-213919-WilcoxonScoresVariablePEB.jpg]] I like the wilcoxon comparison test below, because it compares each education level against the others. the following have significant differences: 2 vs 5, 2 vs 4, and 5 vs 3. because those p-values are all less than 0.05. The p-values of 2 vs 3, 4 vs 5, and 4 vs 3 are not significant, because they are all p > 0.05. This table is easier to understand than the "Least Square Means for Effect education" above. ![[20250303 Pairwise Two-Sided Multiple Comparison Analysis 1.jpg]] You can see a screenshot of my SAS environment here to see my setup. One-way ANOVA: ![[2025-03-03-213431-SAS-Studio-One-Way-ANOVA.jpg]] Nonparametric one-way ANOVA: ![[20250303-220531-SASStudioInterface.jpg]] ## Assignment Directions Assignment 4 (20 points) The dataset used for this assignment (and subsequent assignments) was created from a Value-Belief-Norm (VBN) Theory-based survey designed to assess the factors that influence pro-environmental behavior in the Missouri area.  You will recall that PEB is the arithmetic mean of 20 questions from the pro-environmental behavior scale developed by Markle (2013). In Assignment 4, you will again use PEB as your analysis (dependent) variable, but you will analyze differences between levels of education (the group or classification variable).  Education is compartmentalized into five groups: 1=Less than HS, 2=HS grad or GED, 3=Associate degree or certificate/license, 4=Four-year degree, 5=Masters, doctoral or professional degree.  However, we did not sample any people with education=1, so you will only analyze four education groups (2,3,4,5) for this assignment.  We learned about one-way ANOVA in Chapter 9 that enables us to objectively compare more than two groups.  We will use one-way ANOVA to compare mean PEB for the four education groups for these survey respondents. Import the data (repeated from Assignment 1): The dataset is an Excel file named: “EDUC7215_Assignment_Dataset.xlsx”.  You will find under Modules -> Assignments on our Canvas page. You need to upload it into your SAS Profile Folder in the Cloud so SAS Studio can access it.  There are three worksheets in the Excel workbook: Final Data, ReadMe, and Coding Description.  The ReadMe and Coding Description worksheets contain details about all the variables in the dataset. The Final Data worksheet contains the data, and you need to type “Final Data” in the “Worksheet Name” box in the Import Data pane.  Also, you can change the Output Data name from “Import” to whatever you choose; I chose “Behavior”. Once you click the Run icon, the dataset will be loaded into SAS Studio (these are the same steps that I described in the lecture ppt & video for Chapter 5).  There are many variables in the dataset, but we will only use a few of them for this assignment.  Now you are ready for data analysis! For this assignment, I want you to compare PEB and the four education groups in the Missouri area.  You will answer the research question, “Is pro-environmental behavior (PEB) the same across levels of education in the Missouri area?”, through analysis with the one-way ANOVA and the non-parametric one-way ANOVA (Kruskal Wallis test).  You will need to address the two assumptions of one-way ANOVA, normality and equal variances, through the appropriate visual assessments and formal inference tests.  After you have analyzed the assumptions, you will test the following hypotheses with the one-way ANOVA and the Kruskal Wallis test at the Type 1 error rate of 0.05 or 5%. - Ho: PEB is equal across the four education groups. - Ha: At least one inequality exists in PEB between the four education groups. Remember to include all the elements of a formal inference test (hypotheses, type 1 error, decision rule, conclusion) and the necessary graphs and tables in your narrative. For post hoc analysis, use the Tukey and SNK Multiple Comparison tests to determine which education groups differ.  You should also include a Methods paragraph, and Summary Statistics for PEB by education group. Use the Chapter 9 Example Problems document as a guide for how I want your assignment to appear.