STAT
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Lab 9: One and Two- Way ANOVA
Depending on a student’s lifestyle choices, there may be evidence of a difference in their weight change throughout their college years. As a part of the weight trajectory in college students study, the researchers also obtained each of the 120 subjects’ choice of commute (Commute) and are interested to see if this impacts their change in weight (WeightChange).
Open the lab dataset from Blackboard Learn or from where you previously saved it.
Part 1
The column Commute_catNum contains the numerical values corresponding to each level of risk (Commute). Running ANOVA in SPSS requires the categorical variable be represented by a number. This has already been done for you.
Note: “Commute_catNum”: 1 = bike, 2 = drive/bus, 3 = walk.
1. (2 points) Looking at the side-by-side boxplot, are there any outliers? Discuss between what groups would you expect to see significant differences, and why. Be sure to state whether the side-by-side boxplot displays sample or population data.
2. (2 points) Is it reasonable to pool the variances for One-Way ANOVA? Why or why not? Show your work. Note: You should have already ran the One-Way ANOVA in SPSS and that gives you the descriptive statistics table. Make sure your descriptive statistics table output is attached.
3. (4 points) State your hypotheses for a One-Way ANOVA test for this story
4. (2 points) Identify the following from your One-Way ANOVA output. Make sure your One Way ANOVA output is attached.
F = ______________ P-value = ___________________
5. (4 points) What are your conclusions in terms of the story (using a significance level of 0.05)? Be sure to state whether your results refer to the sample or the population.
6. (4 points) Report the R-squared and the pooled estimate of the standard deviation. These calculations should be done by hand using information from the SPSS output. Show all your calculations. Round to 4 decimal places.
R2 = _____________ sp = ___________________
7. (2 points) Is it legitimate to use Bonferroni to establish which means are significantly different? Give your reason why or why not. If you believe it is legitimate please identify which means are significantly different.
Part 2
Someone mentioned that there might also be a relationship status effect on the amount of weight change throughout college years, as well as a potential interaction effect between relationship status and type of commute.
Now re-run the analysis for WeightChange using Commute and RelationshipStatus in a Two-Way ANOVA, make a means plot and descriptive statistics table. Include your output and use it to answer the following questions.
8. (0 points) Using your output, is it reasonable to pool the variances? Why or why not?
9. (0 points) Looking at your means plot (“Estimated Marginal Means” in your SPSS output), what does it tell you about each of the main effects and their interaction? Please explain how the plot tells you this.
10. (0 points) State the hypotheses (including variable names) for the Two-Way ANOVA tests.
a.
b.
c.
11. (0 points) Report the F-test statistics and p-values (include outputs showing these values).
a. F = ______________ P-value = ___________________
b. F = ______________ P-value = ___________________
c. F = ______________ P-value = ___________________
12. (0 points) State your conclusion to the hypothesis tests in terms of the story. Assume α=0.05. Be sure to state whether your results refer to the sample or the population.
a.
b.
c.
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