Sta-209 (Fall 2026) Homework #6

Directions:

• Submit your final answers and all supporting work on Canvas (under the “Assignments” tab)
• You must submit HTML output generated using R Markdown for this assignment.
• Homework is intended to be individual work. While you may discuss the assignment with your peers, you should submit answers that are uniquely your own.
• Any assistance you receive from resources/materials not on our course website (such as other websites, course mentors, peer students, AI, etc.) should be clearly acknowledged

Question #1

An individual’s critical flicker frequency is the highest frequency at which a flickering light source can be detected. At frequencies above the critical frequency, the light source appears to be continuous even though it is actually flickering.

In this question you’ll analyze data from a study titled “The effect of iris color on critical flicker frequency” published in the Journal of General Psychology. The study measured the critical flicker frequency and iris color (part of the eye) of \(n=19\) subjects.

flicker = read.csv('https://remiller1450.github.io/data/flicker.csv')

• Part A: Construct side-by-side boxplots showing the distribution of critical flicker frequencies for each eye color group. Does there appear to be more within-group or between-group variability?
• Part B: Use the group_by() and summarize() functions (introduced in Lab 5) to find the mean and standard deviation of critical flicker frequencies for each eye color group.
• Part C: Based upon your responses to Parts A and B, do the assumptions of the ANOVA model seem reasonable for these data? Explicitly comment on whether each of the model’s main assumptions appears reasonable.
• Part D: Based upon your answers to Parts A-C, would you expect the ANOVA \(F\)-statistic to be relatively large or relatively small? Explain your reasoning.
• Part E: Use aov() to fit the one-way ANOVA model, then print the ANOVA table and use the \(p\)-value of the \(F\)-test to make a conclusion about the relationship between iris color and critical flicker frequency. Be sure that you include every component of a proper statistical conclusion (evidence, context, and the effect).
• Part F: If you found statistical significance in Part E, perform post-hoc testing to evaluate which pairs of groups differ. If you did not find statistical significance, briefly explain why post-hoc testing is not necessary.

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Question #2

The data provided below come from a randomized experiment comparing the efficacy of three weight loss diets. Each subject was randomly assigned to a diet (labeled 1, 2 or 3), which is stored in the variable Diet. Because this variable was coded numerically, the code below converts it to a categorical variable for you.

diet = read.csv('https://remiller1450.github.io/data/diet.csv')
diet$group = factor(diet$Diet, labels = c("Diet1", "Diet2", "Diet3"))

• Part A: These data contain two variables that could be reasonably considered the response variable in a statistical analysis: postWeight and weightChange. Which of them is better to use as the primary outcome variable? Briefly explain.
• Part B: Construct side-by-side boxplots showing the distribution of weightChange by group. Does there appear to be more within-group or between-group variability?
• Part C: Use the group_by() and summarize() functions to find the mean and standard deviation of weightChange for each diet group. Based upon these results and the boxplots you created in Part B, do the assumptions of the ANOVA model seem reasonable?
• Part D: Consider using one-way ANOVA to analyze the relationship between diet and weight change. Participant #66 was a 41 year-old female weighing 76 kg at the start of the study who was assigned to Diet #3 and experienced a weight change of -5.0 kg. What is this participant’s residual under the null model? What is this participant’s residual under the alternative model? Show your calculations of each residual.
• Part E: Use ANOVA to determine if there is statistical evidence that diet is associated with weightChange. Be sure that you provide every component of a proper statistical conclusion (evidence, context, and the effect).
• Part F: Now consider the other possible outcome variable, postWeight. Use ANOVA to determine whether diet is associated with postWeight. Your answer should show the ANOVA table and interpret the results of the test.
• Part G: Briefly explain how it is possible that analyses involving postWeight and weightChange yield different conclusions. That is, why was a statistically significant result found in one analysis but not in the other?
• Part H: Based upon the design of this study, would you expect there to be an association between preWeight and diet group? Briefly explain your reasoning