Sta-209 (Spring 25) Homework #9

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.

The data below come from a study titled “The effect of iris color on critical flicker frequency” published in the Journal of General Psychology. The study recorded the critical flicker frequency and iris color (part of the eye) for \(n = 19\) subjects:

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

• Part A: In words, write the null and alternative hypotheses for the use of one-way ANOVA to analyze these data.
• Part B: Use aov() to fit the one-way ANOVA model. Print the ANOVA table and interpret the \(p\)-value. Be sure to make a conclusion that involves the context of these data.
• Part C: Check both assumptions of the one-way ANOVA model. If one or more assumptions are unreasonable, apply a log-transformation and re-check the assumptions or perform a Kruskal-Wallis Test.
• Part D: If you found statistical significance in Part B, perform post-hoc testing to evaluate which pairs of groups differ. If you did not find statistical significance, briefly explain why post-hoc testing should not be done.

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Question #2

For this question you’ll use “diet” data set provided below. These data come a randomized experiment comparing the efficacy of 3 different weight loss diets. Each subject’s randomly assigned diet (labeled 1, 2 or 3) is stored in the variable Diet. The code below loads these data and creates a categorical variable group indicating the assigned diet.

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 these is the better outcome variable? Briefly explain.
• Part B: Create a set of side-by-side boxplots of the variable weightChange. Then, based upon this graph, briefly explain whether you believe weightChange is associated with diet.
• Part C: Use ANOVA to statistically determine whether diet is associated with weightChange. Your answer should show the ANOVA table and interpret the results of the test. Hint: be sure you’re using group, which is categorical.
• Part D: Use post-hoc testing to follow up on the ANOVA performed in Part C to determine which pairs of diets were statistically different from each other.
  
• Part E: Now consider the other logical 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 F: Compare the conclusion you made in Part E with the one you made in Part C and briefly explain why they are different. That is, considering the data and context, why was a statistically significant result found in one analysis, but not in the other?
• Part G: Based upon the design of this study, would you expect there to be an association between preWeight and diet? Briefly explain, then use ANOVA to verify or refute what you suspect. You do not need to show all of the formal hypothesis testing steps here. Instead, you can simply report the \(p\)-value and explain what it tells you in regard to the premise of this question.