Sta-209-04 (Spring 24) Homework #10

From the Introduction to Modern Statistics (IMS) textbook, complete the following exercises:

• Ch 22.5 Exercises: #3, #6, #13, #14

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Additionally, complete the following exercise using R:

Question #1: 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 assigned diet (labeled 1, 2 or 3) is stored in the variable Diet.

https://remiller1450.github.io/data/diet.csv

• 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. Hint: you may use the factor() function to ensure the variable “Diet” is treated as categorical.
• Part C: Use ANOVA to statistically determine whether diet is associated with weightChange. You should use factor() to ensure the variable “Diet” is treated as categorical in your model formula. Your answer should clearly state the null and alternative hypotheses (words is okay), report the test statistic and \(p\)-value (you may calculate both using R), and provide a conclusion based upon the \(p\)-value.
• 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. You should use factor() to ensure the variable “Diet” is treated as categorical in your model formula. Your answer should clearly state the null and alternative hypotheses (words is okay), report the test statistic and \(p\)-value (you may calculate both using R), and provide a conclusion based upon the \(p\)-value.
• 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.