Question

Simpson's Paradox, Exercise -vs- Diet: Averaging across categories can lead to misleading results.

Below is a table for the mean weight lost (in pounds) by moderately (BMI < 40) and severely (BMI > 40) obese participants in a weight loss study over the course of 6 months. Some of these participants employed a diet only plan while others used an exercise only plan.

The bold-faced number gives the mean weight loss in each category (x). The number in parentheses gives the number of participants in each category (w).

	Mean Weight Loss (# of Participants)
	Extremely	Moderately
	Obese	Obese
Exercise Plan	23 (5 participants)	16 (45 participants)
Diet Plan	19 (45 participants)	12 (5 participants)

(a) Under the category of Extremely Obese, which plan was more effective?

Exercise PlanDiet Plan    

(b) Under the category of Moderately Obese, which plan was more effective?

Exercise PlanDiet Plan    

(c) Using a weighted average across both obesity categories, calculate the mean weight loss for those on the Exercise Plan. Round your answer to 1 decimal place.

x_Exercise =

(d) Using a weighted average across both obesity categories, calculate the mean weight loss for those on the Diet Plan. Round your answer to 1 decimal place.

x_Diet =

(e) When averaging across categories, which plan appears more effective?

Exercise PlanDiet Plan    

(f) What made the Diet Plan appear better when averaging across categories?

The large number of Extremely Obese participants on the Diet Plan.The small number of Moderately Obese participants on the Diet Plan.     Extremely Obese participants lost more weight on average than Moderately Obese participants.All of these reasons contributed to the problem.

Answer 1

Result:

Simpson's Paradox, Exercise -vs- Diet: Averaging across categories can lead to misleading results.

Below is a table for the mean weight lost (in pounds) by moderately (BMI < 40) and severely (BMI > 40) obese participants in a weight loss study over the course of 6 months. Some of these participants employed a diet only plan while others used an exercise only plan.

The bold-faced number gives the mean weight loss in each category (x). The number in parentheses gives the number of participants in each category (w).

	Mean Weight Loss (# of Participants)
	Extremely	Moderately
	Obese	Obese
Exercise Plan	23 (5 participants)	16 (45 participants)
Diet Plan	19 (45 participants)	12 (5 participants)

(a) Under the category of Extremely Obese, which plan was more effective?

Exercise Plan

(b) Under the category of Moderately Obese, which plan was more effective?

Exercise Plan

(c) Using a weighted average across both obesity categories, calculate the mean weight loss for those on the Exercise Plan. Round your answer to 1 decimal place.

x_Exercise    = (23*5+16*45)/(5+45)

=16.7

  

(d) Using a weighted average across both obesity categories, calculate the mean weight loss for those on the Diet Plan. Round your answer to 1 decimal place.

x_Diet

= (19*45+12*5)/(5+45)

=27.9

  

(e) When averaging across categories, which plan appears more effective?

Diet Plan    

(f) What made the Diet Plan appear better when averaging across categories?

The large number of Extremely Obese participants on the Diet Plan.

The small number of Moderately Obese participants on the Diet Plan.    

Extremely Obese participants lost more weight on average than Moderately Obese participants.

Answer: All of these reasons contributed to the problem.