14D InClass

Question 1

1) Consider the comic strip presented by your instructor. Think about the statistical tests being performed. Do you agree with the claim presented in the headline at the bottom?

An open jar of jelly beans

Credit: iStock/Floortje

In In-Class Activity 14.C, your elderly aunt asked, “What treatment works best to  prevent osteoporosis?”

Now that we have shown that there was an overall difference, let’s investigate the  difference in the treatment options to answer your aunt’s question. It is tempting to use the following boxplot to determine the answer, so we need to be careful. This method  does not provide statistical EVIDENCE to support your conclusion.

image

It is also tempting to only show the comparisons you want to show based on the  boxplot. For example, only looking at comparisons including Calcium Pill Plus Exercise.

This is called data snooping or data fishing. You cannot look at your results and then  determine the comparisons that you want to make.

Question 2

2) Let’s investigate the difference in the treatment options for all pair-wise comparisons to answer your aunt’s question at the family-wise 5% significance level.

Part A: Complete the second column of the following table of comparisons.

Comparison Difference Compared

(Part A)

 Adjusted

Confidence Interval  (Part B)
Placebo vs. Milk Powder �Placebo − �Milk Powder (−0.62, −0.36)
Placebo vs. Calcium Pill �Placebo − �Calcium Pill (−0.62, −0.36)
Placebo vs. Calcium Pill +  Exercise
Milk Powder vs. Calcium Pill
Milk Powder vs. Calcium Pill +  Exercise
Calcium Pill vs. Calcium Pill +  Exercise �Calcium Pill − �#$%&'() +’%% , -./0&’1/ (−0.59, −0.33)

Part B: Go to the DCMP ANOVA: Analysis of Variance tool at https://dcmathpathways.shinyapps.io/ANOVA/. Choose the “From Textbook” option and select the dataset “Osteoporosis.”

Select the option to perform “Pairwise Comparisons and Confidence  Intervals,” and select a confidence level of 95%, as shown below. Complete the third column of confidence intervals in the previous table.

A selection menu titled “Options,” with a checkbox selected reading “Pairwise Comparisons & Confidence Intervals.” Beneath this is a heading reading “Adjustment Method,” with “Turkey” having been selected from a dropdown. Beneath this is a heading reading “Select Confidence Level,” under which there is a percentage bar set to 95%.

Question 3

3) Using the adjusted confidence intervals from the table in Question 2, Part A, add the  remaining five comparisons to the appropriate column.

Significantly Different Mean  Bone Density NOT Significantly Different Mean  Bone Density
Placebo vs. Milk Powder

Question 4

4) Which treatment for osteoporosis would you recommend to your elderly aunt?  Explain.

Question 5

5) Your other aunt is now deciding between the Milk Powder treatment and the Calcium  Pill treatment. What would you recommend?