14C InClass

Osteoporosis is a bone disease in which the bones in a person’s body have lost density, making them weak and brittle. The condition is most common in older women, and researchers have been searching for ways to treat and prevent osteoporosis for many years. In this in-class activity, we’ll use a simplified version of a real healthcare research study to explore the factors we consider when deciding if a one-way ANOVA is an appropriate test to use.

A comparison between a healthy bone and osteoporosis. The healthy bone shows lots of white lines on it, while the osteoporosis bone shows less.

Credit: iStock/wetcake

Question 1

1) What are some different ways researchers could use an ANOVA to study osteoporosis?

Question 2

2) A 1995 study used a one-way ANOVA to compare different osteoporosis prevention  strategies on the bone density of older women.1 The women were randomly  assigned to receive either a placebo treatment, milk powder containing calcium,  calcium pills, or calcium pills with an exercise program.

Part A: In your own words, identify the conditions/assumptions we need to consider  before using an ANOVA.

Part B: What information do you need in order to know if this research study used an ANOVA appropriately? Explain.

1 Prince, R., Devine, A., Dick, I., Criddle, A., Kerr, D., Kent, N., Randell, A. & Price, R. (1995). The effects  of calcium supplementation (milk powder or tablets) and exercise on bone density in postmenopausal  women. Journal of Bone and Mineral Research, 10(7), 1068–1075.

Question 3

3) In order to compare the groups, the researchers measured the densities of the thigh  bones for each of the treatment groups after a period of two years. Results were  recorded as percentage changes in bone density from the beginning of the study.  There were 168 participants in the study (42 in each group). The data provided in  the following table (continued on the next page) are based on the summary statistics  in the study presented in Question 2. The values represent the changes in bone  density (%) for the patients within that group.

Placebo Milk Calcium Pill Calcium Pill Plus Exercise
-0.46 -0.02 -0.2 0.53
-0.57 -0.43 -0.07 0.54
-0.7 -0.24 -0.3 0.11
-0.61 0.05 -0.26 0.42
-0.65 -0.44 -0.38 0.73
-0.62 -0.1 0.01 1.21
-0.93 -0.35 -0.23 0.67
-0.83 -0.02 0.11 0.63
-0.7 -0.21 0.1 0.25
-0.65 0.31 0.07 0.07
-0.62 -0.06 -0.28 0.34
-0.92 -0.4 -0.19 0.32
-0.33 -0.04 0.02 0.18
-0.7 -0.14 -0.14 -0.02
-0.47 -0.39 -0.25 0.53
-0.71 0.05 -0.21 0
-0.94 -0.05 0 0.34
-0.47 0.06 -0.54 0.04
-0.52 -0.35 -0.2 0.6
-0.85 -0.4 -0.06 0
-0.38 -0.34 -0.27 0.35
-0.76 -0.3 0.06 -0.45
-0.71 -0.35 -0.14 -0.26
-0.77 -0.2 -0.33 0.33
-0.73 -0.38 -0.4 -0.05
-0.67 -0.27 -0.21 -0.12
-0.68 0.3 -0.23 0.51
-0.67 -0.29 -0.38 0.29
-0.68 -0.25 -0.43 0.32
-0.52 -0.1 -0.27 0.39
-0.18 -0.34 0.1 0.38
-0.8 -0.36 -0.21 -0.32
-0.99 -0.22 -0.34 0.36
-0.49 -0.06 -0.13 0.39
-0.81 -0.26 -0.18 0.58
-0.8 -0.27 0 -0.07
-0.66 0.1 -0.37 0.37
-0.84 0.03 0.07 0.61
-0.83 -0.18 0.19 0.04
-0.86 -0.25 -0.42 0.5
-0.31 -0.2 -0.17 -0.34
-0.82 -0.37 -0.47 0.47

Part A: Based on this information, do you have any concerns about the type of data  the researchers were testing with the one-way ANOVA? Explain.

Part B: The following are the descriptive statistics for each group. Based on this  information, do you have any concerns about the variability of the groups in this ANOVA? Explain.

A table and box plot. The table is labeled “Descriptive Statistics” and has columns “Group,” “Sample Size,” “Mean,” “Standard Deviation,” and “Standard Error.” The first row reads “Placebo,” 42, -0.672, 0.161, 0.0280. The second row reads “Milk Powder,” 42, -0.184, 0.189, 0.0292. The third row reads “Calcium Pill,” 42, -0.179, 0.181, 0.0279. The last row reads “Calcium Pill Plus Exercise,” 42, 0.280, 0.330, 0.0509. Beneath the table is the box plot, labeled “Bone Density (% Change)” on the horizontal axis, with “Placebo,” “Milk Powder,” “Calcium Pill,” and “Calcium Pill Plus Exercise” on the vertical axis. For Placebo, the low point is at approximately -1 and the high point is at approximately -0.3. The low end of the box is at approximately -0.8, the high end is at approximately -0.6, and the middle line is at approximately -0.7. There is also a point at approximately -0.2. For Milk Powder, the low point is at approximately -0.45 and the high point is at approximately 0.3. The low end of the box is at approximately -0.35, the high end is at approximately -0.05, and the middle line is at approximately -0.25. For Calcium Powder, the low point is at approximately -0.55 and the high point is at approximately 0.2. The low end of the box is at approximately -0.3, the high end is at approximately 0, and the middle line is at approximately -0.2. For Calcium Power Plus Exercise, the low point is approximately -0.45 and the high point is approximately 0.75. The low end of the box is at approximately 0.05, the high end is at approximately 0.5, and the middle line is at approximately 0.35. There are also points “y bar sub 1” at approximately -0.7, “y bar sub 2” and “y bar sub 3” at approximately -0.2, and “y bar sub 4” at approximately 0.3.

Part C: In this case, consider the experimental design. Do you have any concerns  about how the groups were created? Explain.

Question 4

4) Write the null and alternative hypotheses for this ANOVA. Use statistical notation  AND write out the hypotheses in the context of the problem.

Question 5

5) Go to the DCMP ANOVA: Analysis of Variance tool at https://dcmathpathways.shinyapps.io/ANOVA/. Under “From Textbook,” select  “Osteoporosis.”

Part A: Write your F-statistic and P-value.

Part B: What is your interpretation of the P-value?

Question 6

6) Your elderly aunt asks, “What treatment works best to prevent osteoporosis?” Can  you use the results of your ANOVA to answer her question? Explain.

Question 7

7) In this example, it is very tempting to make assumptions based on the obvious  differences in the group means, but further testing is needed to confirm and provide  statistical evidence of our conclusions. This testing will be the focus of our next in class activity.

Part A: As you prepare to start analyzing specific differences, what is one hypothesis  you would like to test?

Part B: What other treatment options might be valuable for researchers to  investigate?