The study used for exercises in Sections 8.1 and 8.2 actually included a fifth degree of baldness, extreme. Here is a table that summarizes the full data set:

What stands out about the new category is the tiny sample size: only three patients with extreme baldness. This exercise explores what can happen when a category has so few observational units. Use the data set HeartDiseaseAndBaldness2. Simulation-based test using MAD.

a. Use the Multiple Proportions applet to find the MAD, its simulation-based null distribution, and the p-value.

b. Compare the null distribution with the null distribution you obtained in Exercise 8.1.15 (re create it if you need to). What are the main differences? How do you account for these differences?

c. Compare the conclusions from the two simulation-based analyses using the MAD. Which conclusion do you consider more trustworthy? Why? Simulation-based test using chi-square.

d. Use the Multiple Proportions applet to find the chisquare statistic, its simulation-based null distribution, and the p-value.

e. Compare the shape of the distribution for chi-square with the shape of the simulation-based distribution in part (a).

f. Compare the conclusions from the simulation-based analysis using MAD in part (c) above and using chi-square. Which conclusion do you consider more trustworthy? Why? Theory-based test using chi-square.

g. Use the applet to find the p-value and contributions to chi-square for a theory-based test.

h. Is the theory-based test trustworthy? Why or why not? The bottom line.

i. Which analysis do you consider more persuasive: the one based on four degrees of baldness or the one based on all five? Justify your answer.

j. A third approach to the data analysis would be to omit the extreme category. What results do you expect from this analysis? Explain your reasoning. Which test?

k. What lesson should you take away from your comparison of the three tests?

Transcribed Image Text:

Counts None Little Some Much Extreme Total 251 165 165 Yes 195 50 663 331 221 No 185 772 34 3 Total 582 386 1,435 380 84 3 2.