Discussion Session Chapters 8 updated (2)

2 1. Find the proportion of males that own smartphones and the proportion of females that own smartphones. 2. Determine the MAD statistic. 3. When comparing two proportions, you could use the difference in the proportions or the MAD as the statistic. How do these two statistics compare in this example? Will they always have the same relationship as in this example? Explain. 4. Put the data from the table in the Multiple Proportions applet and make null distributions using both the difference in proportions and the MAD statistic. Describe how these distributions are different. 5. Based on your answer from part (c), explain why a distribution of MAD statistics is skewed right when the distribution of differences in proportions is bell-shaped. Heart disease and baldness* 8.1.15 Many studies have been done to look at the relationship between heart disease and baldness. In one study, researchers selected a sample of 663 heart disease male patients and a control group of 772 male patients not suffering from heart disease from hospitals in eastern Massachusetts and Rhode Island. Each was asked to classify their degree of baldness. The results are given in the following table. Use these data to answer the following questions. EXERCISE 8.1.14 Baldness N one Little Some Much Total Heart disease Yes 251 165 195 52 663 N o 331 221 185 35 772 Total 582 386 380 87 1,435 Notice the degree of baldness uses ordered categories. This makes it possible to reduce the 2 × 42 × 4 table to a simpler one: 1. Of those in the control group, what percent claimed to have: i. Little or no baldness? ii. Some or much baldness? 2. Of those with heart disease, what percent claimed to have: i. Little or no baldness? ii. Some or much baldness? 3. At this stage in the investigation, state whether you think there is a relationship between heart disease and baldness. Explain your answer. We are now going to run a test of significance on these data using all four degrees of baldness. Use the data set HeartDiseaseAndBaldness . Males with smartphones 25 50 0.5 Females with smartphones 3 0.6 10.6 0.51 1 0.10 Inthis example the MAD is the absolute value of the diff in proportions because there is only 1 comparison happening not multiple with thediff in proportions you get a bell shaped distribution with a two sided p valof0.42 For the MAD stat you get a right skewed distribution but w the same p value Null distributions of Mean group diff are skewed right because the values are closer to o whereas the other is bell shaped because it's centered normally around a specific value 2214,31 35,51 9 715 71.5 y 0 285 28.51 1656631 0.627 62.71 52 66195 0.373 37.31 I think there is a correlation between heart disease baldness because the difference in proportions withthe control group suggests they are dependent on eachother Baldness appears to be more common among individual with heart disease