|
4.62 |
Because this was actually an experiment (i.e., a study in which a treatment was imposed), we can assert a cause-and-effect relationship between aspirin use and a striking reduction in heart attack risk, at least among subjects similar to the older male physicians used in this study.
Aspirin reduced the heart attack risk by 72% in the subjects tested. In the placebo group, the overall heart attack risk was 239/11,034, or 2.17%. In the aspirin group, that risk dropped to only 139/11,037, or 1.26%. [Later in the course, we will be able to prove (using a 2- proportion z test) that this different is highly statistically significant, with a p-value of about 1/10,000,000. For now, we have to settle for calling the difference "striking."]
A disturbing fact, however, is that aspirin appears to have increased the risk of stroke in these subjects by about 21%. In the placebo group, the stroke risk was 98/11,034, or 0.89%. In the aspirin group, the stroke risk increased to 119/11,037, or 1.08%. [The p-value for the 2-proportion z test this time is 0.076, meaning that chance alone could have caused a difference this great about 8% of the time. By tradition, most scientists would not call this difference statistically significant; the usual criterion for statistical significance is a p-value of 0.05 or less.] |
|
4.66 |
Like every Simpson’s Paradox situation, this problem has a lurking variable. Here, the lurking variable appears to be engineering discipline. If we made a 3-way table of gender, discipline, and salary ranges, we would probably discover that many of the women worked in lower-paid fields such as civil engineering, while many of the men worked in higher-paid fields such as biomedical engineering, electrical engineering, etc. Therefore, the women’s median would be pulled to the low end, and the men’s median would be pulled to the high end, even though the women (apparently) are beginning to earn nearly as much as men in every engineering and scientific discipline.
[This problem is a great illustration of the old saying, "Figures don’t lie, but liars figure." A politician who wanted to make the case that women were making progress in salary parity would prefer to cite statistics that are broken down by job title, whereas a politician who wanted to make the case that women are still underpaid would prefer to use the aggregate data. When someone has an axe to grind, be very skeptical about any statistics that person offers, since the figures (even if factually true and not exaggerated) will probably not tell the whole story.] |