Question: Refer to Exercise, in which one or more third variables are at least partially likely to account for the observed relationship between religious activities and reduced incidence of high blood pressure. Is this an example of Simpson's paradox? Explain.
Exercise: Case Study was called "Does Prayer Lower Blood Pressure?" One of the results quoted in that study was, "People who attended a religious service once a week and prayed or studied the Bible once a day were 40% less likely to have high blood pressure than those who don't go to church every week and prayed and studied the Bible less."
a. What is the explanatory variable in this study?
b. What is the response variable in this study?
c. Give an example of a third variable that might at least partially account for the observed relationship.
Case Study: Does Prayer Lower Blood Pressure?
Read the original source on the companion website, http:// www.cengage.com/statistics/Utts4e.
News headlines are notorious for making one of the most common mistakes in the interpretation of statistical studies: jumping to unwarranted conclusions. A headline in USA Today read, "Prayer can lower blood pressure" (Davis, 1998). The story that followed continued the possible fallacy it began by stating, "Attending religious services lowers blood pressure more than tuning into religious TV or radio, a new study says." The words "attending religious services lowers blood pressure" imply a direct cause-and-effect relationship. This is a strong statement, but it is not justified by the research project described in the article. The article was based on an observational study conducted by the U.S. National Institutes of Health, which followed 2391 people aged 65 or older for 6 years. The article described one of the study's principal findings: "People who attended a religious service once a week and prayed or studied the Bible once a day were 40% less likely to have high blood pressure than those who don't go to church every week and prayed and studied the Bible less" (Davis, 1998). So the researchers did observe a relationship, but it's a mistake to think that this justifies the conclusion that prayer actually causes lower blood pressure. When groups are compared in an observational study, the groups usually differ in many important ways that may contribute to the observed relationship. In this example, people who attended church and prayed regularly may have been less likely than the others to smoke or to drink alcohol. These could affect the results because smoking and alcohol use are both believed to affect blood pressure. The regular church attendees may have had a better social network, a factor that could lead to reduced stress, which in turn could reduce blood pressure. People who were generally somewhat ill may not have been as willing or able to go out to church. We're sure you can think of other possibilities for confounding variables that may have contributed to the observed relationship between prayer and lower blood pressure.
Moral of the Story: Cause-and-effect conclusions cannot generally be made on the basis of an observational study.
Definitions: An observational study is one in which participants are merely observed and measured. Comparisons based on observational studies are comparisons of naturally occurring groups. A variable is a characteristic that differs from one individual to the next. It may be numerical, such as blood pressure, or it may be categorical, such as whether or not someone attends church regularly. A confounding variable is a variable that is not the main concern of the study but may be partially responsible for the observed results.