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AGENDA: DG11 --- 15 minutes Complete Section 4.3 Mon --- DG 12; Media Center Tues --- Begin Ch. 5 Wed --- Quiz 4 Fri --- Test Ch. 4. Advanced Placement Statistics Section 4.3: Establishing Causation.
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AGENDA: • DG11 --- 15 minutes • Complete Section 4.3 • Mon --- DG 12; Media Center • Tues --- Begin Ch. 5 • Wed --- Quiz 4 • Fri --- Test Ch. 4
Advanced Placement StatisticsSection 4.3: Establishing Causation EQ:What are three waysin which theassociationbetweentwovariablescan be explained?
Firemen are always present at fires. Can you conclude that firemen cause fires? Scenario 1: The crime rate diminished during Governor Jones’ administration. Can you conclude that it was her policies that were responsible? Scenario2:
When we study the relationship between two variables, we often hope to show that changes in the explanatory variable causechanges in the response variable. However, a strong association between two variables is not enough to draw conclusions about cause and effect.
In the figures on the slides in this presentation: • A solid line represents a causal relationship. • A dashed line represents an observed association between the variables x and y. Causation
Explaining Association: Causation • This is causation. • You can see that changes in x cause changes in y. Causation --- changes in x cause changes in y
Causation • A drop in temperature causes an increase in natural consumption for heating.
Explaining Association: Common Response • This is a common response. • We can see from the diagram that changes in both x and y are caused by a third lurking variable z. Common Response --- changes in both x and y are caused by changes in a lurking variable
Common Response • Families that eat together have children that are more well-balanced. Is there some other variable influencing both of these?
Explaining Association: • Confounding • This is confounding. • Confounding occurs when the effect of x on y is unclear because of the effect of a lurking variable z. Confounding --- the effect (if any) of x and y is confounded with the effect of a lurking variable
Many studies have found that people who are active in their religion live longer than nonreligious people. But people who attend church or mosque or synagogue also take better care of themselves than non-attenders. They are less likely to smoke, more likely to exercise, and less likely to be overweight. The effects of these good habits are confounded with the direct effects of attending religious services.
Decide whether the relationship between the two variables involves causation, common response, or confounding. Identify possible lurking variable(s). 1. x = monthly flow of money into stock mutual funds y = monthly rate of return for the stock market
Mutual Funds and the Stock Market • There is a strong positive correlation between how much money individuals add to mutual funds each month and how well the stock market does the same month. Is the new money driving the market up? The correlation may be explained in part by common response to underlying investor sentiment: when optimism reigns, individuals send money to funds and large institutions also invest more. The institutions would drive up prices even if individuals did nothing.
2. x = mother’s body mass y = daughter’s body mass index
BMI in Mothers and Daughters • Body type is in part determined by heredity. Daughters inherit half their genes from their mothers. As a result, there is a direct causal link between BMI of mothers and daughters. The mothers’ BMI only explain 25.6% (r2) of the variation among the daughter’s BMI. Other factors, such as diet and exercise, also influence BMI. • Note: Even when direct causation is present, it is rarely a complete explanation of an association between two variables.
We noted in the association of BMI of daughters and mothers that inheritance explained part of the causation. • It is possible that mothers who are overweight also set an example of little exercise, poor eating habits, and lots of TV. As a result, their daughters pick up these habits to some extent, so the influence of heredity is mixed up with influences from the girls’ environment. • It is this mixing of influences that we call confounding.
3. x = amount of the artificial sweetener saccharin in a rat’s diet y = count of tumors in the rat’s bladder
Saccharin in Rats • The best evidence for causation actually comes from experiments that actually change x while holding all other factors fixed. If y changes, we have good reason to think that x caused the change in y. • Experiments have shown conclusively that large amounts of saccharin in the diet cause bladder tumors in rats. Should we avoid saccharin as a replacement for sugar in food? • Rats are not people. Although we cannot experiment with people, studies of people who consume different amounts of saccharin show little association between saccharin and bladder tumors. • Note: Even well-established causal relations may not generalize to other settings.
4. x = the number of years of education a worker has y = the worker’s income
Education and Income It is likely that more education is cause of higher income – many highly paid professions require advanced education. However, confounding is also present. People who have high ability and come from prosperous homes are more likely to get many years of education than people who are less able or poorer. Of course, people who start out able and rich are more likely to have high earnings even without much education. We can’t say how much of the higher income of well-educated people is actually caused by their education
5. x = a high school senior’s SAT score y = the student’s first-year college GPA
SAT and GPA • Students who are smart and who have learned a lot tend to have both high SAT scores and high college grades. The positive correlation is explained by this common response to students’ ability and knowledge.
6. People who do well in school or at work tend to feel good about themselves. Can you think of explanations for the association between high self-esteem and good school/work performances other than “Self-esteem causes better work in school/on the job”?
7. A study of elementary school children, ages 6 to 11, finds a high positive correlation between shoe size and score on a test of reading comprehension. What explains this correlation?
8. Members of a high school language club believe that the study of a foreign language improves a student’s command of English. From school records, they obtain the scores on an English achievement test given to all seniors. The mean score of seniors who studied a foreign language for at least two years is much higher than the mean score of seniors no foreign language. These data are not good evidence that language study strengthens English skills. Identify the explanatory and responsive variables in this study. Then explain what lurking variable(s) prevents the conclusion that foreign language study improves students’ English scores.
A study showed that women who work on a production line manufacturing computer chips have abnormally high numbers of miscarriages. Can you explain a reason for this high positive association?
10. In 2008, the Atlanta Symphony advertised a “Mozart for Minors” program with an advertisement making the claim “Question: Which students scored 51 points higher in verbal skills and 39 points higher in math? Answer: Students who had experience in music.” What do you think of the claim that “experience in music” causes higher test scores?
