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Advanced Placement Statistics Section 4.3: Establishing Causation EQ: What are three ways in which the association between two variables can be explained?

More firemen at a fire result in more damage to the structure More firemen at a fire result in more damage to the structure. Do firemen cause larger fires? Scenario 1: The crime rate diminished during Governor Jones’ administration. Can you conclude that it was her policies that were responsible for a decrease in crime rate? Scenario 2:

Scenario 3:

Scenario 4:

Scenario 5:

When we study the relationship between two variables, we often hope to show that changes in the explanatory variable cause changes in the response variable. However, a strong association between two variables is not enough to draw conclusions about cause and effect.

Causation 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

Variable x and y show a strong association (dashed line) Variable x and y show a strong association (dashed line). This association may be the result of any of several causal relationships (solid arrow).

Explaining Association: Causation --- changes in x cause changes in y

Causation Explanatory Variable- __________________ A drop in temperature causes an increase in natural consumption for heating. Explanatory Variable- __________________   Response Variable - ___________________ temperature heating consumption

Common Response Common Response --- changes in both x and y are caused by changes in a lurking variable

Common Response The number of storks present in a town cause an increase in number of babies born in that town. Address the association that appears to exist : Although there might be a strong, positive, association between number of storks present and number of babies born in a particular town,

Common Response The number of storks present in a town cause an increase in number of babies born in that town. Address that association does not imply causation: Although there might be a strong positive association between number of storks present and number of babies born in a particular town, the presence of storks does not cause more births.

Common Response The number of storks present in a town cause an increase in number of babies born in that town. State a possible lurking variable. A possible lurking variable could be construction of more homes.

Common Response The number of storks present in a town cause an increase in number of babies born in that town. Address how the lurking variable impacts the explanatory and/or response variable(s): The presence of more homes would supply more rooftops for storks’ nests and allow more growing families to move into the town.

Common Response Refer Back to Scenario 1: More firemen at a fire result in more damage to the structure. Do firemen cause larger fires?

Common Response More firemen at a fire result in more damage to the structure. Do firemen cause larger fires? Address the association that appears to exist : Although there might be a strong, positive, association between number of firemen present at a fire and the amount of damage done by the fire,

Common Response More firemen at a fire result in more damage to the structure. Do firemen cause larger fires? Address that association does not imply causation: Although there might be a strong positive association between number of firemen present at a fire and the amount of damage done by the fire, more firemen at a fire do not cause more damage to the structure.

Common Response More firemen at a fire result in more damage to the structure. Do firemen cause larger fires? State a possible lurking variable. A possible lurking variable could be the size of the fire.

Common Response More firemen at a fire result in more damage to the structure. Do firemen cause larger fires? Address how the lurking variable impacts the explanatory and/or response variable(s): More firemen would be called for a serious or very large fire. A serious or large fire would more than likely cause more damage to the structure.

Confounding Confounding --- the effect (if any) of x and y is confounded with the effect of a lurking variable

Explaining Association: Confounding Two variables are confounded when their effects on a response variable cannot be distinguished from each other. The confounded variables may be either explanatory variables or lurking variables. ?

Confounding Parents who eat regular meals with their children have children who grow up to be well-adjusted adults. That is one seen as mentally and emotionally stable. Address the association that appears to exist : Although there might be a strong, positive, association between families eating meals together and the children of these families growing up to be stable, well-adjusted adults,

Confounding Parents who eat regular meals with their children have children who grow up to be well-adjusted adults. That is one seen as mentally and emotionally stable. Address that association does not imply causation: Although there might be a strong, positive, association between families eating meals together and the children of these families growing up to be stable, well-adjusted adults, families eating meals together will not cause the children to grow up as stable well-adjusted adults.

Confounding Parents who eat regular meals with their children have children who grow up to be well-adjusted adults. That is one seen as mentally and emotionally stable. State a possible lurking variable. A possible lurking variable could be the personality of the child.

Confounding Parents who eat regular meals with their children have children who grow up to be well-adjusted adults. That is one seen as mentally and emotionally stable. Address how the lurking variable impacts the explanatory and/or response variable(s): The personality of a child usually remains the same as that child matures. A stable, well-adjusted child is more likely to grow to be a well-adjusted, stable adult.

Confounding Refer Back to Scenario 2: The crime rate diminished during Governor Jones’ administration. Can you conclude that it was her policies that were responsible for a decrease in crime rate? Address the association that appears to exist : Although there might be a strong association between the implementation of Gov Jones’ policies and the city’s crime rate,

Confounding Refer Back to Scenario 2: The crime rate diminished during Governor Jones’ administration. Can you conclude that it was her policies that were responsible for a decrease in crime rate? Address that association does not imply causation: Although there might be a strong association between the implementation of Gov Jones’ policies and the city’s crime rate, her policies may not have caused the crime rate to decrease.

Confounding Refer Back to Scenario 2: The crime rate diminished during Governor Jones’ administration. Can you conclude that it was her policies that were responsible for a decrease in crime rate? State a possible lurking variable. A possible lurking variable could be changing economics within the city.

Confounding Refer Back to Scenario 2: The crime rate diminished during Governor Jones’ administration. Can you conclude that it was her policies that were responsible for a decrease in crime rate? Address how the lurking variable impacts the explanatory and/or response variable(s): A growing economy may increase the jobs available for the citizens. Employed citizens may not feel the need to steal in order to survive. Job security gives people a sense of self-worth and hope which may reduce drug/alcohol related crimes.

Confounding For U.S. colleges and universities, a standard entrance examination is the SAT test. The side-by-side boxplots below provide evidence of a relationship between the student's country of origin (the United States or another country) and the student's SAT Math score. The distribution of international students' scores is higher than that of U.S. students. The international students' median score (about 700) exceeds the third quartile of U.S. students' scores. Can we conclude that the country of origin is the cause of the difference in SAT Math scores, and that students in the United States are weaker at math than students in other countries?

Confounding Address the association that appears to exist : Although there might be a strong association between a student’s nationality and his or her SAT score,

Confounding Address that association does not imply causation: Although there might be a strong association between a student’s nationality and his or her SAT score, being a particular nationality does not cause a student to have a particular score on the SAT.

Confounding State a possible lurking variable. A possible lurking variable could be student’s initiative to use additional educational resources.

Confounding Address how the lurking variable impacts the explanatory and/or response variable(s): A student who has used additional available resources beyond what’s offered in the classroom may perform better than a student from another country who had access to these same resources but chose not to use them.

Criteria for Establishing Causation without an Experiment The association is strong. The association between smoking and lung cancer is very strong. 2. The association is consistent. – Many studies of different kinds of people in many countries link smoking to lung cancer. That reduces the chance of a lurking variable specific to one group or one study explaining the association.

3. Larger values of the explanatory variable are associated with stronger responses. – People who smoke more cigarettes per day or who smoke over a longer period get lung cancer more often. People who stop smoking reduce their risk.

The alleged cause precedes the effect in time The alleged cause precedes the effect in time. – Lung cancer develops after years of smoking. The number of men dying of lung cancer rose as smoking became more common, with a lag of about 30 years. Lung cancer kills more men than any other form of cancer. Lung cancer was rare among women until women began to smoke. Lung cancer in women rose along with smoking, again with a lag of about 30 years, and has now passed breast cancer as the leading cause of cancer death among women.

5. The alleged cause is plausible 5. The alleged cause is plausible. – Experiments with animals show that tars from cigarette smoke do cause cancer.

Association does not imply causation! Medical authorities do not hesitate to say that smoking causes lung cancer. The U.S. Surgeon General states that cigarette smoking is “the largest avoidable cause of death and disability in the U.S.” The evidence for causation is overwhelming – but it is not as strong as the evidence provided by a well-designed experiment. Conducting an experiment in which some subjects were forced to smoke and others were not allowed to would be unethical. In cases like this, observational studies are our best source of reliable information. Association does not imply causation!

Assignment: p. 312 #41, 42, 45