Correlation is not Causation Causation. If we have high correlation, we d like to determine causation.

Transcription

1 Correlation is not Causation Causation If we have high correlation, we d like to determine causation.

2 Correlation is not Causation Causation If we have high correlation, we d like to determine causation. To visuall represent the direction of causalit between variables, use arrows. For example, if x causes, we draw an arrow from x to.

3 Correlation is not Causation Causation If we have high correlation, we d like to determine causation. To visuall represent the direction of causalit between variables, use arrows. For example, if x causes, we draw an arrow from x to. The was in which two variables ma have strong correlation are: I. Simple Causalit x II. Reverse Causalit x III. Mutual Causalit x x IV. Hidden/Confounding Variable z V. Complete Accident/Coincidence x

4 Correlation is not Causation Simple Causalit I. Simple Causalit x We sa that variables x and are related b simple causalit if the level of x determines the level of.

5 Correlation is not Causation Simple Causalit I. Simple Causalit x We sa that variables x and are related b simple causalit if the level of x determines the level of. Example 2 (pp ): High blood pressure. There is high correlation in the plot of blood pressure vs. deaths from heart disease.

6 Correlation is not Causation Simple Causalit I. Simple Causalit x We sa that variables x and are related b simple causalit if the level of x determines the level of. Example 2 (pp ): High blood pressure. There is high correlation in the plot of blood pressure vs. deaths from heart disease. A chain of causation argues for simple causalit: high blood pressure arteries clog lack of oxgen in heart heart disease

7 Correlation is not Causation Simple Causalit I. Simple Causalit x We sa that variables x and are related b simple causalit if the level of x determines the level of. Example 2 (pp ): High blood pressure. There is high correlation in the plot of blood pressure vs. deaths from heart disease. A chain of causation argues for simple causalit: high blood pressure arteries clog lack of oxgen in heart heart disease Genetics... Man factors have been determined that increase the chance for heart disease. Stress Heart Disease... HDL Exercise

8 Correlation is not Causation Reverse Causalit II. Reverse Causalit x We sa that variables x and are related b reverse causalit if the level of x is determined b the level of.

9 Correlation is not Causation Reverse Causalit II. Reverse Causalit x We sa that variables x and are related b reverse causalit if the level of x is determined b the level of. Example. Islanders in South Pacific found a correlation between health and bod lice. Health people had bod lice and sick people didn t.

10 Correlation is not Causation Reverse Causalit II. Reverse Causalit x We sa that variables x and are related b reverse causalit if the level of x is determined b the level of. Example. Islanders in South Pacific found a correlation between health and bod lice. Health people had bod lice and sick people didn t. Hence: More bod lice means better health.

11 Correlation is not Causation Reverse Causalit II. Reverse Causalit x We sa that variables x and are related b reverse causalit if the level of x is determined b the level of. Example. Islanders in South Pacific found a correlation between health and bod lice. Health people had bod lice and sick people didn t. Hence: More bod lice means better health. However, everone had lice. Lice just preferred health hosts.

12 Correlation is not Causation Reverse Causalit II. Reverse Causalit x We sa that variables x and are related b reverse causalit if the level of x is determined b the level of. Example. Islanders in South Pacific found a correlation between health and bod lice. Health people had bod lice and sick people didn t. Hence: More bod lice means better health. However, everone had lice. Lice just preferred health hosts. Example. Human birth rate and stork population: Storks bring babies.

13 Correlation is not Causation Mutual Causalit / Feedback III. Mutual Causalit x We sa that variables x and are related b mutual causalit if changes in x produce changes in and vice versa.

14 Correlation is not Causation Mutual Causalit / Feedback III. Mutual Causalit x We sa that variables x and are related b mutual causalit if changes in x produce changes in and vice versa. Example. Car dealers. There is a strong correlation between Dealer car sales and Dealer advertising budget.

15 Correlation is not Causation Mutual Causalit / Feedback III. Mutual Causalit x We sa that variables x and are related b mutual causalit if changes in x produce changes in and vice versa. Example. Car dealers. There is a strong correlation between Dealer car sales and Dealer advertising budget. Do car sales pa for advertising or does advertising drive sales?

16 Correlation is not Causation Mutual Causalit / Feedback III. Mutual Causalit x We sa that variables x and are related b mutual causalit if changes in x produce changes in and vice versa. Example. Car dealers. There is a strong correlation between Dealer car sales and Dealer advertising budget. Do car sales pa for advertising or does advertising drive sales? These are mutuall reinforcing. This is an example of mutual causalit.

17 Correlation is not Causation Hidden Variable Causes Both IV. Hidden/Confounding Variable z We sa that x and are in a spurious relationship if the levels of both x and are determined b the level of a confounding variable z. x

18 Correlation is not Causation Hidden Variable Causes Both IV. Hidden/Confounding Variable z We sa that x and are in a spurious relationship if the levels of both x and are determined b the level of a confounding variable z. Example. In a cit, the number of churches there are is highl correlated with the number of liquor stores. x

19 Correlation is not Causation Hidden Variable Causes Both IV. Hidden/Confounding Variable z We sa that x and are in a spurious relationship if the levels of both x and are determined b the level of a confounding variable z. Example. In a cit, the number of churches there are is highl correlated with the number of liquor stores. Simple causation would impl: x

20 Correlation is not Causation Hidden Variable Causes Both IV. Hidden/Confounding Variable z We sa that x and are in a spurious relationship if the levels of both x and are determined b the level of a confounding variable z. Example. In a cit, the number of churches there are is highl correlated with the number of liquor stores. Simple causation would impl: x Reverse causation would impl:

21 Correlation is not Causation Hidden Variable Causes Both IV. Hidden/Confounding Variable z We sa that x and are in a spurious relationship if the levels of both x and are determined b the level of a confounding variable z. Example. In a cit, the number of churches there are is highl correlated with the number of liquor stores. Simple causation would impl: x Reverse causation would impl: In this instance, there is a confounding variable:.

22 Correlation is not Causation Complete Accident V. Complete Accident/Coincidence x If none of the above four cases appl, x and are unrelated.

23 Correlation is not Causation Complete Accident V. Complete Accident/Coincidence x If none of the above four cases appl, x and are unrelated. Take two dice. Roll each five times. Plot the value of one die versus the value of the other die for the five rolls. Often there will be no correlation.

24 Correlation is not Causation Complete Accident V. Complete Accident/Coincidence x If none of the above four cases appl, x and are unrelated. Take two dice. Roll each five times. Plot the value of one die versus the value of the other die for the five rolls. Often there will be no correlation. One instance of correlation occurred, with an R 2 of (relativel high!)

25 Correlation is not Causation Complete Accident V. Complete Accident/Coincidence x If none of the above four cases appl, x and are unrelated. Take two dice. Roll each five times. Plot the value of one die versus the value of the other die for the five rolls. Often there will be no correlation. One instance of correlation occurred, with an R 2 of (relativel high!) An example of a correlation b coincidence.

26 Correlation is not Causation Complete Accident V. Complete Accident/Coincidence x If none of the above four cases appl, x and are unrelated. Take two dice. Roll each five times. Plot the value of one die versus the value of the other die for the five rolls. Often there will be no correlation. One instance of correlation occurred, with an R 2 of (relativel high!) An example of a correlation b coincidence. Example. Perhaps with students and SSN s?

27 Correlation is not Causation Complete Accident V. Complete Accident/Coincidence x If none of the above four cases appl, x and are unrelated. Take two dice. Roll each five times. Plot the value of one die versus the value of the other die for the five rolls. Often there will be no correlation. One instance of correlation occurred, with an R 2 of (relativel high!) An example of a correlation b coincidence. Example. Perhaps with students and SSN s? The chance of this occurring decreases as more observations are taken.

28 Correlation is not Causation Correlation does not impl causation! Groupwork: Justif the correlations between the following variables: As ice cream sales increase, the rate of drowning deaths increase. The more firemen fighting the fire, the larger the fire grows. With fewer pirates on the open seas, global warming has increased. The more people in m Facebook group, the faster it grows. What is the joke below? Source: