1. Correlation vs. Causation
Cum hoc ergo propter hoc:
“With this, therefore because of this”

2. Correlation
A relation existing between phenomena or things or between mathematical or statistical variables which tend to vary, be associated, or occur together in a way not expected on the basis of chance alone.
In other words, if two properties/events are correlated, this simply means when one changes, the other tends to change in a consistent manner.
Examples:
The correlation of brain size and intelligence
Researchers have found a direct correlation between smoking and lung cancer.
She says that there's no correlation between being thin and being happy.
What are some other examples of two things that are correlated?

3. Causation
Cause:
Something or someone that produces an effect, result, or condition : something or someone that makes something happen or exist.
Effect:
A change that results when something is done or happens : an event, condition, or state of affairs that is produced by a cause
Examples:
The act of decapitation will cause a person’s death.
Gravity causes objects to fall downwards.

4. Correlation vs. causation
Just because two events or properties are correlated (linked) does not mean that one causes the other.
Going to the hospital is positively correlated with dying, but it is obvious that going to the hospital does not cause you to die.
The more firefighters at a fire is positively correlated with the amount of damage done to the building, but firefighters do not cause more damage.

5. Correlation vs. causation
It is very difficult to say definitively that one thing causes another, but here are some tools you can use:
If the cause is taken out, does the effect still occur to the degree that it would have if the cause was present?
Could there be any other causes that could contribute to the effect?
Example: Smoking causes lung cancer.
Do those who don’t smoke have the same chance of getting lung cancer as those who do? (No)
Could something else cause lung cancer? (Yes)
Here we could say that smoking probably contributes to lung cancer, but is not the only cause. (Asbestos, pollution, etc…)

6. Can you tell?
Discuss with your group whether or not you think the following correlations are also causal relations:
There is a positive correlation between age and income.
There is a positive correlation between house size and the value of the house.
There is a negative correlation between the distance you drive and the amount of gas in your tank.
Student Answers:
There is a positive correlation between age and income.
Not causal. Students should identify that just because you are older does not mean you are going to make more money.
There is a positive correlation between house size and the value of the house.
Possibly causal. Students should identify that there are other contributing causes include location, age, condition, etc.
There is a negative correlation between the distance driven and amount of gas in the tank.
Probably causal. Students should note that there are not many other factors (besides there being a hole in your gas tank) that could lead to a decrease in the amount of gas in your tank. In other words, more driving causes the car to use more gas.

7. Belief: XY (X causes Y) Reality: YX (Y causes X)
Reverse Causation
Occurs when the cause and effects of a situation is confused or reversed.
Belief: XY (X causes Y)
Reality: YX (Y causes X)
Example:
“I notice that when I see windmills spin faster (X), there are stronger winds (Y). Therefore I can conclude that the spinning of windmills are causing the strong winds.”
Can you think of any other examples of reverse causation?
Example (depending on age of students):
In a 1997 study of Peruvian toddlers, there was a strong correlation between breastfeeding in excess of 12 months and the child’s stunted growth and malnutrition. This lead some researchers to conclude that breastfeeding longer contributed to child malnutrition. In fact, the reverse was true. Those children whose mother’s saw signs of malnutrition tended to breastfeed longer.
“In 1999, Hubertus Fischer et al. from Scripps Institution of oceanography compiled the records of the Vostok, TD, and Byrd ice cores and pointed out this lag between CO2 and temperature over the last 270,000 years. 7 A glacial termination begins at a temporal minimum and ends at a temporal maximum. In termination III (from 270,000 years BP – 230,000 years BP) CO2 concentrations reached a maximum of over 300 p.p.m.v. 600 (+/-200) years after temperature had peaked at a change of ~2o C. Then again in termination II (160,000 years B.P ,000 years B.P.), CO2 concentrations reach their maximum 400 (+/-200) years later than the recorded temperature peak. Other sources, such as Eric Monnin et al., Callion et al., and Petit et al., all estimate this CO2 lag to be ~800 (+/-200) years after temperature8,3,5. However, they also give notice that the 800-year lag period is very short and insignificant compared to the 5,000-year period in which the lag occurs. This makes the lag insufficient evidence to rule out CO2 as a forcing factor on climate change.”

8. Common causal variable
Occurs when two events/measurements are correlated and the assumption is made that one causes the other; however, there is a “lurking” variable that is actually contributes to the occurrence of both events/measurements.
Belief: XY (X causes Y)
Reality: ZX & ZY (Z causes both X and Y)
Example:
Bob notices that every time he has a temperature, he does not feel well. He reasons that because he has a high body temperature, this causes him to not feel well. Bob then jumps into an ice bath concluding that if he lowers his body temperature he will begin to feel better.
Notice that both the high body temperature and Bob’s not feeling well are results of him contracting the flu virus. The common cause here is the virus.
Example (depending on student age):
“Menopausal hormone therapy once seemed the answer for many of the conditions women face as they age. It was thought that hormone therapy could ward off heart disease, osteoporosis, and cancer, while improving women's quality of life. But beginning in July 2002, findings emerged from clinical trials that showed this was not so. In fact, long-term use of hormone therapy poses serious risks and may increase the risk of heart attack and stroke.”
The discrepancy in the data was attributed to the fact that women who were taking hormone replacement therapy were of a higher socio-economic group and on average had healthier eating habits and more rigorous exercise routines.

9. Can’t you see the flaw?
A study from the University of Pennsylvania, published in the May 13, issue of Nature, that found babies younger than 2 years old who slept with a light on were at increased risk of developing myopia - nearsightedness - later in childhood.
In the current study of 1,220 children, Ohio State University researchers found no association between nighttime lighting and the development of nearsightedness. It didn't matter if the child had slept in a dark room, with a night light on or in a fully lit room. What the researchers did find, however, was a strong link between nearsighted parents and nearsighted children.
The researchers noticed that nearsighted parents were more likely to use a nightlight in their child's room. "We think this may be due to the parents' own poor eyesight," Zadnik said. Also, Zadnik said her study found that genetics plays a significant role in causing myopia.

10. Oversimplification (Multiple causes)
This fallacy occurs more often than the others in the media. You may have heard of statements like: “You will do better at work/school if you have a good breakfast”. While this may be true on average, there are many causes that contribute to increased performance such as preparation, motivation, good health, etc
Belief: AZ (A causes Z)
Reality: AZ & BZ & CZ & DZ & EZ etc…
(Many factors cause Z)
Can you think of any more examples of an oversimplified cause?
What other events have many reasons for occurring?
Examples:
How fast you read a book. Causes may include reading ability, book length, reading environment, etc…
How long you spend on your homework. Causes may include homework length, difficulty, level of understanding, work environment, assistance, etc…

11. Bidirectional cause
When two events are a result of bidirectional causation, one event causes another while the other event causes the first. For example:
Belief: XY (X causes Y)
Reality: XY & YX (X causes Y and Y causes X)
Example:
The number of lions in Kenya affects the number of gazelles in Kenya (lions eat gazelles). But it is also true that the number of gazelles in Kenya affect the number of lions in Kenya (if lions don’t have food, they will begin to die off). So, increased/decreased lion population can cause an increase/decrease in the gazelle population, and vice versa.
This is called the predator/prey model.
Question: Can you think of any other examples of bidirectional cause?
Another example of bidirectional cause could be Jimmy’s behavior and his parents frustration towards him. Jimmy’s behavior can cause his parents to become more frustrated. In turn his parent’s frustration can cause Jimmy to act out more.

12. Coincidence Belief: XZ Reality: YZ
Many times the fact that two events are correlated (linked) is pure coincidence and there is no causal relationship that exists between the two. Take the following graph as an example. Can we say that oil imports from Venezuela cause people to eat more corn syrup?

13. Identify the fallacy
You notice that students with a tutor have lower than average GPAs. So tutors must cause bad grades.
You notice that the less money people make, the more often they are sick. So being poor causes illness.
You notice that the taller your friend is the higher his/her IQ. So increased height causes increased IQ.
You notice that the more your friend likes a class, the better grade s/he earns. So liking a class causes him/her to get better grades.
You notice that the more sunscreen that is purchased, the higher the crime rate. So using sunscreen causes people to commit crimes
You notice that students with a tutor have lower than average GPAs. So tutors must cause bad grades. (Fallacy: Reversing cause and effect)
Students should realize that tutoring does not cause lower grades, but lower grades is a cause for being tutored.
You notice that the more sunscreen that is purchased, the higher the crime rate. So using sunscreen causes people to commit crimes. (Fallacy: Common cause)
Students should identify that the use of sunscreen does not cause people to commit crimes, but both crime and sunscreen use increase with warmer weather.
You notice that the less money people make, the more often they are sick. So being poor causes illness. (Fallacy: Oversimplification)
Students should notice that there are many factors that contribute to both illness. Low income may contribute lower quality health care, decreased living conditions and less access to medications. These factors may, in conjunction, lead to higher incidence of illness.
You notice that the more your friend likes a class, the better grade s/he earns. So liking a class causes him/her to get better grades. (Fallacy: Bidirectional causation)
Students may assert causation (which is a valid assertion), but should also notice that causation would go in both directions. The more a student likes a class may be a cause for higher grades, but in turn better performance in a class may cause a student to like the class more.
You notice that the taller your friend is the higher his/her IQ. So increased height causes increased IQ. (Fallacy: Coincidence)
Students should acknowledge that there is no obvious logical reason that the height of a person would affect the person’s intelligence.

14. Crickets vs. temperature
Cricket Chirps (15s)
Temperature 20
88.6 16
71.6
19.8
93.3
18.4
84.3
17.1
80.6
15.5
75.2
14.7
69.7 82
15.4
69.4
16.2
83.3 15
78.6
17.2
82.6 17
83.5
14.1
76.3
Note: Data was collected in a controlled setting
Calculate (using your graphing calculators) the correlation coefficient of the data.
Determine if there is or is not a correlation between the speed at which a cricket chirps and the temperature of the crickets environment.
Determine if one variable is a cause of the other by using the correlation coefficient and your logic/reason. Some questions you might want to ask yourself are:
“How strongly are the two variables correlated?”
“Does it make sense that one variable could cause the other?”
“Could there be a common cause, or multiple causes, or coincidence?”
Given the following data, students will calculate (using technology) the correlation coefficient and determine if the data is correlated, causal or both. Students should identify that a high correlation may support, but cannot prove a causal relationship. Students should note that because the observations were held in a controlled setting (all other factors such as time of day were held constant) the high correlation coefficient strongly supports a causal relationship.
Correlation coefficient: 0.84

15. Erroneous Conclusions?
Erroneous Conclusion: Engineers love mozzarella cheese.

16. Erroneous Conclusions?
Erroneous Conclusion: Studying science causes people to hang themselves.

17. Erroneous Conclusions?
Erroneous Conclusion: Eating chicken makes people want to buy oil.

18. Erroneous Conclusions?
Erroneous Conclusion: Skiing facilities are responsible for death by bed sheets.

19. Erroneous Conclusions?
Erroneous Conclusion: Sour cream kills motorcyclists

20. Erroneous Conclusions?
Erroneous Conclusion: Getting divorced in Mississippi causes people to commit murder.

21. closure Discuss the following questions with your group:
What is the main difference between two statements:
A and B are correlated
A causes B (or B causes A)
What are some techniques we can use to differentiate between correlation and causation?
How is the correlation coefficient used in helping determine causation?
How can the correlation coefficient be deceiving (and how can it help) when determining causation?
Why is it difficult to determine strict causation?
 What is the main difference between two statements:
A and B are correlated
 A causes B (or B causes A)
When there is a correlation between A and B we can infer that the two are linked in some way after using logic and reason to eliminate the possibility of coincidence.
When A causes B there is a much stronger relationship that implies the occurrence of B is a direct result of the occurrence of A.
Note: correlation does not imply causation.
Sample Student Answer: Correlated means two events tend to happen together, caused means when one event occurs it is a direct result of another event occurring.
What are some techniques we can use to differentiate between correlation and causation?
 By using randomized experiments that hold all other variables constant can support (but not prove) a causal relationship.
Using logic and reason to eliminate any other possible causes/influence.
Sample Student Answer: Controlled random experiments. (The only thing changing is the variable you are looking at.
How is the correlation coefficient used in helping determine causation?
When the absolute value of the correlation coefficient is closer to 1, there is a higher possibility for a causal relationship.
Sample Student Answer: The closer the coefficient is to 1 or -1, the more likely it is a cause.
How can the correlation coefficient be deceiving (and how can it help) when determining causation?
The correlation coefficient can be deceiving in the sense that high correlations are often associated with causal relationships.
 (High correlation can help support causal relationships, but cannot prove them).
Correlation is necessary but not sufficient for causation.
Sample Student Answer: If there is a common cause, the coefficient will be higher, but that doesn’t mean that one causes the other.
Why is it difficult to determine strict causation?
Strong correlation coefficients may still point to a common causal variable (multiple causes) and not strict causation.
 Many (even most) real-world events do not have one single cause, but multiple contributing factors.
We can conclude that one event is a cause of another, but to conclude that it is the cause is much more difficult.
Sample Student Answer: More than one thing may cause something to happen.