Correlation vs. Causation

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

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? http://www.merriam-webster.com/dictionary/correlation

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

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.

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…)

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.

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?

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.

Can’t you see the flaw? • A study from the University of Pennsylvania, published in the May 13, 1999 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. http://researchnews.osu.edu/archive/nitelite.htm

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?

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?

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?

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

Crickets vs. temperature • 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?”

Erroneous Conclusions?

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?

Correlation vs. Causation