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Correlation vs. Causation

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

Correlation vs. Causation

Correlation vs. CausationCum hoc ergo propter hoc:With this, therefore because of thisCorrelationA 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 intelligenceResearchers 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?


CausationCause: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/causeEffect:A change that results when something is done or happens : an event, condition, or state of affairs that is produced by a causehttp://www.merriam-webster.com/dictionary/effect

Examples:The act of decapitation will cause a persons death.Gravity causes objects to fall downwards.

3Correlation vs. causationJust 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. causationIt 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 dont 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.

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.6Reverse CausationOccurs when the cause and effects of a situation is confused or reversed.

Belief: XY (X causes Y)Reality: YX (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 childs 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 mothers saw signs of malnutrition tended to breastfeed longer. http://ije.oxfordjournals.org/content/26/2/349.full.pdf

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. - 120,000 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.


7Common causal variableOccurs 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: XY (X causes Y)Reality: ZX & ZY (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 Bobs 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.http://www.nhlbi.nih.gov/educational/hearttruth/lower-risk/hormone-therapy.htmThe 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.

8Cant 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.


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, etcBelief: AZ (A causes Z)Reality: AZ & BZ & CZ & DZ & EZ 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, etcHow long you spend on your homework. Causes may include homework length, difficulty, level of understanding, work environment, assistance, etc10Bidirectional causeWhen two events are a result of bidirectional causation, one event causes another while the other event causes the first. For example:Belief: XY (X causes Y)Reality: XY & YX (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 dont 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 Jimmys behavior and his parents frustration towards him. Jimmys behavior can cause his parents to become more frustrated. In turn his parents frustration can cause Jimmy to act out more.11CoincidenceBelief: XZReality: YZMany 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 ex

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