Please write an example of two numerical variables, which show a numerical correlation but one does not cause the other.

Feel free to use the examples from the CMU readings

OR

Some sample responses from previous semesters are shown below

I

On such example of a misleading correlation is between shoe size (explanatory variable) and reading exam score (response variable).  While the two variables would probably show a strong positive correlation together, shoe size is not causing an individual to have a higher reading exam score.  The two variables show a correlation because as you grow, naturally resulting in larger feet and larger shoe sizes, your reading ability will naturally increase as well.  So while these two variables clearly show a correlation, you can not argue that the size of one’s shoe has any effect on their ability to read well.  Other examples of explanatory variables that would correlate with reading exam score would be glove size, hat size, belt size, etc.

Source:  University of Texas (http://www.ma.utexas.edu/users/mks/statmistakes/causality.html)

II

A positive correlation would be when one variable increases, the other does as well. The same is for when one variable decreases the other does as well. A negative correlation would be when one variable increases the other decreases. A real life example of a correlation that doesn’t necessarily mean that one is affecting the other would be an increase in both autism and organic food consumption. The chart is saying that as organic food is consumed more and more autism increases as well. These two variables aren’t directly affecting each other rather the awareness of autism and its diagnosis have gotten better,

also sales of organic food have increased  over time.

http://www.buzzfeed.com/kjh2110/the-10-most-bizarre-correlations

III

First, correlation measures the linear association between two variables. It measures the strength of that relationship. I found some research done using two quantitative variables but still one of them doesn’t necessarily causes the other. The research was realized to determine if the amount of study hours given to American students (or more homework) will give higher standardized test scores. The results were inconclusive because researchers found out very complex issues. Students from lower economic classes usually had a part time job, elementary school students don’t benefit from more study time, too much study creates burnout and the amount of sleep also affects test scores. So ultimately, more study time doesn’t necessarily create higher standardized test scores.

Marshall Patrick. “Homework Debate”. CQ Researcher. Volume 12 Issue 42 (2002). Web. (8 June 2014).

IV

Correlation, as defined in the oli website, is known as the correlation coefficient (r), which is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables. An example of a relationship that does not correlate is children shoe size and reading skills. This being because the child’s shoe size does not determine the level of reading skill they may develop now or later on in the future. More information on this relationship can be found in the link.

http://stat.ethz.ch/~mmarloes/teaching/stat220/handouts/Chapter9.pdf

V

An article by Local 8 News in Idaho, stated that as temperatures rise, the price of gas also rises.  These two quantitative variables are correlated, yet one is not necessarily causing the other.  Just because the temperature is rising, does not directly effect the rise in the price of gas.  While it is true that people tend to travel more once the weather gets warmer which may be a reason to raise the price of gas,  the temperature is not the direct cause of an increase in price. This is a case of correlation not meaning causation in the real world.

http://www.localnews8.com/news/gas-prices-rise-with-temperature/24530544

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