A Lesson in Correlation

1. A Lesson in Correlation REPEAT AFTER ME: Correlation is NOT causation! Correlation is NOT causation! Correlation is NOT causation! Correlation is NOT causation!

2. What is a correlation? • Correlation shows how two variables relate together. • It is often confused that correlation can show a cause • Examples: ACT scores correlate to college success (or failure) • Parents who have children before the age of 18 are more likely to have children who have children before the age of 18 • Correlations may be influenced in either direction • Example: Friends tend to dress and act the same. Is it because of how they dress that they are friends or is it that because they are friends they choose to dress and act similar? • With Correlation, one can never tell. Graph showing illusory correlations

3. What does a correlation measure? • Correlations measure the STRENGTH of a relationship • Correlation coefficient (r value) • Between 1.00 to zero to -1.00 • The closer to 1.00 or -1.00, the stronger the relationship • The closer to zero, the weaker the relationship. • The +/- indicates the direction of the relationship • Which of the following correlation coefficients represents the STRONGEST relationship? -.87 .64 -.32 .24 • Which is the weakest?

4. What do correlations look like? • Correlations are represented visually through scatter plots • Scatter plot – a cluster of dots, with each dot showing the values of two variables Each dot in the instance above shows a husband’s age (x-axis) and his wife’s corresponding age (y-axis)

5. What types of correlations are there? • Correlations are either positive or negative • Zero correlation = no relationship exists – such as age and eye color • Positive: As one variable increases, the other increases (and vice versa) • Negative: As one variable increases, the other decreases (and vice versa) • In math terms: • positive correlation = direct relationship • negative correlation = inverse relationship. Which correlation is positive, and which is negative in the examples above? Video Clip: The Joy of Stats

6. Why can’t correlation show cause-effect? • Correlation only shows that TWO variables relate to each other, but most issues are far more complex • Intervening variables – a variable that may explain a correlation’s existence • EX: Education and income are positively correlated, but does education actually provide any income? • The intervening variable in this case is a job. An education provides a chance at a better job and better jobs pay more which leads to more wealth • So, the reason for education and income’s correlation is job opportunity

7. Why can’t correlation show cause-effect? • Illusory correlations - The perception of a relationship between two variables where none exists • Example: There is more crime on a full moon • Example: My horoscope can predict my future • Here’s why this is so convincing. In psychology, we’ll study a concept called confirmation bias and it is the root of all evil. It states that as people we always look for things that confirm our belief and dismiss things that contradict that belief. • This is called Type I error. The reality is false, but we perceive it as true Both of the above examples are not true; study after study has shown that no more crime happens on a full moon than any other moon phase and numerous studies have confirmed that horoscopes have no predictive value. But Type I error is SO powerful that these ideas remain.

8. Why can’t correlation show cause-effect? • Extraneous (or 3rd) variables – Sometimes a correlation does not exist at all but it appears that it does because of a third variable. • There is a positive correlation between ice cream and murder rates • Does that mean that ice cream causes murder? • What does ice cream and murder have in common? • Video Clip: Correlation vs. Causality (poor ice cream getting a bad rap)

9. What are some other real-life examples of bad correlations? • People who eat Frosted Flakes as children had half the caner rate of those who never ate the cereal. Further, children who ate oatmeal as kids had 4x the cancer rate than those who did not. • Illusory correlation: Frosted Flakes was not invented until 1951, at the time of the study, those who ate frosted flakes were not likely to get cancer because they weren’t old enough yet (cancer is correlated with age) • This is my favorite correlation story! In the early twentieth century, thousands of Americans in the South died from pellagra, a disease marked by dizziness, lethargy, running sores, and vomiting. • Finding that families struck with the disease often had poor plumbing and sewage, many physicians concluded that pellagra was transmitted by poor sanitary conditions. In contrast, Public Health Service doctor Joseph Goldberger thought that the illness was caused by an inadequate diet. He felt that the correlation between sewage conditions and pellagra did not reflect a causal relationship, but that the correlation arose because the economically disadvantaged were likely to have poor diets as well as poor plumbing. • How was the controversy resolved? • The answer demonstrates the importance of the experimental method. He selected two patients—one with scaling sores and the other with diarrhea. He scraped the scales from the sores, mixed the scales with four ml of urine from the same patients, added an equal amount of feces, and rolled the mixture into little dough balls and he, his assistants, and his wife ate them. None of them came down with pellagra. • He then conducted another experiment on prison inmates who either got a balanced diet or a bad diet. The bad diet inmates all got pellagra and the balanced diet inmates did not.