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Fundamentals: Correlation and Causation
Hello, I'm Paul Henne and I'm a philosophy graduate student at Duke University and in this video I'm going to talk to you about correlation and causation. Maria and Andy are high school students in Arizona. Andy always gets an A on his math test when it's sunny outside. On one sunny day, before Andy goes to math class he tells Maria, "I'm going to ace this test today because it's sunny!" Maria objects, "No Andy. You'll not ace this test because it's sunny. You'll ace test because you studied. The fact that it's sunny outside has nothing to do with it." Andy responds, "But Maria. I always ace my tests when it's sunny." Maria replies, "Okay, sure, but that's just because you always study for your math test, and it's always sunny here in Arizona. The sunniness does not cause you to ace the test. Maria is correct. Andy's making a mistake right? The sunniness doesn't cause Andy to ace his test. The two events, the sunniness and Andy acing his test occur together without one causing the other. In other words, the two events are correlated in some way but there's no causal relation between them. Andy's reasoning here is fallacious. Simply because two events are correlated does not mean that one caused the other. This conflation of correlation and causation is what we will talk about in this video. First let's consider some other examples. Fido barks when his tail wags. People with higher grades in college have higher grades in high school. People who take vitamin C recover more quickly from a cold. These are correlations. That is, there's a correspondence between these events. For example, the dog, Fido, barks when his tail wags but there's no reason to suspect that there's a causal relation between these events. While these events often occur together There are many times when Fido's tail wags and he doesn't bark and there are times when Fido barks but doesn't wag his tail. Furthermore, we may suspect that there is some common cause for these events like Fido's excitement when his owner comes home. Now that we can agree that these are cases of correlation without causation We can discuss two types of correlation, positive and negative. In the next video we'll discuss how these types of correlations specifically relate to different types of causation. But for now let's just introduce them. When events frequently occur together like in the examples above they are positively correlated. If two events are positively correlated Then when one event is present the others often present as well. In our first example it being a sunny day in Arizona is positively correlated with Andy succeeding on his math test. On the other hand, two states are negatively correlated when it's likely that when one event occurs the other will not occur. For instance, when it snows, it's often not very sunny, so snowing and sunniness are negatively correlated. We often hear about positive and negative correlations, especially in the news. headlines like "taking vitamin C helps you recover more quickly from a cold" indicate positive correlations. Taking vitamin C is positively correlated with recovering from the common cold more quickly than if one had not taken vitamin C. Or headlines like "eating more nuts makes you less likely to have higher levels of bad cholesterol" indicates that eating more nuts is negatively correlated with having higher levels of bad cholesterol. You may have heard headlines like these and had conversations with some friends about them and you may have heard someone say something like, "Awesome, so I'll just like eat more nuts and get rid of my bad cholesterol." You may have also had the experience of someone else saying, "Yeah but that's just correlation not causation." Of course it's person may just be a jerk, but they are right to point this out. Unless you had evidence that a causal relation held it Is a mistake to suggest that this correlation is actually a causal relation. So it'd be wrong to say that eating more nuts will cause you to have lower levels of bad cholesterol, unless you have evidence that the causal relation held. So let's consider an example where two events are positively correlated when neither causes the other. Consider this again, people with higher grades in college have higher grades in high school. Here, earning higher grades in college is positively correlated with earning higher grades in high school. Now, it's incorrect, as we've discussed a claim, that earning high grades in high school always causes someone to earn high grades in College. Nonetheless, earning high grades in high school may sometimes cause a person to earn high grades in college. For example, Jane may have gotten good grades during high school and some of those grades transferred to her college, which causes her success in college. Here, success in high school for Jane causes her success in college. But most of the time it is not the success in high school that causes success in college. It is usually someone's working hard in college courses that causes that person to succeed in college. And at that type level of the statement where we are identifying a correspondence of two data sets, the causal claim is false. So again, the two events, high school success and college success are positively correlated, but they do not cause one another. When two events are correlated it may seem that one causes the other but there may be alternative explanations we've ignored, like working hard in college courses causes that person's overall success in college. So it's fallacious to conclude from only the fact that two states are positively or negatively correlated that one causes the other because there may be another cause that explains the outcome. It may be that there's a common cause for both of the events or that there's some alternative cause all together. On the other hand, the correlation might just simply be a coincidence. But this explanation and other questions will have to wait for part two where we will talk more about the analysis of causation and how it relates to different types of correlation. If you're interested in these false cause fallacies, you may also want to check out our video on the post hoc fallacy. Thank you for watching. To subscribe to Wireless Philosophy on YouTube click here.