Correlation and causality (video) | Khan Academy
A relation between “phenomena or things or between mathematical or statistical variables Causal relationship is something that can be used by any company. On the other hand, if there is a causal relationship between two variables, they could be other reasons—the student may not have studied well, for example. The mathematics of statistics is not good at identifying underlying causes, which .. Labour economists want to estimate the causal relationship of education on.
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.
Causal and non-causal relationships
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.
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.
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.
- Fundamentals: Correlation and Causation
- Correlation and causality
- Causation and Correlation
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.
But what I want to do here is to think about what a lot of articles you might read or a lot of research you might read are implying and to think about whether they really imply what they claim to be implying. So this is an excerpt of an article, and the title of the article says "Eating breakfast may beat teen obesity. The title itself says if you eat breakfast then you're less likely-- or you won't be obese.
You're not going to be obese.
So the title right there already sets up this. That eating breakfast may beat teen obesity. And then they tell us about the study. It looks like a good sample size. It was over a large period of time. I'll just give the researchers the benefit of the doubt, assume that it was over broad audience, that they were able to control for a lot of variables.
But then they go on to say, "The researchers write that teens who ate breakfast regularly had a lower percentage of total calories from saturated fat and ate more fiber and carbohydrates. Breakfast tends to be things like cereals, grains. You eat syrup, you eat waffles-- that all tends to fall in the category of carbohydrates and sugars. And frankly, that's not even necessarily a good thing. Not obvious to me whether bacon is more or less healthy than downing a bunch of syrup or Fruit Loops or whatever else.
Examples for teaching: Correlation does not mean causation - Cross Validated
But we'll let that be right here. Regular breakfast eaters seemed more physically active than the breakfast skippers. So the implication here is that breakfast makes you more active. And then this last sentence right over here, they say "Over time, researchers found teens who regularly ate breakfast tended to gain less weight and had a lower body mass index than breakfast skippers.
So the entire narrative here, from the title all the way through every paragraph, is look, breakfast prevents obesity. Breakfast makes you active. Breakfast skipping will make you obese. So you just say then, boy, I have to eat breakfast. And you should always think about the motivations and the industries around things like breakfast.
Australian Bureau of Statistics
But the more interesting question is does this research really tell us that eating breakfast can prevent obesity? Does it really tell us that eating breakfast will cause some to become more active? Does it really tell us that breakfast skipping can make you overweight or make it obese? Or, it is more likely, are they showing that these two things tend to go together? And this is a really important difference. And let me kind of state slightly technical words here.
And they sound fancy, but they really aren't that fancy. Are they pointing out causality, which is what it seems like they're implying.
Eating breakfast causes you to not be obese. Breakfast causes you to be active. Breakfast skipping causes you to be obese. So it looks like they are kind of implying causality. They're implying cause and effect, but really what the study looked at is correlation. The whole point of this is to understand the difference between causality and correlation because they're saying very different things.
And, as I said, causality says A causes B. Well, correlation just says A and B tend to be observed at the same time. Whenever I see B happening, it looks like A is happening at the same time. Whenever A is happening, it looks like it also tends to happen with B. And the reason why it's super important to notice the distinction between these is you can come to very, very, very, very, very different conclusions.
So the one thing that this research does do, assuming that it was performed well, is it does show a correlation. So the study does show a correlation. It does show, if we believe all of their data, that breakfast skipping correlates with obesity and obesity correlates with breakfast skipping.
We're seeing it at the same time. Activity correlates with breakfast and breakfast correlates with activity-- that all of these correlate.
What they don't say-- and there's no data here that lets me know one way or the other-- what is causing what or maybe you have some underlying cause that is causing both. So for example, they're saying breakfast causes activity, or they're implying breakfast causes activity.
They're not saying it explicitly. But maybe activity causes breakfast. They didn't write the study that people who are active, maybe they're more likely to be hungry in the morning. And then you start having a different takeaway. Then you don't say, wait, maybe if you're active and you skip breakfast-- and I'm not telling you that you should. I have no data one way or the other-- maybe you'll lose even more weight.
Maybe it's even a healthier thing to do. So they're trying to say, look, if you have breakfast it's going to make you active, which is a very positive outcome. But maybe you can have the positive outcome without breakfast.