If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra 1 (Eureka Math/EngageNY)>Unit 2

Lesson 14: Topic D: Lesson 19: Interpreting correlation

# Correlation and causality

Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise). Created by Sal Khan.

## Want to join the conversation?

• So how do we know, given some data, that two variables are just correlated or there's some causality between them?
• I'm a statistician and I can categorically state that causality is ideological.

That is, if the data is related (correlated), and if you susplect one causes the other, you are making an ideological statement. It might be true, it might not be – there isn’t enough information to supported or rejected that assertion.

Sometimes the statement is very obvious - the temperature is correlated to the length of the day... well... the length of the day relates to the amount of sun shine, and therefore we can safely say that the length of the day causes changes in temperature. Sometimes the statment isn't so obvious, like above example. What appears to be a perfectly logical assumption has no basis. The same used to happen in history where people though bad smells gave you diseases (rather than both bad smells and diseases being related to poor hygene and microbial action).

So at the very least causation is a hypothesis (hypothetical thesis – unproven theory), and at best an accepted theory (i.e. previous studies have confirmed that one is likely to cause the other).

What does this mean? If you find that data are correlated (related), you should then determine if one causes the other.
• So what is the perfect definition for the causality?
• Causality is relation between something as cause and other thing as effect.
So, it's not "just" about relation (correlation), there must be cause and effect. To make it clear, we have to distinguish causality from correlation.

Let say we have two variables: A and B.
A and B correlates when the value of A and B changes together; for example, when A's values increase, B's values decrease. However, we cannot say yet that A causes the change of B.

Here are great examples that correlation doesn't equal causation:
http://www.tylervigen.com/spurious-correlations
• What is the difference between causality and causation?
• Hmmm, I think they are pretty close, but used in different contexts. "Causality" is a general, absolute property of the universe, which most scientists believe is an important building block of the real world. They want their theories to respect "causality" meaning that the cause (or causes) of every specific event must happen before the event (say, the decay of a radioactive atom must happen before the click in the geiger counter). "Causation" is usually used to refer to categories, and often only in a probabilistic sense, such as "smoking causes lung cancer", or "global warming causes floods".
• Maybe a combination of eating healthy meals and exercise can result in a decrease in obesity?
• Yes of course. Nutrition are and exercise repeated over long periods of time are the only significant causes for weight loss.
• idk if this is math
• This video doesn’t discuss math, it dives into causation. Math comes later. >:)
• Are there real world applications of causality?
(1 vote)
• Yes..Oil prices are causal to inflation to most if coutries
• But I will add to my previous comment, just to be fair and balanced, the point of your discussion was spot on… always question the narrative, whether it be in “statistical analysis” or life in general. Regards.
• i need help
• I like how the rest is about scatter plots but then this is about obesity
• Great point addressed here, to distinguish causality and correlation. Eating breakfast might in certain circumstances leads to a less likelihood of having obesity given an ideal situation where the individual practice a healthy life routine.

But I wonder if Sal has neglected one word in the title of the webMD article---"may". When the title goes "Eating Breakfast May Beat Teen Obesity", is it necessarily suggesting a causality or it is in effect indicating a correlation?

It sounds to me that the difference between causality and correlation is when the occurrence of event A leads to B, and it can't go the other way. This indicates 1) a strict time order, A has to happen before B, and 2) A has the strongest correlation with B amongst all the other factors that may or may not contribute to the occurrence of event B so that A has the determining power for B's occurrence which makes the correlation between A and B not simply a correlation but a causation as well.
• The title "Eating Breakfast May Beat Teen Obesity" suggest correlation not causation as mentioned by Sal.

It sounds to me that the difference between causality and correlation is when the occurrence of event A leads to B, and it can't go the other way.

This is not what correlation is about. casuality would mean that A causes B it does not say whether B cause A. Let suppose for particular person dust exposure causes asthma. This does not mean if a person has asthma they been exposed to dust. It could be there was some other trigger.

2) A has the strongest correlation with B amongst all the other factors

There could be many other factors involved. It might be A does not have highest correlation with B amongst the factors studied.