No correlation would exist between X and Y, because they are not causative factors. Also in your example, you are using negative and positive values to give a correlation of 0. However, I do think it is next to impossible for causation to exist in the real world without correlation.
Causal claims require knowledge to be justified, and therefore require correlation. Here is an example that I think works. Take for example a study that looks at the factors which make people vote for the Republican Party Y. However we also know that older people access the internet less than younger people. That is age which we will call z has a negative correlation with X. We also know that older people are more likely to vote Republican i,e z has a positive correlation with Y.
If the correlations are of similar magnitude, it is possible that a raw correlation coefficient between x and y would be 0 even if we know X causes Y. Every probabilistic problem requires a histogram and corresponding probability distribution function PDF. So, there cannot be causation without correlation, where correlation is defined typically by a PDF.
To me it seems we are mincing words. What your examples appear to prove is not that causation does not require correlation, rather than the lack of correlation in one set of observations does not necessarily negate causation. It seems here that we are more raising questions with the question of whether the appearance of correlation is necessary for causation which, of course, it is not.
The appearance of correlation may not exist at all given poorly constructed studies that ignore important factors. However, in actuality, with all other things appropriately controlled, illness causes death and causation requires correlation. Search for: Follow the blog. Why all these options? The Incidental Economist The health services research blog. Interested in having Aaron or Austin speak to your group? For information on Aaron speaking, click here.
For information on Austin speaking, contact the Leigh Bureau. Causation without Correlation is Possible. Austin Frakt. Share this That much drinking per day will kill you for any number of reasons. Why is this insidious? While the above is an extreme example, there are plenty of times marketers make this mistake.
Any time you do a survey or study of your customers, you are automatically reducing variation. While surveying only your customers makes a great deal of sense if you want to understand how customers feel about your products or services, surveying only your customers to get a sense of the industry can create the same distortions as the alcohol and drunk driving example above.
Causation can exist without correlation. Keep this in mind as you read through surveys, infographics, etc. Join my Analytics for Marketers Slack Group! Your email address will not be published. Yes I do consulting. Click here ». So, if you were going to study the effect of radiation on cancer risk and you just got a bunch of typical people and somehow measured how much exposure they had, chances are well, we know there's a correlation, but if you don't get some extreme cases you're probably not going to see it.
So, if you are only looking at people who are both low sum threshold of radiation exposure, there's probably going to be no way you're really going to see the relationship. So, you have to be a little careful about these threshold cases. Also, this is one that I added myself here, if you look at this top graph, what I have is a little experiment where I'm looking at plant growth and I've got plants that received almost no water and plants that received a lot of water, and there's really no difference.
There's no correlation between water and plant growth. But in the middle you can see okay, well if we had collected data at moderate levels of watering, we'd see a decent growth on the plant. So, there is a strong relationship, but you don't see it because you only looked at two data points and the relationship was quadratic. So, that's another way you can miss out when there's no correlation, miss a cause and effect.
And the last one is a lot of times there's a lot of noise in the system, you can't see the cause and effect or correlation.
Without exploring further, you might conclude that exercise somehow causes cancer! Based on these findings, you might even develop a plausible hypothesis: perhaps the stress from exercise causes the body to lose some ability to protect against sun damage.
This shows up in their data as increased exercise. At the same time, increased daily sunlight exposure means that there are more cases of skin cancer.
Both of the variables—rates of exercise and skin cancer—were affected by a third, causal variable—exposure to sunlight—but they were not causally related. Distinguishing between what does or does not provide causal evidence is a key piece of data literacy. Determining causality is never perfect in the real world.
However, there are a variety of experimental, statistical and research design techniques for finding evidence toward causal relationships: e. Beyond the intrinsic limitations of correlation tests e. For example, imagine again that we are health researchers, this time looking at a large dataset of disease rates, diet and other health behaviors.
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