Covariation and Correlation
Covariation describes the relationship between two variables, usually drawn on a scatter plot. Correlation describes how related two variables are. That is, when one changes so does the other one.
Correlation Coefficient
Don’t worry, you don’t need to know how to calculate these coefficients, but you should know what they represent.
- Pearson correlation coefficient (r): is for numerical data (interval or ratio), like looking at salt consumption vs systolic blood pressure
- Spearman rank-order correlation coefficient (rs): used for ordinal data, such as two doctor’s rankings of disability levels of a patient. These data don’t have numerical values, but are just ranked. This is a good way to check agreement between two doctors, Dr. Ansari and Dr. Bayram.
These are good for capturing linear relationships. If it’s not linear, like BMI and mortality, such as J-shape, these coefficients will underestimate the relationship between the two. For example, both people who are underweight (low BMI) and overweight (high BMI) will have a high mortality. Those in the middle (mid BMI) will have lower mortality.
One more coefficient we should look at. Coefficient of determination (r2) is the percent of variance in one variable that can be accounted for by the other variable. So in this video we had an r2 of 16% for salt intake compared to blood pressure. That means that 16% of the variation in blood pressure can be attributed to the amount of salt ingested. The other 84% of the variation is due to other factors.
But remember that correlation is not causation! Just because 16% of of the change in blood pressure was linked to salt intake, that doesn’t mean one is causing the other. Want more info? Watch the next video.
If you need a refresher on the types of data, watch this video.
Correlation is not Causation
Just because two things seem to change together, that doesn’t mean that one is causing the other. For example, the taller you are, the heavier you are. However, your height doesn’t cause your weight. But they are linked by a common cause. This third common factor might be what you eat, your level of growth hormone, or something else.
Or as ice cream sales go up, so do the number of drownings. Does ice cream cause deaths? No, there is a third cause: when it is warm outside, more people buy ice cream AND more people go swimming.
And though it may seem that eating chocolate doesn’t make you smarter, can it hurt? Oh yeah… the rampage killers. While we’re at it, we should also ban ice cream. Watch this video from TEDxDelft for many examples of how correlation is not causation.
Test your comprehension
With this associations problem set.
patwari 