Correlation is an important statistical tool. This method in statistics can help us to determine and to describe the relationship between two variables. We must be careful to use and interpret correlation correctly. One such warning is to always remember that correlation does not imply causation. There are other aspects of correlation that we must be careful with. When working with correlation we must also be cautious of ecological correlation.

Ecological correlation is a correlation based on averages. Although this can be helpful, and sometimes even necessary to consider, we must be careful not to assume that this type of correlation applies to individuals as well.

## Example One

We will illustrate the concept of ecological correlation, and stress that it not be misused, by looking at a few examples. An example of an ecological correlation between two variables is the number of years of education and average income. We can see that these two variables are positively correlated quite strongly: the higher the number of years of education, the greater the average income level. It would be a mistake to then think that this correlation holds for individual incomes.

When we consider individuals with the same education levels, the income levels are spread out. If we would construct a scatterplot of this data, we would see this spread of points. The result would be that the correlation between education and individual incomes would be much weaker than the correlation between years of education and average incomes.

## Example Two

Another example of ecological correlation that we will consider concerns voting patterns and income level. At the state level, wealthier states tend to vote at a higher proportion for Democratic candidates. Poorer states vote in higher proportions for Republican candidates. For individuals this correlation changes. A larger portion of poorer individuals vote Democratic and a larger portion of wealthy individuals vote Republican.

## Example Three

A third instance of ecological correlation is when we look at the number of hours of weekly exercise and average body mass index. Here the number of hours of exercise is the explanatory variable and the average body mass index is the response. As exercise increases, we would expect body mass index to go down. We would thus observe a strong negative correlation between these variables. However, when we look at the individual level the correlation would not be as strong.

## Ecological Fallacy

Ecological correlation is related to the ecological fallacy and is one instance of this kind of fallacy. This type of logical fallacy infers that a statistical statement pertaining to a group also applies to the individuals within that group. This is a form of the division fallacy, which mistakes statements involving groups for individuals.

Another way that ecological fallacies appear in statistics is Simpson’s paradox. Simpson’s paradox refers to the comparison between two individuals or populations. We will distinguish between these two by A and B. A series of measurements may show that a variable always has a higher value for A rather than B. But when we average the values of this variable, we see that B is greater than A.

## Ecological

The term ecological is related to ecology. One use of the term ecology is to refer to a certain branch of biology. This part of biology studies the interactions between organisms and their environment. This consideration of an individual as part of something much larger is the sense In which this type of correlation is named.