# Observed / expected vs odds ratio

I am trying to understand the difference between the O/E ratio vs the odds ratio.

I think the odds ratio can handle small samples better than the O/E ratio. I am wondering if anybody has more information or a paper which distinguishes between these two.

## 1 Answer

These are two ratios, and they are both associated with the chi-squared test, but otherwise they aren't that similar. In the sense that they are both calculated on your sample data, you can think of them both as statistics, but they are different kinds of statistics:

• The O/E ratio is part of calculating the chi-squared test statistic. That is, it is an inferential statistic; it is used to help decide if you think the variables are independent.
• The odds ratio helps you understand how large the shift is from one column (row) to the next. That is, it is a descriptive statistic / effect size measure.

In other words, these serve different purposes. To decide whether to use one or the other, you need to consider what you are trying to do, determine significance or assess the magnitude of the association.