# Beginner's question—Dealing with ordinal data (scoring of a medical effect)

I'm a biology PhD student dealing with ordinal data (scoring of a medical effect: 0–3 points) for the first time and I'm looking for information regarding differences in treating ordinal numbers in

• calculating Mean, Median, SD, SEM etc.
• performing significance tests between two ordinal datasets
• calculating correlations

For the last point, I stumbled across the Spearman's coefficient. So far so good, but can I treat ordinal datasets the same way as cardinal datasets in terms of Mean, Median, SD, SEM and significance tests?

Any comments appreciated, I'm also happy with good literature, if it's not too hard to understand.

• Is the difference between 0 and 1 the same as between 1 and 2 and between 2 and 3? In typical cases, these differences are not the same, and you should avoid using mean/standard deviation. Median should still be okay, though. – Gschneider May 21 '12 at 20:10

## 1 Answer

In short, use Spearman's rho when calculating a correlation coefficient for ordinal data. As to statistical tests, use the Mann-Whitney U test to compare two independent groups when you have ordinal data. Means do not make sense for ordinal data (although occasionally you will find people reporting means for ordinal data), but medians make sense, as do distributions and cross tabulations and their associated Chi Square tests. Most any introductory statistics text will go over the above-mentioned statistical techniques. Social science textbooks tend to be more applied in orientation than mathematical statistics textbooks. One of the more rigorous social science textbooks is "Statistics for the Social Sciences" by Rand Wilcox (1996). Since you are a student, it probably makes sense to talk to a faculty member who teaches statistics, either in your department or some other department because doing a statistical analysis can get complicated for all sorts of reasons. Also, if you collect data such as these in the future, you might consider a finer scale, if feasible. Good luck!

• Since Spearman's rho is just a Pearson correlation type computation on the ranks of the data and ranking makes sense for ordinal data Joel is quite right. For continous data pearsons correlation estimate will be 1 or -1 if the data fall on a straight line. For continuous, discrete or ordinal data Spearman's rho will be 1 or -1 if the data monotonically increase or decrease respectively. So you can think of Pearson as measuring the degree of linearity and Spearman as measuring tendency fro both variable is to increase together or one tends to decrease as the other increases. – Michael R. Chernick May 22 '12 at 21:05