# How to succinctly report the correlation between two variables for 20 different subsets of the data in a table?

I have 20 correlation coefficients (r) to report, for example, .34, .45, .67, .23. and so on. These are correlations between Variable A and Variable B, based on gender, age, education levels etc.

I am after a succient method to show all the correlations in one glance. Is there any best practice in regard to reporting all these correlations in a table format?

A table like the following would be my first thought:

.........................................
Category           r AB
.........................................
Gender
Male             .36
Female           .23
Age
Under 30         .27
30-50            .63
...
...
..........................................


• A row indicating the overall correlation without subsetting
• Information on whether the correlations significantly differ across categories for a given variable (e.g., gender)
• Additional columns with things like p-values, confidence intervals, sample size for the category, etc.
• I am just learning the usefulness of stating the confidence interval of a correlation. Is reporting CI necessary? – Adhesh Josh Oct 1 '11 at 12:13
• I think that confidence intervals on correlations are informative in this context. With sample sizes per group and sample estimates of correlations confidence intervals could be derived by an informed reader. Given the nature of the table, there is certainly room for a few extra columns. – Jeromy Anglim Oct 2 '11 at 3:21

You might consider a figure along these lines (from Carr & Pickle (2011) Visualizing data patterns with micromaps).

This is basically a visual table. It's not a set of correlations, but hopefully you get the idea. The key features are (a) sorting the correlations, (b) putting them in groups (here, of 4), (c) white grid lines on a light gray background.

• This is fascinating. Can you please explain a bit more (as I do not have access to that book). What do the blue dots represent? – Adhesh Josh Sep 29 '11 at 18:13
• If you go to Amazon, you'll find the authors' discussion. (Click "Look inside"; it's Figure 1.2 on pg 3.) – Karl Sep 29 '11 at 18:22
• That's nice, but I'd use a dotplot like @Peter suggests above. Here, each group has a different scale and it's difficult to see exactly how two points on the same line compare. To identify the two groups, I'd use different colors or symbols. – Charlie Sep 30 '11 at 2:56
• Instead of blue dots, I think it might be more helpful to print the numerical values. Think of it as a table where the numbers as well as the spatial relationship between them both convey information. – ashaw Sep 30 '11 at 7:20

The micromap example that @karl suggested is very nice; I think it would, though, be similar to a dot plot, which are easy to implement in R or SAS (and probably other software). Something like

corr <- c(.4, .4, .3, .2)
group = c("Education", "gender", "age", "more")
dotchart(corr, labels = group)


works in R