How best to graphically represent an r-square effect-size measure?

Question

It is easy to graph effect size (r) for a correlation in the form of a scatterplot.

However, how do I graph the variance (r-squared)? Any thoughts on best practice?

Answer 1

Short Answer

• If you have bivariate data, then a scatterplot suggests as much about $r$ as it does $r^2$.

Longer Answer

• The points on a scatterplot can be extracted to yield $r$ or $r^2$.
• Graphs are commonly used instead of summary statsitics or raw data in order to take advantage of the power of the human visual-perceptual system. As such, when we look at a scatterplot we can get a sense of the direction, form, and degree of the relationship between two numeric variables.
• The degree of linear relationship in the data from a scatterplot is captured in $r$ and $r^2$. $r$ is directional and $r^2$ is not. They also quantify the degree of relationship in different ways.
• In some sense $r$ and $r^2$ are not directly communicated by the scatterplot. Rather you can train your intuition over time to estimate the $r$ or $r^2$ for a given scatterplot. Alternatively, the scatterplot can be seen as a tool to train your intuition of the meaning of $r$ and $r^2$. If you need practice, check out this applet.
• If you are wanting to combine the plot with the summary statistic, you can always add $r$ or $r^2$ to the plot. I find this useful for slide presentations. There are also functions like pairs.panels in the psych package in R which will print a scatterplot matrix with scatterplots in the lower triangle of cells and the value of the correlation in the upper triangle of cells. See here for an example.