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

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?

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I've slightly altered the meaning of your original title. Please, check that it does indeed correspond to what you initially meant. – chl Sep 20 '11 at 11:39
@chi Thanks! That makes more sense! – Adhesh Josh Sep 20 '11 at 12:44
A description of the dataset or of your purpose would help. After all, both $r$ and $r^2$ are just numbers: you might just as well report them. – whuber Sep 20 '11 at 17:07
Finally, how does this question differ from your previous one, as pointed out by @Thomas? – chl Sep 21 '11 at 19:08

• If you have bivariate data, then a scatterplot suggests as much about $r$ as it does $r^2$.
• The points on a scatterplot can be extracted to yield $r$ or $r^2$.
• 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.