3
$\begingroup$

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?

$\endgroup$
4
  • 1
    $\begingroup$ I've slightly altered the meaning of your original title. Please, check that it does indeed correspond to what you initially meant. $\endgroup$
    – chl
    Sep 20, 2011 at 11:39
  • 1
    $\begingroup$ 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. $\endgroup$
    – whuber
    Sep 20, 2011 at 17:07
  • 2
    $\begingroup$ stats.stackexchange.com/questions/15168/… $\endgroup$ Sep 21, 2011 at 8:00
  • $\begingroup$ Finally, how does this question differ from your previous one, as pointed out by @Thomas? $\endgroup$
    – chl
    Sep 21, 2011 at 19:08

1 Answer 1

5
$\begingroup$

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.
$\endgroup$
2
  • $\begingroup$ Thanks. I am just confused. If r is 0.5, than r squared is 25%. How does the scatterplot show both values? $\endgroup$ Sep 21, 2011 at 10:56
  • $\begingroup$ @AdheshJosh I've elaborated on my original answer. I hope it helps. $\endgroup$ Sep 21, 2011 at 11:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.