# What does a correlation of 0.4 mean?October 19, 2009 10:32 AM   Subscribe

What does a correlation of 0.4 mean?

There's supposed to be a correlation of 0.4 between LSAT scores and first-year grades in law school. What does that mean? Does it mean that LSAT scores explain 40% of the variance in law school grades? 16%? Something else? Can anyone provide a plain-English explanation of what a 0.4 correlation between these two variables would mean?

Just wondering...
posted by JamesJD to Science & Nature (18 answers total) 1 user marked this as a favorite

See Coefficient of Determination on Wikipedia.
posted by JakeWalker at 10:43 AM on October 19, 2009

If the correlation was zero, then if you knew someone's LSAT score you wouldn't be able to say anything about their first year grades; they would be like two completely random unrelated things. If the coefficient was 1.0 then if you knew someone's LSAT scores you could predict their first year grades with exactitude and certainty.
posted by Rhomboid at 10:53 AM on October 19, 2009

Correlation indicates the strength between two variables. In other words a correlation of 0.4 for LSAT scores and grades indicates that there is a positive linear relationship between the two. As LSAT scores increase so do law school grades.

Note that this does NOT mean that high LSAT scores necessarily cause higher law school grades. Correlation does not prove causation. There may be a third variable out there explaining the correlation between the two variables.
posted by dfriedman at 10:55 AM on October 19, 2009

I'm wondering about the magnitude of the 0.4. What percent of variation in first-year law grades would the LSAT explain given a correlation of 0.4.
posted by JamesJD at 10:56 AM on October 19, 2009

In plain-English: 0.4 correlation means that people with higher LSAT scores often have higher first year grades in law school.
posted by chrisalbon at 10:57 AM on October 19, 2009

correlation is % / 100, so correlation of 1 = 100%
posted by idiopath at 11:02 AM on October 19, 2009

Hey idiopath, so that would mean LSAT scores explain 40% of variation in 1L grades? Deeaaaumn.
posted by JamesJD at 11:06 AM on October 19, 2009

A correlation of 0.4 probably isn't even statistically significant, but it depends on the sample size. Basically it means that the LSATs don't predict the first year performance very well. And it means that 16% of the variance is explained by the model.
posted by 517 at 11:08 AM on October 19, 2009

I take that back, it probably is statically significant, even with alpha at 0.01. And the LSATs do explain some aspect of first year performance well.
posted by 517 at 11:20 AM on October 19, 2009

oh it's one of those days.
posted by 517 at 11:21 AM on October 19, 2009

I thought it was 16%...
posted by JamesJD at 11:22 AM on October 19, 2009

Here is an interactive correlation demo. Imagine that you are putting LSAT scores along the x axis, and first year grades along the y axis. You can see that with 0.0, it's just a random collection of dots. As the correlation increases, they become more closely grouped until at 1.0 it's a straight line.
posted by Rhomboid at 11:23 AM on October 19, 2009 [1 favorite]

Rhomboid gives a great demo. I don't think that LSAT scores "explain" any portion of your first year performance. That language seems to indicate that you're falling into the causality trap that dfried identifies. I think that it's better to think about an LSAT score as a predictor of where in the pack you're likely to fall.

To go out on a limb, I think that if you got a score solidly in the middle of the pack, then you're about 40% likely to get grades in law school that are in the middle of the pack. Even more out on a limb, as the number of people with the same score in your sample size increases you'll see a normal distribution around that score.
posted by hue at 11:50 AM on October 19, 2009

Correlation of 0.4 translates into 16% of variance explained. Whether that has any practical implications unfortunately depends on your point of view. 0.4 is considered high in the social sciences AFAIK, but very low in the natural sciences. Statistically, it might not be very meaningful given that the predictor is probably rather truncated (people with low LSAT scores do not go to law schools) and that the GPA is discrete with very few levels (from 2.0 to 4.0 in increments of 0.1 probably).

If you want you know what your chances of a 4.0 are given your LSAT score you need to engage in more advanced data-digging, which I would think the LSAT has done. The term you’re looking for is “predictive validity.”

Finally, an obligatory warning when discussing correlations – correlation does not imply causation.
posted by Dotty at 11:52 AM on October 19, 2009

So in some sense a correlation of 40% means that 16% (i.e. the square of the correlation) of the variance of first-year grades is explained by LSAT scores (or vice-versa). But there are many caveats. In particular:

- You don't know anything about the causal direction; and
- This assumes that the relationship between the variables is linear. If there is a different relationship between the variables (logistic, for instance) then it could be that the % of variance accounted for is actually higher than 16%.
posted by goingonit at 11:59 AM on October 19, 2009

Finally, an obligatory warning when discussing correlations – correlation does not imply causation.

Careful, Correlation implies some causal relationship, either A causes B, B causes A or C causes A and B. We know that grades can't cause higher LSAT scores in the past, so that relationship is foreclosed. Can higher LSAT scores, alone, cause higher grades? It's unlikely to have much of an effect (maybe through higher self-esteem? That wouldn't have much of an impact, I would imagine), so there is probably some third cause of both high LSATs and good grades.
posted by delmoi at 1:46 PM on October 19, 2009

Careful, Correlation implies some causal relationship, either A causes B, B causes A or C causes A and B.

No, there's a fourth option -- by sheer happenstance, A and B covary.
posted by ROU_Xenophobe at 2:13 PM on October 19, 2009

« Older I will not eat them in a bowl / I will not eat...   |   There's this song in my head. What is it? Newer »