<p>R^2 values are not the measure of linear correlation. The R (EMPHASIS HERE) is the measure of linear correlation, with a value of 1 being a perfect linear correlation.</p>
<p>So the correlation is VERY strong, which makes sense because people don't magically get smarter during college.</p>
<p>r=.5, .54, and .6. those are mediocre at best.</p>
<p>Shiboing Boing,</p>
<p>Well...no. The square of r is conventionally used as a measure of the association between x and y as told by a regression line. The corellation coefficient itself (r) is also useful, but like sreis pointed out, .5, .54., and .6 aren't terribly strong (even in social science regression analysis).</p>
<p>But let's use an example. .5 is .25 when squared. That means that only .25 of the variance between x and y can be accounted for by x and the linear changes in x and y.</p>
<p>Both r and r^2 are useful measures, but in this case, since I'm interested in the variance, I used r^2.</p>
<p>Here is some more information on this question from a good source. Scan to near the bottom of the page: </p>
<p><a href="http://www.unm.edu/%7Epre/law/lsat_prep.html%5B/url%5D">http://www.unm.edu/~pre/law/lsat_prep.html</a></p>
<p><em>yawn</em></p>
<p>An r value of .5-.6 is quite strong. Combined, both parts of the SAT give a predictive linear model that has a correlation of .6. This value is enough to invalidate any null hypothesis test that there is not a correlation between SAT and LSAT performance.</p>
<p>There obviously is. In social sciences a correlation of .6 between 2 simple variables is usually cause for more investigation. Because performance on the SAT and LSAT are dependent on so many measures, there isn't perfect correlation of course but not many things, if any, are perfect correlated in real life.</p>
<p>There is a real relationship there and it is obvious that an SAT score can be used as a fair predictor of your LSAT score. You can argue tiny, quibbling details all day, about just how strong this relationship is, but numbers don't lie, and if people are more curious about the question they should read up on what linear correlation is, how sample size affects the generalizability of a model, and the various ways of getting false positives instead of listening to random people online banter back and forth.</p>
<p>.5 to .6 is quite strong? Are you kidding me? At an r value of .6, we can only predict only approximately 36% percent of the variation of the y values. That's not that strong. </p>
<p>I'm not denying that there is a correlation, but looking at the scatterplot alone tells us that it's a weak relationship. </p>
<p>
[quote]
You can argue tiny, quibbling details all day, about just how strong this relationship is, but numbers don't lie, and if people are more curious about the question they should read up on what linear correlation is, how sample size affects the generalizability of a model, and the various ways of getting false positives instead of listening to random people online banter back and forth.
[/quote]
</p>
<p>Do you have proof of this relationship other than that site?</p>
<p>
[quote]
but numbers don't lie
[/quote]
</p>
<p>Numbers don't, but the people manipulating them do. We don't even know everything behind the sampling method used to procure that data.</p>
<p>It's also important to remember that a relationship can be strong but not significant. Furthermore for small samples, it is easy to produce a strong correlation by chance-- you have to pay attention to significance. You don't want to end up rejecting a true null hypothesis.</p>
<p>It's not as easy as looking at a sample of LSAT/SAT scorers, seeing an r^2 of .36, and saying, "Ahhah! The correlation explains it all!"</p>
<p>I'm not denying that there's a correlation. That's obvious. I'm denying the causality of it all. It's VERY hasty to jump to any conclusions based on this data.</p>
<p>I never said there was causality. I just said that a correlation will give you an idea of what your LSAT score would be. Obviously since the correlation is "only" .6, the 95% probability range will be quite large.</p>
<p>But in general, at least for my 20+ friends that have scored in the top 3 percent, I have seen a decent enough relationship between SAT scores and LSAT scores. 1500's top out around 170. And the only other 178+'s I knew all had 1600 and 1590's on their SAT (though one 1600 also got a 170). Since there are no random, large-sample studies out there, you gotta work with what you got.</p>
<p>It's interesting to hear two people with experience in statistics debate these issues. A few thoughts from a math-challenged bystander:</p>
<p>The sample size in that single geocities analysis is really small. (In fact, we don't even know for sure if those are real scores or just a problem set for someone's statistics class.) </p>
<p>I'm inclined to believe the advice that the University of NM Law School is giving their applicants--in effect a kind of meta-analysis: some studies suggest a correlation between SAT/LSAT. That's consistent with the numbers in that geocities analysis: significant correlation, but not an overpowering one.</p>
<p>Context is everything: The r^2 value for SAT-I/SATII in a recent study was .77. The r^2 value for SAT-I/first-year college GPA is usually measured at < .2-something, depending on the study; yet only the most strident critics of the SAT argue that it doesn't give some incremental criterion validity within the admissions process. The SAT/LSAT correlation appears to be in between, but closer to the SAT/GPA end of the spectrum. </p>
<p>Maybe time to call it a draw?</p>
<p>Shiboing Boing,</p>
<p>Oh, far be it for me to say that there's absolutely NO correlation. .6 is not awfully weak, but, as I've been arguing it's not really that strong. It's solid enough that we can say, "hmm...that's interesting." But looking at the scatterplot gives me a feeling that the relationship, while linear, is not that predictive. Furthermore, we have to be careful with how the tests has changed, time intervals between both tests, preparation, etc. I'd be MUCH more interested in a data set that factored in prep.</p>
<p>
[quote]
Maybe time to call it a draw?
[/quote]
</p>
<p>Meh. I think we ended up arguing different things.</p>
<p>My opinion- standardized testslike the SAT, GMAT, GRE, LSAT, etc are all cut from the same mold, and are all modified IQ tests and the scores can all be correlated to IQ. These tests a way for colleges to screen for high IQ's in their admissions process. </p>
<p><a href="http://members.shaw.ca/delajara/GREIQ.html%5B/url%5D">http://members.shaw.ca/delajara/GREIQ.html</a></p>
<p>Everyone keep in mind that those statistics are not right for the current SATs. We don't need anymore hugely inflated egos.</p>
<p>To convert, subtract ~80 points from the current SAT to estimate the pre 1995 SAT composite score.</p>
<p>
[quote]
To convert, subtract ~80 points from the current SAT to estimate the pre 1995 SAT composite score.
[/quote]
</p>
<p>oh... so if, say, someone scored a 2400 on the SAT, then a 2320 is his actual recentered score, which gives him an IQ of above a 168 [roll eyes].</p>
<p>Don't be smug, speds. Had you actually clicked the link, you'd see that the SAT in question was pre-writing addition.</p>
<p>I was being facetious.</p>
<p>Oh, and you used "smug" incorrectly.</p>
<p>
[quote]
To convert, subtract ~80 points from the current SAT to estimate the pre 1995 SAT composite score.
[/quote]
Are you serious? I'm not sure that comparison can be made. If yes, well I'm way smarter than any real IQ test has put me at.</p>
<p>Check out this page- It converts SAT to GRE to IQ, you have to scroll to the bottom.</p>
<p><a href="http://hem.bredband.net/b153434/Index.htm%5B/url%5D">http://hem.bredband.net/b153434/Index.htm</a></p>
<p>I stand corected, it's more like 90-100 points.</p>
<p>The correlations in the charts don't take account of male versus female SAT scores at 18 versus 22 or so (although few take the SAT at 22, obviously). Males keep developing physically and mentally somewhat longer than females, on average, so their SAT scores may be lower at 18 than they would be a few years later. That would lessen the correlations with the LSAT as they are shown in the charts at geocities, in other words, the correlation might actually be higher. That seems to be consistent with anecdotal evidence in this thread, at least.</p>
<p>Statisticians in this crowd might have a better way to make this point.</p>