HaHaHa!

http://en.wikipedia.org/wiki/Phrenology

Posted by underthechestnuttree from LaSalle, Ontario, Canada on 08/21/08 at 11:35 AM ET

These people obviously never took a statistics class. Their numbers are extraordinarily inconclusive to be published. It looks like there’s a greater probability of no correlation whatsoever than a positive correlation.

Posted by Muéro on 08/21/08 at 02:54 PM ET

I’m not really a super-stats-man, Muéro, but I don’t think that’s the case.

A low correlation coefficient implies a weak correlation, not that no correlation exists.  There are plenty of examples of very real weak correlations.  A poor example off the top of my head might be the correlation between draft position and career points for hockey players--an early pick won’t always do well, but he’s statistically more likely to than a later pick.

If there were no correlation, one would expect a study of a random hockey team to find a positive correlation roughly 50% of the time.  They only looked at six teams, but each had a positive correlation.  This gives us a (very rough estimate of the) p-value of about 3.1%.  Or in other words, if there really is no correlation, the probability of getting a result this unlikely is about 3.1%--pretty low.  Basically, there’s a good chance that some correlation exists.

P.S. This isn’t a real statistical analysis, which would take too much time and research for me to do.  It’s only meant to be instructive.  Don’t mistreat it.

Posted by Ryan from Toronto on 08/21/08 at 06:46 PM ET

A low correlation coefficient implies a weak correlation, not that no correlation exists.  There are plenty of examples of very real weak correlations.

You’re right, Ryan.

A correlation coefficient can be thought of roughly as how much of the variability observed in a parameter Y (penalty minutes) is explained or associated with the variability in X (face width).  A positive number indicates that the two parameters vary in the same direction - as one increases, so does the other.  The number close to zero (which would mean no correlation whatsoever) indicates that the variability in face width only “accounts for” a small proportion of the variability in penalty minutes, with the rest of the variability in penalty minutes accounted for by other factors.

A low number does not mean a weak correlation in the sense of being inconclusive - there are other statistical tests for that (strength of relationship), and I’m sure those are covered in the original paper.  Most people are clueless about stats so they never make it into something intended for general readership like a newspaper without being a bit distorted.

Posted by Baroque from Michigan on 08/21/08 at 11:13 PM ET

A correlation coefficient can be thought of roughly as how much of the variability observed in a parameter Y (penalty minutes) is explained or associated with the variability in X (face width).  A positive number indicates that the two parameters…

Dear God, let’s get this season started before we all go mad.

Posted by OlderThanChelios from Grand Rapids on 08/22/08 at 11:16 AM ET

Dear God, let’s get this season started before we all go mad.

What?  Did I screw up the definition somewhere? 

Posted by Baroque from Michigan on 08/22/08 at 01:03 PM ET