Interpreting a Correlation

Date: 08/06/2004 at 12:40:57
From: Debbie
Subject: correlational statistics

I'm doing a research project and I found that I have a correlation of 
0.60 between teacher attire and student academic performance across 
150 grade schools in my state.  Since 0.60 is a significant positive
correlation, this seems to indicate that encouraging teachers to be
properly attired will increase academic performance.

I think my conclusion is accurate, but there may be other variables
involved.  Do you agree with my conclusion?

Date: 08/06/2004 at 13:05:17
From: Doctor Douglas
Subject: Re: correlational statistics

Hi, Debbie.

Thanks for writing to the Math Forum.

Although your conclusion seems to be reasonable, it's certainly not 
the only reasonable explanation.  For example, it could be that
students in schools that do well somehow "encourage" their teachers
to dress better.  

The mistake that you are making is to infer that because two variables
are correlated, one necessarily causes the other.  It could be that
variable X affects Y, or Y affects X, or both are affected strongly by
some other variable Z.  And there are other possibilities as well,
including simple chance.

Your conclusion is that teacher attire (X) leads to an increase in
student performance (Y).  But perhaps a teacher with high-performing
students feels positively about himself or herself, and this gets
reflected in how they dress (Y affects X), or perhaps schools in 
wealthier communities (with students that do better) also are staffed
by teachers that dress better (Z affects Y and X).

There is a well-known phrase that is used to describe this situation:
   
  "correlation does not imply causation"

I hope that this helps.  Please write back if you have more questions
about this.

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/