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/
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