Sunday, April 26, 2015

Math is math, except in social science

"So how are the eggs?" "Eggs are eggs." "Eggs are eggs. That is very profound. By the same token, couldn't you say fish is fish? I don't think so." 

So goes a Seinfeld dialog.  Similarly Sigmund Freud is alleged to have said, "Sometimes a cigar is just a cigar," although researchers question whether he really said it.

And by the same logic, math is math, whether it is taught in high school or college, a 2 year community college or a 4 year college, etc. Right?  I found a counter-example of this in statistics.

I recently taught an intro to statistics class in a psychology department using a statistics book for the behavioral sciences.  This book defines the sample standard deviation for descriptive purposes as SX with an N denominator while defining the sample standard deviation for inferential purposes as sX with an N-1 denominator.  I found a second statistics book for behavioral sciences that agrees with this.

Is there a recent textbook in the math or statistics world that defines the sample standard deviation with an N denominator?  I haven't seen it.  And not only will the student of this psychology class find this definition conflicts with the math world, but she will also find (and did find) it conflicts with the Excel world, not only for the Excel standard deviation function but for the Excel statistics Data Analysis add-in functions.

Why can't we all just get along?