If I told you that only 26% of the population can demonstrate a basic understanding of calculus, and 63% of those are women, you might be surprised.  It would appear that calculus must be a niche specialty where women are well ahead of men.  You could not help but wonder how men have dominated the STEM fields for so long, given this apparently superior mathematical aptitude that women have. 

The truth is, both men and women are equally capable of advanced mathematical reasoning, and the above statistics are fictitious.  It is a proven fact that we find statements accompanied by precise numbers far more compelling than vague assertions.  We trust statistics, with little regard for how they were obtained.  A cautionary view is often attributed to Mark Twain (who himself credited British Prime Minister Benjamin Disraeli) – “There are three kinds of lies; Lies, Damned Lies, and Statistics.”  Statisticians have a language all their own, which only makes things worse.

A statistician approaching the aforementioned question of mathematical acuity would begin with a test of some sort and form a hypothesis – something like “There is no difference in standardized mathematical test scores based on gender.”  In stat-speak, this is the “null hypothesis.”  If the data showed no difference in test scores based on gender, you might say men and women are equally proficient at math.  A statistician, with an apparent aversion to commitment, would only say their study “failed to reject the null hypothesis.”  If nothing else, reading this paragraph should convince you that Mark Twain was on to something.  <continue reading>