By Arnold Kling
I try to use the 2000 election in Florida and the question of Iraq’s weapons of mass destruction to illustrate statistical concepts.
In statistics, a parameter (not to be confused, as it is often is by laymen, with perimeter), is an unknown quantity. In this case, the unknown quantity might be described as “the proportion of voters in Florida who intended to vote for Gore when they cast their ballots.” This parameter is unknown for a variety of reasons. Partially-punched ballots made voters’ intentions less than clear. Moreover, even if there had been no “hanging chad” issues with the vote counting, the “butterfly ballot” raised the question of whether voters intending to vote for Gore wound up accidentally voting for Buchanan.
My article also describes Type I and Type II error.
On another statistical topic, Stephen T. Ziliak and Deirdre N. McCloskey contrast material significance with statistical significance.
a merely statistical significance cannot substitute for the judgment of a scientist and her community about the largeness or smallness of a coefficient by standards of scientific or policy oomph…
Of the 137 relevant papers [published in the American Economic Review] in the 1990s, 82% mistook statistically significant coefficients for economically significant coefficients.
When I teach Advanced Placement statistics in high school, I like to give an exam question in which students are asked “as a statistician” to recommend a diet pill to a relative. One pill has reduces weight on average by 20 pounds with a standard deviation of 10 pounds, and another pill reduces weight on average by 4 pounds with a standard deviation of 1 pound. The second pill achieves results that are more significant statistically. However, the first pill achieves results that are more significant materially.
For Discussion. In the diet pill example, how high would the standard deviation have to be on the first pill in order to lead you to recommend the second pill?