Benjamin Disraeli coined the phrase “Lies, damn lies, and statistics,’’ and the phrase (as well as the sentiment) has last- ed—though I like “Truths, half-truths, and statistics’’ bet- ter. In any case, even relatively simple applications of statis- tics can cause problems, not to mention the horrors associ- ated with things like the often misinterpreted SPSS com- puter software (Statistical Programs for the Social Sciences).Probability and statistics, like geometry and mathemat- ics in general, come in two flavors: pure and applied. Pure probability theory is a formal calculus whose primitive terms are uninterpreted and whose axioms are neither true nor false. These axioms originally arise from and are made meaningful by real-life interpretations of terms like “prob- ability,’’ “event,’’ and “random sample.’’ The problem with applying probability and statistics is often not in the formal mathematical manipulations themselves, but in the appro- priateness of the application, the validity of the interpreta- tion, and indeed the “reasonableness’’ of the whole enter- prise. This latter activity goes beyond mathematics into the sometimes murky realm of common sense and the philoso- phy of science (grue-bleen, ravens, etc.). Even though 1 plus 1 equals 2, one glass of water plus one glass of popcorn does not equal two glasses of mixture. The mathematics is fine, the application is not.