Eric Bohlman wrote: > bill margolis <[EMAIL PROTECTED]> wrote in > news:[EMAIL PROTECTED]: > >> Howdy all, >> The elementary statistics textbook (which shall remain nameless) which >> we are using in class defines a normal distribution as a distribution >> that is symmetrical. >> >> Is this a very isolated case? How long have we been falsifying our >> concepts for the sake of the equationless society!? > > My experience has been that if I encounter any argument that asserts that > there is no such thing as bisexuality in human males, I will not have to > read very far before the author defines a "continuous distribution" in > terms roughly corresponding to "symmetric," and then asserts that all > distributions are either symmetric or dichotomous (though without using > either term). I've actually seen, flatly stated, "if a distribution can > take on more than two values, then most of the population has to be in the > middle." > > More generally, these types of confusion seem to be based on the logical > fallacy of affirming the consequent, or what I consider to be the > probabilistic analog of the fallacy, namely confusing P(A|B) with P(B|A). > And both of those fallacies would be *much* harder to commit if people > merely had a grasp of extremely *elementary* set theory. > > I think you're shirking your moral duty by not naming the textbook . Alas, it is in a book that I absolutely love, and recommend especially for all our mathophobes who are reluctantly required to take a statistics course, and it is filled with incredibly interesting data, namely: Bachman & Paternoster's Statistics for Criminology and Criminal Justice, 2nd edition. Please do not be put off by the title: in my experience, new students of statistics NEED interesting and concrete data, and there is nothing quite so juicy as crime statistics ;) And, the chapters on bivariate and multivariate analysis are quite gentle and patient with the beginning student.
However, I am embarrassed to see statements in Chapter 3: "For statistical purposes, one important shape of a continuous distribution is normal". Then, what I take and what I assume the student will take as a definition (since the term normal distribution appears in bold): "A normal distribution is a distribution which is symmetrical, which means ... It is followed by other shape properties: A normal distribution has a single peak in the middle ... with fewer cases as you move away from this middle". Well, we could all grudgingly accept this as ascribing some true properties, but sort of like saying: an American citizen is a vertebrate. Unfortunately a following paragraph begins: "When a distribution departs from normality it is said to be skewed." Suddenly some of our favorite symmetric but not normal distributions have suddenly been classified as skewed ;) Avoiding this inference requires us to accept symmetry as just about defining the normal distribution. A later chapter (chapter 6) does introduce the proper family of exponential curves to (re)define normal distributions. But, it does appear that some minor warnings do need to be sounded, until then... -Bill. -- -Bill . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
