Unit 5: Thinking Statistically
NOTE: This guide supercedes the one in the book. The version in the textbook (written in December 1999) is not inaccurate, but is a little imprecise. To be a little more precise, the tests for Unit 5 will consist of two kinds of questions:
These are multiple choice questions of the variety: "circle all that apply". Sometimes you might have to circle every answer following the question; sometimes you will circle none. The material for them is drawn entirely from the descriptions of the fallacies found in the Philosophy and Logic textbook. Pay particular attention to (a) understanding the following technical concepts:
These were listed in the study guide in the textbook. I won’t ask you for the definitions of any of these terms, but you should definitely understand what they mean. Be sure you understand the notions of sampling, of measurement, and of probable error.
In addition, the multiple choice questions will focus on: (b) the necessary and sufficient conditions for committing a particular kind of fallacy; and (c) the distinctions between different kinds of fallacies. As examples of (b), you might be asked about the problems of using a biased sample, or why the mean is the wrong kind of average to use in a skewed distribution. As an example of (c), you almost certainly will be asked about the distinction between "ignoring dispersion" and "ignoring probable error". Study the descriptions of the different fallacies very carefully: all the answers are found in them!
Darrell Huff’s book is quite good at providing vivid examples that make the technical notions easier to understand. In my textbook I cite page numbers of various examples found in Huff. They are very much worth looking up!
There aren’t any exact duplicates of the multiple choice questions from the test in the textbook, but try exercises 5.1 - 5.4 on the fundamental notions of sampling.
Some passages commit more than one error; you need identify only one. (See the "important note about these problems" at the beginning of section 5.7.) Note that the error you cite must be an error that is definitely present in the passage; it cannot be one which is merely possible, given the text; or one which the text merely fails to definitively rule out. These errors have names, and you should be able to name each kind of error.
It is hard to learn them all. Section 5.7 gives a summary: a checklist to use to detect deviations from healthy statistical inference. But then you simply need to practice on lots of examples.
The critical exercises: 5.5 through 5.8. Exercises 5.6 through 5.8 are actual items from old tests on statistical fallacies. (5.5 has good items too, but I have never used them in a test.)
Fallacies identified with asterisks ("converse accident", for example) are less common and more technical, and are included here for the sake of completeness and to help you understand Huff. But you will not be responsible for the ones with asterisks, and I won’t ask questions about them in tests (in either part 1 or part 2).
Recommended sections from Patrick Hurley’s Concise Introduction to Logic:
This is the optional but recommended text for this course, and it has some useful exercises for this unit.
Section 9.4, Statistical Reasoning, p 545-62, has a useful description of sampling, probable error (under the label "sampling error"), dispersion, types of averages, and other core concepts for part 1 of our test. Exercise 9.4, p 563, part I is good practice for our part 2; his part III is good practice for our part 1. (Unfortunately these exercises are not on the LogicCoach CD Rom.)
Section 9.2, Causality and Mill’s Methods, p. 505, provides considerable supplementation to my description of making causal inferences. If you want to understand how to avoid the post hoc fallacy, I recommend reading this section, though our tests do not cover Mill’s methods.