## Statistics, Volume 1: A Toolkit for Empiricists (The Empiricist's Toolkit)

### Gordon Bear Ph.D.

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A textbook written for college courses in statistics and class-tested extensively at Ramapo College of New Jersey. In my book I teach statistics not as mathematical theory but as techniques useful for solving problems that arise in empirical research. My book is unusual, even unique, in several ways: 1. It is lengthy - divided among three volumes - and thus rich and complete. It does not require a teacher to explain the contents and augment them; it states everything required for full mastery of the subject matter. 2. It teaches statistics in the context in which it is applied: the analysis of data (observations). Throughout the book I accordingly emphasize the functions that statistical techniques serve, and I show how these functions vary from one kind of investigation to another (Bear, 1994, 1995). The reader comes to appreciate three fundamental points: (a) In sample surveys, statistics serves the purpose of generalization, permitting us to extrapolate from a sample to its parent population. (b) In experimentation, statistics serves the purpose of comparison, assessing the differences among the batches of observations collected in the several conditions. (c) In correlational work, statistics serves the purpose of association, detecting clustering and covariation in the variables under observation. 3. I present all techniques for categorical data (classifications such as yes or no, male or female) before the techniques for numerica data (scores). The advantages are threefold: (a) Because the mathematics of categorical data is simpler than that of numeric, the reader is less burdened with mathematics at the beginning of the book, and the review of mathematics that so many of today’s students require can be more leisurely. (b) Because the descriptive techniques for categorical data are simple, the book quickly progresses to the most interesting—and challenging—topics, the inferential techniques that reckon with chance in interpreting data. (c) Because the later section on numeric data covers techniques of the same kind that the earlier section on categorical data does—techniques for univariate and bivariate description plus inferential devices for generalization, comparison, and association—the reader goes through the logic of these techniques twice. The second pass at the material reviews and consolidates the information studied earlier. 4. I acknowledge what many other textbooks do not: Most experiments and most correlational studies fail to select their subjects by means of random sampling. Instead of condemning such studies or pretending that statistical techniques predicated on random sampling are still appropriate for them, I show how research can be informative absent random sampling, and I present the techniques truly appropriate to experiments: randomization tests (Edgington & Onghena, 2007), which few other books teach. I accordingly devote little attention to the t test, and I show that in most applications the chi-square test must be understood as an approximation to a randomization test such as Fisher’s Exact Test. For correlational data absent random sampling, I endorse Clifford Lunneborg’s procedures (1996, 2000), which test for what he calls stable description, a matter of internal consistency. These too are missing in conventional treatments of statistics. 5. My book is not a technical manual. It addresses larger issues: the limits of empiricism, pitfalls in gathering data by questioning people, ethical considerations that arise in experimentation, and numerous other matters of concern to educated people and thoughtful citizens. Here and there my reader also encounters enrichment: a note on the Latin origin of the words matrix and matriculation, for example; a brief description of the computerized interviews that politicians use in overnight polling; two paragraphs on the unique power of mathematics to model reality; a quick history of the SAT and the controversies it has sparked; and much more.

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