Using Statistics [antikvár]

introduction Using Statistics is intended for a one- or two-semester course for students who have successfully completed at least one year of high school algebra. The book has been developed over several years as a cooperative project between the Department of Mathematics and the College of Education at the University of Illinois. That project, in turn, was based on fundamental work done by Professor Julian Simon at the University of Illinois, College of Commerce. Using Statistics can serve as an introductory course in statistical concepts, a course in mathematics for general education, or as a supplementary reference for innovative and challenging topics in computer mathematics. For a one-semester course, Chapters One through Six would be appropriate, with Chapters Seven and Eight as optional material. Chapters One through Twelve are appropriate for a two-semester course, with Chapters Thirteen and Fourteen as optional material. A grasp of the elements of statistics is essential for every educated citizen. This book presents these concepts in a simplified manner, minimizing the symbolism and formulas typically utilized in such a course but preserving the integrity of the fundamental concepts. A typical presentation of a concept involves the use of an interesting example, the conduct of an experiment or activity, the collection of data, and discussion of the data. The progression is usually from concrete experience to abstract concept formulation. A five-step procedure for solving probabilistic and statistical problems was devised at the University of Illinois and utilized successfully with students at a wide variety of ability levels. Overview of Content The book begins with elementary topics in descriptive statistics and in Chapters Three and Four presents key concepts of probability in a highly intuitive, experience-based manner, relying heavily upon laboratory activities. Chapter Five, Making Statistical Decisions, provides an elementary introduction to hypothesis-testing. The chi-square statistic is discussed in Chapter Six and is done by first discussing a "D" statistic. The D statistic has proved in our experimental classroom work to be easier to utilize to present the notion of correspondence between expected and obtained outcomes that is the chi-square. The other novel and pedagogically important feature of this chapter is that the distributions are developed initially from values generated as class activities. The curve-smoothing idea is utilized in order to arrive at theoretical chi-square distributions and tables. Bivariate statistics is introduced in Chapter Seven in an informal way, using the idea of a simple rule that relates two measures. There is sufficient material in this chapter to cover the basic notion of linear regression. However, more able students could cover Chapter Eight, as well, which leads to the standard formulations of the regression and correlation coefficients, but from the point of view of searching for the line that minimizes the error of prediction (estimation) of one variable from the other.