This book has as main objective to provide basic statistical theory for a course which intends a nonmathematical approach to statistics. It gives a distinctive treatment and exposure of modern statistical subjects through sixteen chapters.
In the first chapter the key ideas of statistics are introduced. The role of statistics in nowadays activities precedes the introduction of the concepts of descriptive and inferential statistics, sampling and experimental design among others. The second chapter gives an account of methods for the organization and description of the data. The types of data and the descriptive methods are presented through very well selected examples from different scientific and economical areas. Various graphical display methods are given such as the classic line and dot diagrams and histograms. The measures of frequency distribution, location and accuracy are presented following their useful roles in practice.
The third chapter tackles the description of bivariate data. It is in some scale an introduction to the use of chi-square and correlation- regression analysis. Bivariate frequency tables and scatter plot diagrams are introduced. The correlation coefficient and the linear regression are studied as descriptive statistics.
Chapter four is devoted to the introduction of the basic ideas of probability theory. This chapter is particularly attractive because the relation between statistical reasoning and probabilistic points of view is fixed with great skill. The different approaches to probability theory are given through a concise presentation and intuitive appealings based on examples from real life. The definitions of probability distributions, related concepts, properties of distributions, and discrete random variables are presented in Chapter five. Then the binomial distribution is presented in Chapter six as a probability model of a discrete probability distribution. The study goes from the distribution problem up to testing hypotheses about the theoretical proportion. Therefore the student deals with the ideas of statistical hypotheses and their tests by establishing the frame for analyzing certain binomial problems. The simplicity of this analysis should fix useful ideas for dealing with the general problem. Chapter seven is dedicated to the presentation of the probability model of a continuous random variable and its main properties. The role of location parameters, such as the mean, the median and the percentiles, is fixed by analyzing different density functions. The method of presentation permits to fix their roles without using common mathematical analysis. Then, the normal distribution appears as a particular case. It is remarkable that some methods for evaluating the normality of the data and some transformations for attaining it are given.
The next step is to introduce inferential statistics and it is made with great skill in Chapter eight through the ideas given in examples. The validity of the central limit theorem and its meanings are fixed by the use of simulation experiments. Therefore the inferences about the mean, the proportion and standard deviation, when they are studied in Chapters nine and ten, are not completely new ideas. They are the logical end of a reasoning line which has begun in Chapter six. The test of hypothesis of parameters of two populations is introduced and the use of matched-pairs based methods is also presented. The decision of using a matched sample or an independent one is discussed. This is an unusual and delightful approach for presenting the two means test problem. Both large sample and small sample problems are presented.
The regression problem is taken up again in Chapter twelve. Now an inferential approach is used. The statistical model is fixed, as usual, and the inferential properties and methods are characterized. The following chapter tackles the nonlinear as well as the multiple regression model. Another distinctive feature of this book is that of checking the residuals as a mean for fixing the adequacy of the linear regression model. The use of chi-square tests is presented in Chapter fourteen through the goodness-of-fit and contingency tables problems and Chapter fifteen is devoted to the analysis of variance of one-way classification. The last chapter presents the most commonly used non- parametric alternatives to ”two treatment comparisons” and ”rank- correlation coefficients”. The aims of distribution-free tests are discussed with charm.
Throughout the exposition a great quantity of examples is used for fixing ideas and illustrating the behaviour of the models. Different graphs and plots encourage to go deep into statistical ideas. The use of MINITAB as a computational tool and its use in statistical analysis is introduced from Chapter two on. A considerable amount of exercises is given in each chapter and some solutions to them are worked out. Two appendices permit to work out some theoretical aspects and present statistical tables.
This is a remarkably good textbook which I highly recommend for university courses for non-mathematicians. It is particularly good for statistical courses in the social sciences area.