Statistics: Principles and Methods

As is customary in introductory statistics textbooks, this book is organized into three parts: descriptive statistics, probability and inferential statistics. Part I (Chapters 2 through 11) deals with: summarizing data with tables and graphs; measuring central tendency, variability and shape of univariate data; measuring association in contingency tables; fitting a straight line and measuring correlation in bivariate data. Part II (Chapters 12 through 17) presents the essentials of probability theory: probability of events; discrete and continuous random variables; probability distributions of some special univariate random variables; joint probability distributions of bivariate random variables; law of large numbers and central limit theorem; probability distributions of sample statistics (with special reference to the sample mean and the sample variance). Part III (Chapters 18 through 23) includes: point estimation; confidence intervals and hypothesis testing with a focus on the population mean and variance; inference on the means and variances of two populations; chi-square test for goodness of fit, independence between two categorical variables, and homogeneity of multinomial populations; inference on the simple linear regression model. Compared to other introductory statistics textbooks, the choice of paying greater attention to descriptive statistics is based on the conviction that it is important to provide students with the basic knowledge and skills to manage raw data and produce useful summary statistics. Previous knowledge in this area, possibly gained at the secondary school level, is thus enhanced and systematized, fostering the comprehension of concepts pertaining to probability and inference. Indeed, many properties of frequency distributions have conceptual counterparts in the probability distributions of random variables, and fitting a straight line to a series of bivariate observations (to approximately describe the linear relationship between two variables) is beneficial to the study of the inferential procedures for the simple linear regression model.