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This book describes the probability theory associated with frequently used statistical procedures and the relation between probability theory and statistical inference. The first third of the book is dedicated to probability theory including topics relating to events, random variables, and the Central Limit Theorem. Statistical topics then include parameter estimation with confidence intervals, hypothesis testing, chi-square tests, t tests, and several non-parametric tests. Flow charts are frequently used to facilitate an understanding of the material considered. The examples and problems in the book all concern simple data sets which can be analyzed with a simple calculator; however, the R code required to complete many examples and problems is provided as well for those that are interested.
List of contents
I INTRODUCTION.- 1 Statistics and probability theory.- II PROBABILITY THEORY.- 2 Events.- 3 Probabilities of events.- 4 Probability: One Discrete Random Variable.- 5 Many Random Variables.- 6 Continuous Random Variables.- III STATISTICS.- 7 Introduction.- 8 Estimation of a parameter.- 9 Testing hypotheses about the value of a parameter.- 10 Testing for the equality of two binomial parameters.- 10 Testing for the equality of two binomial parameters.- 11 Chi-square tests (i): tables bigger than two-by-two.- 13 Tests on means.- 14 Non-parametric tests.- Useful charts.- Solutions to problems.
About the author
Warren Ewens is an Emeritus Professor of Biology at the University of Pennsylvania. His research interests focus on the use of Statistics in genetics, in particular in describing the evolutionary process in genetical terms and in DNA sequence analysis.Katherine Brumberg is a PhD candidate in Statistics and Data Science at the Wharton School of the University of Pennsylvania. Her research interests focus on causal inference, in particular attaining optimal covariate balance in observational studies.
