Elementary Statistical Methods

This book is mainly based on lectures given by Professor D. R. Cox and myself at Birkbeck College over a period of eight to nine years. It began as a joint venture, but pressure of other work made it necessary for Professor Cox to withdraw early on. I have throughout received much valuable advice and encouragement from Professor Cox, but of course, I am solely responsible for the text, and any errors remaining in it. The book is intended as a first course on statistical methods, and there is a liberal supply of exercises. Although the mathematical level of the book is low, I have tried to explain carefully the logical reasoning behind the use of the methods discussed. Some of the exercises which require more difficult mathematics are marked with an asterisk, and these may be omitted. In this way, I hope that the book will satisfy the needs for a course on statistical methods at a range of mathematical levels. It is essential for the reader to work through the numerical exercises, for only in this way can he grasp the full meaning and usefulness of the statistical techniques, and gain practice in the interpretation of the results. Chapters 7 and 8 discuss methods appropriate for use on ranked or discrete data, and Chapters 9-12 do not depend on these chapters. Chapters 7 and 8 may therefore be omitted, if desired. Front Matter....Pages iii-xiii Introduction....Pages 15-46 Probability and Probability Distributions....Pages 47-78 Expectation and its Applications....Pages 79-100 Sampling Distributions and Statistical Inference....Pages 101-128 Single Sample Problems....Pages 129-145 Two Sample Problems....Pages 146-161 Non-parametric Tests....Pages 162-176 The Analysis of Discrete Data....Pages 177-215 Statistical Models and Least Squares....Pages 216-223 Linear Regression....Pages 224-244 Multiple Regression....Pages 245-262 Analysis of Variance....Pages 263-297 Back Matter....Pages 298-346