A Course in Statistics with R

Preface

The authors firmly believe that the biggest blasphemy a stat reader can commit is the non-reading of texts which are within her/his mathematical limits. The strength of this attitude is that since mathematical limits are really a perception and consequentially it would be in a decline with persistence, and the reader would then simply enjoy the subject like a dream. We made a humble beginning in our careers and proceeded with reading books within our mathematical limits. Thus, it is without any extra push or pressure that we began the writing of this book. It is also true that we were perfectly happy with the existing books and the purpose of this has not arisen as an attempt to improve on other books. The authors have taken the task of writing this book with a view which is believed to be an empirical way of learning computational statistics. This is also the reason why others write their books and we are not an exception.

The primary reason which motivated us to pick up the challenge of writing this book needs a mention. The Student's t-test has many beautiful theoretical properties. Apart from being a small sample test, it is known to be the Uniformly Most Powerful Unbiased, UMPU, test. A pedagogical way of arriving at this test is a preliminary discussion of hypothesis framework, Type I and II errors, power function, the Neyman-Pearson fundamental lemma which gives the Most Powerful test, and the generalization to the Uniformly Most Powerful test. It is after this ...