Applied Statistics

Preface

We wrote this book for people that have to apply statistical methods in their research but whose main interest is not in theorems and proofs. Because of such an approach, our aim is not to provide the detailed theoretical background of statistical procedures. While mathematical statistics as a branch of mathematics includes definitions as well as theorems and their proofs, applied statistics gives hints for the application of the results of mathematical statistics.

Sometimes applied statistics uses simulation results in place of results from theorems. An example is that the normality assumption needed for many theorems in mathematical statistics can be neglected in applications for location parameters such as the expectation, see for this Rasch and Tiku (1985). Nearly all statistical tests and confidence estimations for expectations have been shown by simulations to be very robust against the violation of the normality assumption needed to prove corresponding theorems.

We gave the present book an analogous structure to that of Rasch and Schott (2018) so that the reader can easily find the corresponding theoretical background there. Chapter 11 ‘Generalised Linear Models’ and Chapter 12 ‘Spatial Statistics’ of the present book have no prototype in Rasch and Schott (2018). Further, the present book contains no exercises; lecturers can either use the exercises (with solutions in the appendix) in Rasch and Schott (2018) or the exercises in the problems mentioned below.

Instead, ...