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, our aim was to demonstrate the theory presented in Rasch and Schott (2018) and that underlying the new Chapters 11 and 12 using functions and procedures available in the statistical programming system R, which has become the golden standard when it comes to statistical computing.

Within the text, the reader finds often the sequence problem – solution – example with problems numbered within the chapters. Readers interested only in special applications in many cases may find the corresponding procedure in the list of problems in Appendix A.

We thank Alison Oliver (Wiley, Oxford) and Mustaq Ahamed (Wiley) for their assistance in publishing this book.

We are very interested in the comments of readers. Please contact:

d_rasch@t‐online.de, [email protected], [email protected].

Rostock, Wageningen, and Klagenfurt, June 2019, the authors.

References

1. 1985 Rasch, D. and Tiku, M.L. (eds.) (1985). Robustness of statistical methods and nonparametric statistics. In: Proceedings of the Conference on Robustness of Statistical Methods and Nonparametric Statistics, held at Schwerin (DDR), May 29‐June 2, 1983. Boston, Lancaster, Tokyo: Reidel Publ. Co. Dordrecht.
2. 2018 Rasch, D. and Schott, D. (2018). Mathematical Statistics. Oxford: Wiley.