“Statistics ist the explanation of variance in the light of what remains unexplained.”

Statistics was originally invented - as so many other things - by the famous mathematician C.F. Gauss, who said about his own work “Ich habe fleissig sein müssen; wer es gleichfalls ist, wird eben so weit kommen”. Even if your aspirations are not that high, you can get a lot out of statistics. In fact, if your work with real data, you probably won’t be able to avoid it. Statistics can

• Describe variation.
• Make quantitative statements about populations.
• Make predictions.

Books: There are a number of good books about statistics:

Douglas G. Altman. Practical Statistics for Medical Research. Chapman & Hall/CRC, 1999

This is my favorite stats book. It does not talk a lot about computers and modeling, but gives you a terrific introduction into the field. Many formulations and examples in this manuscript have been taken from that book.

R.H. Riffenburgh. Statistics in Medicine. Academic Press, 3rd edition, 2012 .

A more modern book, which is more voluminous and in my opinion a bit harder to read.

Daniel Kaplan. Statistical Modeling: A Fresh Approach. Macalester College, 2009

If you are interested in a simple introduction to modern regression modeling, check out

Dobson AJ & Barnett AG: “An Introduction to Generalized Linear Models”, 3rd ed, CRC Press(2008)

A very good introduction to “Generalized Linear Models”. If you know your basic statistics, this is a good, advanced starter into statistical modeling.

WWW: On the web, you find good very extensive statistics information in English under

• http://www.statsref.com/
• http://www.vassarstats.net/
• http://www.biostathandbook.com/
• http://onlinestatbook.com/2/index.html

A good German webpage on statistics and regulatory issues is http://www.reiter1.com/.

Exercises: Many examples are already solved in the text. For the use in lectures (or for self-test), additional exercises are provided at the end of most chapters. For lecturers, solutions to these exercises can be provided on demand. Please contact me directly for that via email.

PDF-Version: A complete PDF-version of this introduction is available from here

Why Statistics?

Statistics will help you to

• Clarify the question.
• Identify the variable and the measure of that variable that will answer that question.
• Determine the required sample size.
• Find the correct analysis for your data.
• Make predictions based on your data.

Without statistics, your interpretation of your data can be massively flawed. Take for example the estimated number of German tanks during World War II, also known as the German tank problem (http://en.wikipedia.org/wiki/German_tank_problem): from standard intelligence data, the estimate for the number of German tanks produced per month was \(1550\); in contrast, the statistical estimate from the tanks observed led to a number of \(327\), which was very close to the actual production number of \(342\).