# Statistics Companion #### Preface:

This little book is a helping hand to users of textbooks in statistics, which often, in relation to shape and size, resemble nothing more than a brick. This can be off-putting and for way to many students, their textbook in statistics literally remains a closed book.

During my teaching of statistics at the Aarhus School of Business and at the University of Southern Denmark I have received countless enquiries from frustrated students who got stuck with their textbook. Therefore, in 2004, I published my edited lecture notes and slides. The many positive responses I received from relieved students indicate that I may have hit the nail on the head.

The current book is a translation of the second edition of Statistik-hjælperen. I am especially grateful to IB student Adam Blatchley Hansen, for his corrections of my translation from Danish to English.

Statistics Companion – The Essential Guide to Statistical Textbooks is, as mentioned above, a helping hand to understanding “bricks”. It is not strictly speaking a textbook as it leaves out many of the less important things in order to keep the book from swelling up too much. The assumptions for use of the various probability distributions are often just listed without further discussion as these assumptions are dealt with in detail in the textbooks which the Statistics Companion is intended to support.

The most important concepts and subjects in theoretical statistics are explained in this book. Practical statistics or descriptive statistics – which is the basis for theoretical statistics – is briefly covered at the start of the book. Full-scale insights into the tools used for descriptive statistics are given in my book Descriptive Statistics (2010).

The Statistics Companion gives detailed instructions on how to use the spreadsheet Excel (version 2007) for statistics. Elementary previous knowledge in Excel is assumed. The statistics to be used in the exercises can be downloaded from the internet via www.swismark.dk.

Aarhus/Odense, September 2010
Erik M. Bøye

#### Contents:

Chapter  1  Statistical Method
Chapter  2  Measures of Location and Measures of Dispersion
Chapter  3  Probability Calculation
Chapter  4  Discrete Probability Distributions
Chapter  5  The Normal Distribution
Chapter  6  Sampling Distributions of the Sample Mean
Chapter  7  Confidence Intervals
Chapter  8  The Chi-square Distribution. Confidence Interval for the Variance
Chapter  9  Hypothesis Testing
Chapter 10 Comparison of Two Variances: F-Distribution
Chapter 11 Comparison of Two Means etc.
Chapter 12 Analysis of Variance
Chapter 13 Simple Linear Regression and Correlation
Chapter 14 Multiple Regression
Chapter 15 Chi-square Tests
Annex. Statistical Tables
Index