March 2014
Intermediate to advanced
306 pages
5h 47m
English
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Chapter 1
Statistical hypothesis testing
1.1 Theory of statistical hypothesis testing
Hypothesis testing is a key tool in statistical inference next to point estimation and confidence sets. All three concepts make an inference about a population based on a sample taken from it. Hypothesis testing aims at a decision on whether or not a hypothesis on the nature of the population is supported by the sample.
In the following we shortly run through the steps of a statistical test procedure and introduce the notation used throughout this book. For a detailed mathematical explanation please refer to the book by Lehmann (1997).
We denote a sample of size 
by 
, where the 
are observations of identically independently distributed random variables 
, 
. Usually some further assumptions are needed concerning the nature of the mechanism generating the sample. These can be rather general assumptions like a symmetric continuous distribution. Often a parametric distribution is assumed with only parameter ...
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