All are welcome to attend the following seminar, 6pm
Monday 1st February, in room 4Q68 at the University of the
West of England, Bristol. There will be tea and coffee at
5:30pm in 4Q68.
Alternatives to the usual Hypothesis Testing
Dieter Rasch
Subdepartment of Mathematics
Wageningen Agricultural University
Paper presented at 1.2.1999 at the
University of the West of England in Bristol
1 Introduction
We consider the situation in a one-way ANOVA model I i.e. with
a fixed factor A with a > 2 levels A1, ..., Aa. The model
equation is
yij = µi + eij i = 1, ..., a, j = 1, ..., ni 1 (1)
with the usual assumption of i.i.d. eij with E(eij) = 0, V(eij)
= 2 and .
Very often researchers believe that a natural experimental
question is that of testing whether the µi are equal or whether
they are different. But during the discussion between the
researcher and a statistical consultant the latter may put the
question "why do you like to know whether the µi are different"?
Not seldom the answer is "Because I like to select the treatment
(factor level Ai) with the largest µi".
Very often the researcher has to act anyway if the experiment is
done. That means he has to select one of the Ai and use it in
practice. And this must be done as well as
- there is a difference between the µi
as also if
- there is no difference between the µi.
But to make a decision between the two possibilities just
mentioned, the observations are used to select one of a whole
collection of multiple comparisons like
- the F-test ( , experimentwise)
- the Tukey test ( experimentwise, comparisonwise)
- the multiple t-test ( , comparisonwise)
These tests have two possible outcomes namely the statements
- the null hypothesis (or hypotheses) of equal µi is (are)
accepted
- the null hypothesis (hypotheses) is (are) rejected.
Both statements can be wrong. It is the aim of this paper to show
that a multiple comparison is not an adequate approach to solve
the problem of selecting the Ai with the largest µi. A selection
problem should be treated by a statistical selection procedure.
We will give a brief introduction to "Bechhofer's indifference
zone approach" in Section 2. Finally in Section 3 a short
introduction to equivalence testing is given by a simple example.
Also this may be considered to be an alternative to the testing
in the usual way.
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Nicky Welton,
Office 2P10 CSM,
University of the West of England,
Coldharbour Lane,
Bristol. BS16 1QY
Tel: (0117) 965 6261 ext 3227
Email: [log in to unmask]
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