In hypothesis testing, one is selecting between two models with one of
the models being 'privileged', in the sense that if one cannot
distinguish between them on the basis of the statistical criterion used,
the privileged model will be used. (So the decision is made on some
other bais such as 'fairness' or 'simplicity' or 'uphold the status
quo'.) The statistical criterion is (usually) the p value. Finally, the
privilege extends to requiring the non-privileged model to perform
'significantly' (in the usual everyday sense of 'substantially') better.
With this understanding, I would express the following example as:
'We should proceed to use the model with the two means equal, rather
than the model in which they differ.'
This is (a) simple and clearcut; and (b) true - it's what we mean!
Regards,
Alan
Donald Burrill wrote:
> > What I have in mind, for instance, is if we found p = .42, then
> >
> > - "we have no strong evidence to reject the assumption that the mean
> > scores of the two groups differ" is OK, but
> >
> > - "the results demonstrate the two means are the same" is not OK
> > because this could be interpreted as implying that the obtained p =
> > p(Ho = True | Data)
>
> Well, not this so much as because the assertion "the two means are the
> same" could (should?) be interpreted as implying that the probability of
> a Type II error (against a minimal useful difference, aka MUD) is
> acceptably low" (when in fact "p = .42" does not of itself imply ANYTHING
> about pr{Type II error} or, equivalently, about power).
>
> > etc.
> >
> > To my mind, statements like "the results are (not) statistically
> > significant at the .05 level" seem quite vacuous to most students &
> > provide little insight into what is really going on.
> >
> > I hope what I'm after is clear from the above.
> >
> > Thanks for any contributions (either public or private) & if there's
> > reasonable interest, I'll post a summary back to the list.
> >
> > Best wishes,
> >
> > Paul Dudgeon
> >
> > AERA Division D: Measurement and Research Methodology Forum
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> ------------------------------------------------------------------------
> Donald F. Burrill [EMAIL PROTECTED]
> 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
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--
Alan McLean ([EMAIL PROTECTED])
Department of Econometrics and Business Statistics
Monash University, Caulfield Campus, Melbourne
Tel: +61 03 9903 2102 Fax: +61 03 9903 2007
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