I've taken the liberty of copying this to the edstat list, and therefore
have quoted the original posting in full, despite having (at the moment)
a comment on only one part of it. -- DFB.
On Tue, 29 Aug 2000, Paul Dudgeon wrote:
> Somewhat tangential to the discussion last week about p values, I'd be
> interested in any comments on the following:
>
> I find one of the hardest aspects of teaching statistical inference to
> students is the linguistic contortions that can arise in moving from a
> strict formal definition of what an obtained p value means in NHST to
> the kind of informal, but easier to write/read, descriptive
> interpretation that is typically given, say, in journal articles.
>
> There are numerous instances in the literature of where even the highly
> regarded (e.e., Cohen) have come unstuck in trying to express the
> meaning of p(Data | Ho = True) in more everyday English.
>
> I thought that presenting students with a range of what are both
> acceptable/correct and unacceptable/incorrect interpretations might
> assist in making their understanding clearer (I have several of my own,
> but I'm sure they are by no means exhaustive of what is possible).
>
> So, I'd be grateful to know what do list members think are:
>
> (a) unacceptable/correct, and (b) acceptable/correct
>
> ways of more informally describing
>
> (i) significant (i.e., say p < .05), and (ii) non-significant p values
>
> from an analysis like a t-test.
>
>
> 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]
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