I agree with Dennis that students need to be exposed to the use of Bayesian
priors within the process of teaching classical hypothesis testing.
I realize that Bayesians might wonder why anyone would go back to classical
hypothesis testing once one has the entire posterior distribution. I
realize that classical frequentists have little motivation to consider the
influence of subjective priors when dealing with a factual state of
knowledge (the value of the population parameter). And as a teacher, I'm
well aware of the difficulty of trying to manipulate priors into
posteriors -- within the time constraints of an intro stats class.
But I've done it (taught classical hypothesis testing while including
Bayesian priors) for several years in Intro Business Stats using Bayes Rule
and a 2x2 table (much like medical tests).
For further details, consult two papers I've written:
"Using Bayesian Inference in Classical Hypothesis Testing", 1996 JSM ASA
"Using Bayesian Strength of Belief to Teach Classical Statistics", 1998
ICOTS-5
On-line copies are available at:
www.augsburg.edu/ppages/schield
Scroll down to PUBLICATIONS IN STATISTICS.
Although I've given many talks on this subject (on 4 different continents),
I've never gotten much usable feedback. Both Bayesians and frequentists
find it "interesting..." My conclusion is that any statistical activity
that involves both Bayesian and frequentist elements is difficult for either
group to support as being useful to students in REALLY understanding
statistics.
The biggest problem I've encountered (per the 2nd paper) is student
difficulty in handling conditional probability. (David Moore noted this
problem in his analysis of the Bayesian-frequentist issue). I don't think
we should de-emphasize conditional probability. I do agree that teaching
conditional probability straight on (algebraically) has not worked well
enough. I'm working at teaching conditional probability in a different way.
Once I've got students up to speed on conditional probability, then I'm
ready to go back and teach classical hypothesis testing while including
Bayesian priors and see whether students really understand what is going on.
Time will tell.
Milo (Feedback appreciated)
===================================================================
dennis roberts wrote in message
<[EMAIL PROTECTED]>...
>it appears to me that we are having the same kinds of discussions on this
>topic as usual .... and we go round and round ... and where we stop depends
>on when people get tired of it
>
>is progress being made? i wonder ...
>finally, i WOULD LIKE to offer some summary points that do seem sensible to
me
>
>A. the reliance on ... and dominance of ... traditional 'significance'
>testing ... in almost all of printed scientific literature ... across most
>disciplines ... is TOTALLY out of whack in terms of what this 'method' can
>tell us about phenomena
>
>B. the failure of statisticians in general, particularly those (me
>included) who TEACH students about this stuff, to build into their psyches
>'priors', in some form, as herman and others have been preaching ... is
>tantamount to unethical statistical instructional practice
>
>and C.
>
>if we do A and don't do B ... we do a tremendous disservice to students we
>work with
>
>now, how we reinvent our strategies ... is difficult INdeed ... but, we
>must try
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