a professor thought that he was producing a test of 50 items at 'about the
50%' difficulty level, that is .. on average, the scores would be about
50%. now, he collected data from a random sample of n=40 of his class ...
gave them the test ... and then did a ttest using 25 as the null ... he found
(now no fair tossing in other considerations like ... well, this is not
planned properly etc .... just take it on face value the way we ACTUALLY
see it in the vast majority of the literature)
MTB > ttest 25 c1
One-Sample T: C1
Test of mu = 25 vs mu not = 25
Variable N Mean StDev SE Mean
C1 40 32.20 9.86 1.56
Variable 95.0% CI T P
C1 ( 29.05, 35.35) 4.62 0.000 <<<<<<-----------------
REJECT THE NULL
----------------------------------------------------------
--------------------------------------------------------------------------
0 25
50
where on the number line might there 'real' level of performance be based
on the rejected null?
another prof looking at the data, and keeping in mind what the professor in
the course thought did the following 95% ci ...
MTB >
MTB > tint c1
One-Sample T: C1
Variable N Mean StDev SE Mean 95.0% CI
C1 40 32.20 9.86 1.56 ( 29.05, 35.35)
<<<<<----------------- CI
----------------------------------------------------------
----------------------------------------------------------------------------
0 25
50
where are the number line do you think the 'real' level of performance is?
now, folks on the list have been trying to argue about what truth is ... or
whether we actually could find it ... and i would say that in this case,
one might define 'truth' at least two ways:
first truth: is the null true?
second truth: what is mu?
the first truth is of so little value (and only really says, we don't think
it is 25) ... but the second gets at the heart of the problem ... what is
going on with the students performance ...
the first truth and our 'proof' of or NOT of it ... just says WE were good
or BAD at formulating the hypothesis ... but does not really get us closer
to the second truth ... which speaks directly to the parameter ...
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