the "act" of "deciding" (using whatever rule/CV you like) to retain the
null or reject the null ... is just that and nothing more
however, you do NOT "act" or "decide" to make a type II error or a type I
error ...
you don't "act" or "decide" to make an incorrect or correct choice ... the
fact that it is correct or incorrect ... is not within YOUR "causative"
ability ... ( i wanted to use the word "power" but ... that would totally
mess things up)
if the null happens to be true ... AND your action was to retain ... YOU
did not take an action to make a correct decision ... the "accident" that
the decision could be called "correct" is of our doing as statisticians ...
conditioned on the null being true ... this is merely a LABEL we have given
to this resulting situation
if the null is not true and ... your ACTION was to retain ... YOU did not
take an action to make an INcorrect choice ... this "accident" was because
we as statisticians have given this label to that ... and is conditioned on
the fact (that you have no awareness of) ... that the null is not true
we can say the same about rejecting the null also
yes, we as investigators do make the decision to retain ... or reject ...
but, we don't make the decision to have the outcome of that decision be
correct or incorrect
finally, i do think that the label we give of correct or incorrect is a
consequence of the fact that you acted one way or the other AND conditioned
on the state of nature with respect to the null ... and, the name we give
to it being correct or not ... is only a consequence of the CONGRUENCE
between YOUR act AND state of nature ... according to my dictionary ...
consequence means result and ... calling an action you take a correct or
incorrect decision is only the result of one overlaying the action (and
that's the only action part of this overall case) WITH the state of nature
... so, the name correct or incorrect ... (type I or type II error, etc.)
is THE result ...
it is NOT the result of what YOU did ... it is the result of comparing what
you did WITH nature ... and the resultant NAME we assign will be a or b or
c or d ... depending on that congruence or lack of that comparison
in this sense ... there is a probability associated with that consequence
... and the probability only makes sense as a consequence ... not as an
action YOU take
the investigator does not make the type I error ... or the type II error
... or either of the correct possibilities too ...
so, as long as that is clear, then ... ok by me
but, the more i examine the notion of power ... the more i fail to see
that this is a very good term to assign to that probability ... alpha and
beta as terms ... have no particular "loaded" meanings (though these can be
differentially "bad" depending on circumstances) ... but one cannot say
that about "power" ... so, by assigning this name to that probability ...
it suggests that this is THE good place to be striving for ... but, as i
said before ... we should be striving for having the consequence of our
action ... be correct ... not correct of a certain type ... though, i
readily admit that the direction of the consequence being where we now
label power ... is probably more often than not ... where we hope to be
but, not always ...
the implication is as follows:
let's say that the null is true and ... you have retained it (call this A)
or, the null is not true and you have rejected it ... (call this B)
in our current layout and discussion of terms ... we try to argue by the
name (power) of B ... that somehow it is a BETTER correct decision than A
i don't buy that
it may not be that interesting of a case but, if true ... it still is good
that we made it
At 11:15 AM 3/5/01 -0500, Donald Burrill wrote:
>In response to Dennis's earlier statement,
>"that is ... power in many cases is a highly overrated CORRECT decision"
>
>I wrote:
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