In response to Dennis's earlier statement,
"that is ... power in many cases is a highly overrated CORRECT decision"
I wrote:
> >Well, no. Overrated it may be (that lies, I think, in the eye of the
> >beholder); but a _decision_ it is definitely not. Power is the
> >_probability_ of making a particular decision -- which, of course,
> >like all decisions, may or may not be correct.
On Mon, 5 Mar 2001, dennis roberts replied:
> sorry .... we don't MAKE this decision ... the only decision we make
> in this case is to reject the null ...
Precisely. We DECIDE to reject the null hypothesis. Why do you say, of
this decision, "we don't MAKE this decision" ???
> it is only the statisticians who overlay on TOP of this ... the
> consequence OF that reject decision ... saying that IF the null had
> been false (of which the S has no clue about) ... THEN the consequence
> of that reject decision is called power
Sorry, Dennis. Power is defined AS A PROBABILITY. In particular, it is
the probability of rejecting the [null] hypothesis being tested. Some
people prefer to define it as a conditional probability (we've been over
this once already), the condition being that the hypothesis being tested
is false.
But power is not a _consequence_ of a decision, in any sense of
"consequence" that I know about. If you know a sense in which
"consequence" applies, I'd be interested in the formal definition, and
where that definition can be found in a standard reference.
As you pointed out in your earlier note, power is sometimes
defined as 1 - beta. This definition, when used, can make sense only if
power is understood as a probability, since beta is a probability.
(At least, I understand beta to be a probability. Are you going to
argue the contrary?)
> this is one reason i raised this issue ... because, we only make 2 possible
> decisions with respect to our investigation ... we retain ... we reject ...
> we DON'T determine the consequence of that decision ... so, in this sense
> ... saying that there is a consequence associated with a particular act ...
> retaining or rejecting ... "power is the probability of MAKING (emphasis
> added from don's comment) ... a particular decision ... " ... sounds like
> WE did this ... when we did NOT DO this
Dennis: the decision in question was to reject the null hypothesis. If
"we did NOT DO this" (your emphasis), who, pray tell, did??
And if the decision you're trying to talk about is not "to reject",
what IS that decision that, you claim, "we did NOT DO"?
> all we did was to reject the null
Yes. Precisely. That was a
decision, and we made it. And the probability of our making that
decision, like all probabilities, depends on the state of nature -- in
particular, on the value of the parameter in question -- when we made it.
That probability is called "power".
> i still think there would be value ... in:
>
> 1. making it clear that the S only makes decisions of the retain kind
> ... and reject kind ... that's it!
But is this somehow not clear from the beginning? Who alleges that any
other kind of decision is made? If one is testing an hypothesis, the
result of the test is a decision to reject or to retain (or, in the
classical mode, to fail to reject). ...
(I do hope that your "S" is not one of the experimental subjects in the
study whose data are being analyzed (although that's what "S" usually
refers to). Those decisions are made by the investigator (or analyst),
not by any participating Subject.)
-- Don.
----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 (603) 535-2597
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
