On 19 Apr 2000 15:22:14 -0700, [EMAIL PROTECTED] (dennis roberts)
wrote:
> let's say that one designs a simple experiment about the effectiveness of a
> weight change program ...
>
> you set your sights on a power of .7 ... (beta therefore being .3) ...
> select a two tailed alpha of .05 ... because the situation is such that
> this program could actually make you gain weight .... though you hope that
> it will help you lose weight
>
> now, let's assume that you want to detect an effect of 3 pounds ... either
> gain or loss ... and you therefore go about estimating the n needed to
WAIT! What do you mean by "want to detect an effect of 3 pounds"?
1) That might be the critical distance for a t-test -- so the CI just
excludes 0, and you are ignoring complicated "power" while being
satisfied with 50% power for the point estimate.
2) That might be the underlying effect size which you are willing to
assume is expected, or would be important, while testing whether two
groups *differ*. That is the usual basis for power computations.
3) That might be an effect size that you want to be SURE of, so you
want to test for an effect that has to be GREATER than 3. That will
take a somewhat-larger N, depending on the Standard deviation. If it
is weight-gain in your pet elephants, then the N won't have to
increase much.
Those are at least 3 interpretations that are distinct and practical,
and they imply different sample Ns; they are not distinguished by the
fuzzily stated intention.
(Maybe this is one of the advantages of relying on a textbook like
Cohen's, compared to using a computer program or a shorter "cookbook"
--The book gives you modeling of realistic statements. As Dennis
illustrates in this post, a naive approximation to a power requirement
is apt to be too vague to be usable.)
> achieve this goal of being able to reject the null with a p of .7 ... if in
> fact the null is not true ... and the gap between the null and the center
> of the treatment effect distribution being 3 ...
>
> now, what if you execute your study rigorously with the n you estimated you
> would need ... and then reject the null with a p = .02 (for illustration
> purposes only) ... at the moment, don't worry if it is a gain or loss ...
> just that you reject the null
>
> here is my question (you were wondering when i would get to it, right?)
>
> WHAT CAN WE SAY, BASED ON THIS REJECTION OF THE NULL, about the treatment
> effect being 3 lbs OR more ... ?
- Of course, that depends on the statement of the Null. If we reject
my (3), then the Confidence Interval is all above 3.0.
> what confidence do we have that the treatment effect is AT LEAST 3 lbs?
It depends how much of the CI is above 3.0, doesn't it?
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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