[R] binom.test appropriate?
mirko.luedde at cellcontrol.de
Tue Jun 19 18:48:42 CEST 2001
Prof Ripley wrote (marked by '>')
> But: the test for p = p0 vs p > p0 is the appropriate test for
> p <= p0 vs p > p0 within this family of tests, by the monotonicity
Thanks, I meanwhile understand that monotonicity, a general property
of the power function w.r.t. exponential families of measures, makes
the binomial test work for our purposes.
> You mentioned a 2 x 2 table and UMPU, but did not say exactly what you are
> doing or how the data were sampled, nor how this hypothesis arises. Under
> one set of assumptions, I believe the UMPU theory you mention tells you to
> use the binom.test for p = p0 vs p > p0, but it may be that other tests
> (Fisher's exact test springs to mind) are more appropriate. (And the last
> U can be insidious, just as it can be for estimation.)
Let me be more elaborate on this point.
We have a certain way of measuring a nonnegative real valued number
that we call "activity". Having found out about the activity, we
experimentally observe some "response" that is a binary variable
"yes", "no". We have defined a threshold for the activity. For an
activity smaller than the threshold, our "prediction" is "yes",
otherwise it is "no".
Writing down the number of coincidences and non-coincidences of
"predictions" and "responses" we get the mentioned 2 x 2 matrix.
Now we would like to learn about the conditional probabilities
p(response = x | prediction = y).
In particular we would like to verify the alternative hypotheses
p(response = "yes" | prediction = "yes") > p0
as well as
p(response = "no" | prediction = "no") > p1
against the nulls "<= p0" and "<= p1" for certain bounds p0 and p1
that came out of our CFO's spreadsheet.
To this end we read the number of "response = 'yes'" cases among the
"prediction = 'yes'" cases from the matrix (and do so for "no" - "no")
and apply the binomial test.
Some questions that remain are
- Does this seem appropriate?
- Would Fisher's exact test be even more appropriate?
- How could we optimize our threshold?
Any comments are appreciated, thanks, Mirko.
Dr. M. Luedde <Mirko.Luedde at CellControl.De>
CellControl Biomedical Laboratories AG
Am Klopferspitz 19, 82152 Martinsried
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