# [R] binom.test appropriate?

Lüdde Mirko mirko.luedde at cellcontrol.de
Tue Jun 19 18:48:42 CEST 2001

```Hi!

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
> properties.

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
+49-89-895275-0 +49-179-5252064
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```