OT: A test with dependent samples.
The only question at issue (i.e. capable of being addressed) is: is giving the drug to non-vomiting cats associated with vomiting? (I would strongly suspect that cats that were vomiting beforehand would have been excluded from the study, as the researcher would have felt that one couldn't then tell whether or not the drug caused vomiting problems for them. No?) There were 73 non-vomiting cats, 12 of which started vomiting after receiving the drug. All I can do is give a confidence interval for the estimated proportion of nonvomiting cats that vomit when given this drug and perhaps ask whether it is consistent with their nonvomiting status before. Which is what I did. And it's pretty convincing that giving the pill is associated with vomiting, right? Whether the vomiting was associated with the giving of this **particular** drug is, of course, impossible to tell, because the researcher failed to include placebo controls. I chose 0 for a null as a representation of their non-vomiting status, but the scientific question of interest is probably to compare them to the proportion of cats that would vomit if given any pill at all. Without any placebo controls, who can tell? Substitute a prior guess if you like for a Null. Which is exactly the point that Marc Schwartz made -- that is, that the data are probably completely useless to answer the question of interest because the researcher messed up the design. -- Bert Gunter -----Original Message----- From: markleeds at verizon.net [mailto:markleeds at verizon.net] Sent: Tuesday, February 10, 2009 2:54 PM To: Bert Gunter Cc: 'David Winsemius'; 'Rolf Turner'; r-help at r-project.org Subject: Re: [R] OT: A test with dependent samples. Hi: Bert: can you do that because the null is that they are equal before and after, not that the proportion is zero ? Thank for any clarification to my lack of understanding.
On Tue, Feb 10, 2009 at 5:43 PM, Bert Gunter wrote:
Ah, experimental units,again ... a subject little taught by statisticians that is often the crux of the matter. As here. The cat is the experimental unit. There are 73 of them. 12 of them experienced vomiting after treatment. What's a confidence interval for the true proportion based on our sample of 73? binom.test(12,72) gives us .088 to .27 for an exact 2 sided interval (and a P value of 2.2e-16 for the null = 0). Seems rather convincing -- and simple -- to me! -- Bert Gunter -----Original Message----- From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of David Winsemius Sent: Tuesday, February 10, 2009 1:51 PM To: Rolf Turner Cc: R-help Forum Subject: Re: [R] OT: A test with dependent samples. In the biomedical arena, at least as I learned from Rosner's introductory text, the usual approach to analyzing paired 2 x 2 tables is McNemar's test. ?mcnemar.test
mcnemar.test(matrix(c(73,0,61,12),2,2))
McNemar's Chi-squared test with continuity correction data: matrix(c(73, 0, 61, 12), 2, 2) McNemar's chi-squared = 59.0164, df = 1, p-value = 1.564e-14 The help page has citation to Agresti. -- David winsemius On Feb 10, 2009, at 4:33 PM, Rolf Turner wrote:
I am appealing to the general collective wisdom of this
list in respect of a statistics (rather than R) question. This
question
comes to me from a friend who is a veterinary oncologist. In a
study that
she is writing up there were 73 cats who were treated with a drug
called
piroxicam. None of the cats were observed to be subject to vomiting
prior
to treatment; 12 of the cats were subject to vomiting after treatment
commenced. She wants to be able to say that the treatment had a
``significant''
impact with respect to this unwanted side-effect.
Initially she did a chi-squared test. (Presumably on the matrix
matrix(c(73,0,61,12),2,2) --- she didn't give details and I didn't
pursue
this.) I pointed out to her that because of the dependence --- same
73
cats pre- and post- treatment --- the chi-squared test is
inappropriate.
So what *is* appropriate? There is a dependence structure of some
sort,
but it seems to me to be impossible to estimate.
After mulling it over for a long while (I'm slow!) I decided that a
non-parametric approach, along the following lines, makes sense:
We have 73 independent pairs of outcomes (a,b) where a or b is 0
if the cat didn't barf, and is 1 if it did barf.
We actually observe 61 (0,0) pairs and 12 (0,1) pairs.
If there is no effect from the piroxicam, then (0,1) and (1,0) are
equally likely. So given that the outcome is in {(0,1),(1,0)} the
probability of each is 1/2.
Thus we have a sequence of 12 (0,1)-s where (under the null
hypothesis)
the probability of each entry is 1/2. Hence the probability of this
sequence is (1/2)^12 = 0.00024. So the p-value of the (one-sided)
test
is 0.00024. Hence the result is ``significant'' at the usual levels,
and my vet friend is happy.
I would very much appreciate comments on my reasoning. Have I made
any
goof-ups, missed any obvious pit-falls? Gone down a wrong garden
path?
Is there a better approach?
Most importantly (!!!): Is there any literature in which this
approach is
spelled out? (The journal in which she wishes to publish will
almost surely
demand a citation. They *won't* want to see the reasoning spelled
out in
the paper.)
I would conjecture that this sort of scenario must arise reasonably
often
in medical statistics and the suggested approach (if it is indeed
valid
and sensible) would be ``standard''. It might even have a name!
But I
have no idea where to start looking, so I thought I'd ask this
wonderfully
learned list.
Thanks for any input.
cheers,
Rolf Turner
######################################################################
Attention:\ This e-mail message is privileged and confid...{{dropped:
9}}
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.