# [R] OT: A test with dependent samples.

Wed Feb 11 03:03:06 CET 2009

```David,

If you really want to do a test on this data, I would suggest
a Fisher's Exact test, but you want to use hypergeometric
probabilities. You would probably want to try the CMH
test, if the function allows a single table and actually uses
hypergeometric probabilities.

My suggestion, would be to calculate the frequency of
vomiting, for animals that didn't vomit before, calculate
the CIs and then use some historical data on the vomiting
rate, for non-treated cats and see whether it falls inside the
CIs for your treated animals. If it does, then you might
conclude that the vomiting rate, for treated cats, is
similar to non-treated cats.

Murray M Cooper, Ph.D.
Richland Statistics
9800 N 24th St
Richland, MI, USA 49083

----- Original Message -----
From: "David Winsemius" <dwinsemius at comcast.net>
To: "Rolf Turner" <r.turner at auckland.ac.nz>
Cc: "R-help Forum" <r-help at r-project.org>
Sent: Tuesday, February 10, 2009 4:50 PM
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
>> 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