[R] OT: A test with dependent samples.
David Winsemius
dwinsemius at comcast.net
Wed Feb 11 00:37:45 CET 2009
Still seems that McNemar's test is the appropriate test for the
matched design, but my first answer sent the input to the function
incorrectly, and it's not clear that a normal theory test would be
accurate in all instances. The matrix should have 61 cats with no
vomiting under either situation, 12 cats vomiting in the condition of
piroxicam, no cats vomiting prior to treatment no cats vomiting under
both situations):
> mcnemar.test(matrix(c(61,0,12,0),2,2))
McNemar's Chi-squared test with continuity correction
data: matrix(c(61, 0, 12, 0), 2, 2)
McNemar's chi-squared = 10.0833, df = 1, p-value = 0.001496
It's very close to 1/2 the value of Bolker's calculation, but the
"sidedness" is not specified in the output. Rosner's text
"Fundamentals of Biostatistics" also describes an exact analogue of
the Normal theory test.
--
David Winsemius
On Feb 10, 2009, at 4:50 PM, David Winsemius wrote:
> 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
>>
>> ######################################################################
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>>
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>
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