[R] OT: A test with dependent samples.

[markleeds at verizon.net]

  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
>>
>> 
>> ######################################################################
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>>
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