# [R] exact trend test

peter dalgaard pdalgd at gmail.com
Thu Jan 7 13:15:20 CET 2016

```On 07 Jan 2016, at 08:31 , David Winsemius <dwinsemius at comcast.net> wrote:

>>
>> On Jan 6, 2016, at 8:16 PM, li li <hannah.hlx at gmail.com> wrote:
>>
>> Hi all,
>> Is there an R function that does exact randomization trend test?
>> For example, consider the 2 by 5 contingency table below:
>>
>>           dose0    dose 0.15    dose 0.5    dose 1.5    dose 5       row
>> margin
>> Yes          4                3                  4               5
>>    8                   24
>> No          4                5                   4               3
>>      0                  16
>> col sum    8                8                   8               8
>>  8                   40
>
> Your data presentation has been distorted by your failure to post in plain text. Surely you have been asked in the past to correct this issue?
>
>>
>> To do the exact trend test, we need to enumerate all the contingency table
>> with the
>> row and column margins fixed.
>
> Er, how should that be done? A trend test? What is described above would be a general test of no association rather than a trend test. Please use clear language and be as specific as possible if you choose to respond.
>
>> Find the probability corresponding to
>> obtaining
>> the corresponding contingency tables based on the multivariate
>> hypergeometric distribution. Finally the pvalue is obtained by adding
>> relevant probabilities.
>
> If there is a trend under consideration, then I do not understand such a trend would be modeled under a hypergeometric distribution? A hypergeometic distribution would suggest no trend, at least to my current understanding.

I'd expect that there is such a beast as a noncentral multivariate hypergeometric (for the 2x2 case that is what we use to get the CI for the odds ratio), but usually, one just wants the null distribution of the test statistic.

>
>>
>> Is there an R function that does this? if not, I am wondering whether it is
>> possible to
>> enumerate all possible contingency tables that has column sun and row sum
>> fixed?
>
> Wel, yes, that is possible and routinely done with `fisher.test`, but it is up to you to describe how that activity leads to a trend test.
>
> If you assume Poisson distributed errors a trend test is fairly easy to construct with glm.
>

Or, more to the point, there is prop.trend.test(). Neither are exact tests, though.

I think package "coin" may something relevant.

-pd

> --
> David.
>>
>> Thanks very much!!
>>
>>  Hanna
>>
>> 	[[alternative HTML version deleted]]
>>
>> ______________________________________________
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>> and provide commented, minimal, self-contained, reproducible code.
>
> David Winsemius
> Alameda, CA, USA
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

```