# [R] data analysis

(Ted Harding) ted.harding at nessie.mcc.ac.uk
Tue Aug 7 01:30:22 CEST 2007

```On 06-Aug-07 19:26:59, lamack lamack wrote:
> Dear all, I have a factorial design where the
> response is an ordered categorical response.
>
> treatment (two levels: 1 and 2)
> time (four levels: 30, 60,90 and 120)
> ordered response (0,1,2,3)
>
> could someone suggest a correct analysis or some references?

For your data below, I would be inclined to start from here,
which gives the counts for the different responses:

Response
--------------------
Trt Time   0    1    2    3
--------+--------------------+----
Tr1  30 |       1         3  |  4
60 |       2    1    1  |  4
90 |       3    1       |  4
120 |       3    1       |  4
--------+--------------------+---
Tr2  30 |       2         2  |  4
60 |       3    1       |  4
90 |       3         1  |  4
120 |  1    2    1       |  4
=================================
Tr1     |  0    9    3    4  | 16
--------+--------------------+---
Tr2     |  1   10    2    3  | 16
=================================

This suggests that, if anything is happening there at all,
it is a tendency for high response to occur at shorter times,
and low response at longer times, with little if any difference
between the treatments.

To approach this formally, I would consider adopting a
"re-randomisation" approach, re-allocating the outcomes at
random in such a way as to preserve the marginal totals,
and evaluating a statistic T, defined in terms of the counts
and such as to be sensitive to the kind of effect you seek.

Then situate the value of T obtained from the above counts
within the distribution of T obtained by this re-randomisation.

There must be, somewhere in R, routines which can perform this
kind of constrained re-randomisation,but I'm not sufficiently
familiar with that area of R to know for sure about them.

up with suggestions!

best wishes,
Ted.

> subject treatment  time   response
> 1       1            30       3
> 2       1            30       3
> 3       1            30       1
> 4       1            30       3
> 5       1            60       3
> 6       1            60       1
> 7       1            60       1
> 8       1            60       2
> 9       1            90       2
> 10      1            90       1
> 11      1            90       1
> 12      1            90       1
> 13      1           120       2
> 14      1           120       1
> 15      1           120       1
> 16      1           120       1
> 17      2            30       3
> 18      2            30       3
> 19      2            30       1
> 20      2            30       1
> 21      2            60       1
> 22      2            60       2
> 23      2            60       1
> 24      2            60       1
> 25      2            90       1
> 26      2            90       1
> 27      2            90       1
> 28      2            90       3
> 29      2           120       1
> 30      2           120       2
> 31      2           120       0
> 32      2           120       1
>
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Date: 07-Aug-07                                       Time: 00:30:19
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