# Re: [R] comparing strength of association instead of strength of evidence?

From: Kjetil Brinchmann Halvorsen <kjetil_at_acelerate.com>
Date: Sat 25 Jun 2005 - 05:27:28 EST

>Hi,
>I asked this question before, which was hidden in a bunch of
>questions. I repharse it here and hope I can get some help this time:
>
>I have 2 contingency tables which have the same group variable Y. I
>want to compare the strength of association between X1/Y and X2/Y. I
>am not sure if comparing p-values IS the way even though the
>probability of seeing such "weird" observation under H0 defines
>p-value and it might relate to the strength of association somehow.
>But I read the following statement from Alan Agresti's "An
>Introduction to Categorical Data Analysis" :
>"Chi-squared tests simply indicate the degree of EVIDENCE for an
>association....It is sensible to decompose chi-squared into
>components, study residuals, and estimate parameters such as odds
>ratios that describe the STRENGTH OF ASSOCIATION".
>
>
>
Here are some things you can do:

> tab1<-array(c(11266, 125, 2151526, 31734), dim=c(2,2))

``` > tab2<-array(c(43571, 52, 2119221, 31807), dim=c(2,2))
> library(epitools) # on CRAN
> ?odds.ratio
```

Help for 'odds.ratio' is shown in the browser  > library(help=epitools) # on CRAN
> tab1

[,1] [,2]
[1,] 11266 2151526
[2,] 125 31734
> odds.ratio(11266, 125, 2151526, 31734) Error in fisher.test(tab) : FEXACT error 40.

```Out of workspace.                 # so this are evidently for tables
```
with smaller counts
> library(vcd) # on CRAN

> ?oddsratio
Help for 'oddsratio' is shown in the browser  > oddsratio( tab1) # really is logodds ratio [1] 0.2807548

``` > plot(oddsratio( tab1) )
> library(help=vcd) # on CRAN  Read this for many nice functions.
> fourfoldplot(tab1)
> mosaicplot(tab1)     # not really usefull for this table

```

Also has a look at function Crosstable in package gmodels.

To decompose the chisqure you can program yourselves:

decomp.chi <- function(tab) {

```        rows <-  rowSums(tab)
cols <-   colSums(tab)
N <-   sum(rows)
E <- rows %o% cols / N
contrib <- (tab-E)^2/E
contrib }

> decomp.chi(tab1)
[,1]         [,2]
```

[1,] 0.1451026 0.0007570624
[2,] 9.8504915 0.0513942218
>

So you can easily see what cell contributes most to the overall chisquared.

Kjetil

>Can I do this "decomposition" in R for the following example including
>2 contingency tables?
>
>
>
>>tab1<-array(c(11266, 125, 2151526, 31734), dim=c(2,2))
>>tab1
>>
>>
> [,1] [,2]
>[1,] 11266 2151526
>[2,] 125 31734
>
>
>
>>tab2<-array(c(43571, 52, 2119221, 31807), dim=c(2,2))
>>tab2
>>
>>
> [,1] [,2]
>[1,] 43571 2119221
>[2,] 52 31807
>
>
>BTW, is there some good forum on the theory of statistics? r-help is a
>good one but I don't want to bother people by asking some questions
>weakly associated with R here.
>
>Thanks,
>
>
>

```--

Kjetil Halvorsen.

Peace is the most effective weapon of mass construction.
--  Mahdi Elmandjra

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