Rob: Fisher's exact test is conceptually possible for any r x c

contingency table problem and uses the observed multinomial table

probability as the test statistic. Other tests for r x c contingency

tables use a different test statistic (Chi-squared, likelihood ratio,

Zelterman's). It is possible that the probabilities for any of these

procedures may differ slightly for the same table configuration even if

the probabilities for each test are calculated by enumerating all possible

permutations (hypergeometric) under the null hypothesis. See Mielke and

Berry 2007 (Permutation Methods: A distance function approach) Chps 6

and7. Mielke has provided efficient Fortran algorithms for enumerating

the exact probabilities for 2x2, 3x2, 4x2, 5x2, 6x2 ,3x3,and even 2x2x2

tables for Fisher's exact and Chi-square statistics. I don't remember

whether Cyrus Meta's algorithms for Fisher's exact can do more. But the

important point to keep in mind is that it is possible to use different

statistics for evaluating the same null hypothesis for r x c tables

(Fisher's exact uses one form, Chi-square uses another, etc.) and the

probabilities can be computed by exact enumeration of all permutations

(what people expect Fisher's exact to do but also possible for Chi-square

statistic) or by some approximation (asymptotic distribution, Monte Carlo

resampling). The complete enumeration of test statistics under the null

becomes computationally intractable for large dimension r x c problems

whether using the observed table probability (like Fisher's exact) as a

test statistic or other like Chi-square statistic.

So in short, yes you can use Fisher's exact on your 4 x 2 problem, and the

result might differ from using a Chi-square statistic even if you compute

the P-value for the Chi-square test by complete enumeration. Note that

the minimum expected cell size for the Chi-square test is related to

whether the Chi-square distributional approximation (an asymptotic

argument) for evaluating the Chi-square statistic will be reasonable and

is irrelevant if you calculate your probabilities by exact enumeration of

all permutations.

Brian

Brian S. Cade, PhD

U. S. Geological Survey

Fort Collins Science Center

2150 Centre Ave., Bldg. C

Fort Collins, CO 80526-8818

email:

[hidden email]
tel: 970 226-9326

From:

viostorm <

[hidden email]>

To:

[hidden email]
Date:

04/29/2011 01:23 PM

Subject:

Re: [R] fisher exact for > 2x2 table

Sent by:

[hidden email]
After I shared comments form the forum yesterday with the biostatistician

he

indicated this:

"Fisher's exact test is the non-parametric analog for the Chi-square

test for 2x2 comparisons. A version (or extension) of the Fisher's Exact

test, known as the Freeman-Halton test applies to comparisons for tables

greater than 2x2. SAS can calculate both statistics using the following

instructions.

proc freq; tables a * b / fisher;"

Do people here still stand by position fisher exact test can be used for

RxC

contingency tables ? Sorry to both you all so much it is just important

for

a paper I am writing and planning to submit soon. ( I have a 4x2 table but

does not meet expected frequencies requirements for chi-squared.)

I guess people here have suggested R implements, the following, which

unfortunately are unavailable at least easily at my library but at least

by

the titles indicates it is extending it to RxC

Mehta CR, Patel NR. A network algorithm for performing Fisher's exact test

in r c contingency tables. Journal of the American Statistical Association

1983;78:427-34.

Mehta CR, Patel NR. Algorithm 643: FEXACT: A FORTRAN subroutine for

Fisher's

exact test on unordered r x c contingency tables. ACM Transactions on

Mathematical Software 1986;12:154-61.

The only reason I ask again is he is exceptionally clear on this point.

Thanks again,

-Rob

viostorm wrote:

>

> Thank you all very kindly for your help.

>

> -Rob

>

> --------------------------------

> Robert Schutt III, MD, MCS

> Resident - Department of Internal Medicine

> University of Virginia, Charlottesville, Virginia

>

viostorm wrote:

>

> Thank you all very kindly for your help.

>

> -Rob

>

> --------------------------------

> Robert Schutt III, MD, MCS

> Resident - Department of Internal Medicine

> University of Virginia, Charlottesville, Virginia

>

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