How to report results of Fisher's test for larger than 2 by 2 tables

Question

This is probably a very easy question but what is an acceptable phrase for reporting a Fisher's test where the number of rows and the number of columns are both $>2$. An example in R:

> x <- as.matrix(data.frame("A"=c(10,4,6),"B"=c(45,2,6),"C"=c(23,4,20),
         row.names=c("df1","df2","df3")))
> x
    A  B  C
df1 10 45 23
df2  4  2  4
df3  6  6 20
> fisher.test(x,, simulate.p.value=TRUE, B=1e5)

Fisher's Exact Test for Count Data with simulated p-value 
(based on 1e+05 replicates)

data:  x 
p-value = 0.00026
alternative hypothesis: two.sided 

I'm looking for a phrase/sentence that would encapsulate the above.

Answer 1

Fisher's exact test tells you only about the probability of your or "more extreme" data given that the null hypothesis holds. It does not tell you about where in the table your data deviate from independence.

Pearson residuals are one way of expressing that. Try chisq.test(x)$residuals to obtain them. Larger absolute values correspond to greater deviance from what would be expected under the null hypothesis, positive values indicate "more than expected", negative values "less than expected".

They can be visualized by mosaicplot(x, shade=T)

If you square them and sum them up, you get Pearson's Chi-squared statistic. They partition this statistic, making visible how much each table entry contributes to it.