Tests for association in two-way tables

Load and examine data

library(vcdExtra)
data(SexualFun)
SexualFun                # show the table

##               Wife
## Husband        Never Fun Fairly Often Very Often Always fun
##   Never Fun            7            7          2          3
##   Fairly Often         2            8          3          7
##   Very Often           1            5          4          9
##   Always fun           2            8          9         14

Test association

assocstats(SexualFun)    # association statistics

##                     X^2 df P(> X^2)
## Likelihood Ratio 15.486  9 0.078421
## Pearson          16.955  9 0.049422
## 
## Phi-Coefficient   : NA 
## Contingency Coeff.: 0.396 
## Cramer's V        : 0.249

fisher.test(SexualFun)   # exact test

## 
##  Fisher's Exact Test for Count Data
## 
## data:  SexualFun
## p-value = 0.1
## alternative hypothesis: two.sided

Tests for ordered factors

CMHtest(SexualFun)       # CMH tests

## Cochran-Mantel-Haenszel Statistics for Husband by Wife 
## 
##                  AltHypothesis Chisq Df    Prob
## cor        Nonzero correlation  10.0  1 0.00155
## rmeans  Row mean scores differ  12.6  3 0.00567
## cmeans  Col mean scores differ  12.3  3 0.00637
## general    General association  16.8  9 0.05246