[R] Can I test if there are statistical significance between different rows in R*C table?

[Yvonnick NOEL]

> With the totally non-committal P-value for Group 2 vs Group 3,
> and the absolutely decisive P-value for Group 1 vs Groups 2&3,
> there is no need whatever to bother with "multiple comparison"
> complications.

Note that you can test this as the formal comparison between three 
nested multinomial models, the first assuming homogeneity of all three 
response distributions (M0), the second assuming a similar multinomial 
distribution for groups 2 and 3, and a specific one for the first group 
(M1), and the saturated model (M3).

Maximum likelihood estimates of the corresponding multinomial 
probabilities are:

M0
      Resp   Bad Better  Good
Group                       
Grp1       0.613  0.067 0.320
Grp2       0.613  0.067 0.320
Grp3       0.613  0.067 0.320

M1
      Resp   Bad Better  Good
Group                       
Grp1       0.298  0.129 0.573
Grp2       0.915  0.008 0.078
Grp3       0.915  0.008 0.078

M2
      Resp   Bad Better  Good
Group                       
Grp1       0.298  0.129 0.573
Grp2       0.938  0.000 0.062
Grp3       0.891  0.016 0.094


Comparing them with a likelihood ratio, rather than a Pearson 
chi-square, is probably more appropriate, given the additivity property 
of likelihood ratio with nested models. You get:

   res. df. res. dev.       df. lik.ratio P(>chi2)    AIC     BIC
M0    4.000   114.023                             154.959 162.026
M1    2.000     1.917     2.000 112.106 4.533e-25  46.852  60.986
M2    0.000 4.122e-10     2.000   1.917     0.383  48.936  70.136


M1 is clearly the best model on these data. You can view this as an 
equivalent of orthogonal contrasts in ANOVA, and so indeed you do not 
have to worry about correcting your alpha.

HTH

Yvonnick Noel
University of Rennes 2
France