Statistical association test between ordered and unordered variable I want to test the association between 2 variables : 
 - one is an ordered factor from quantiles of a numeric value ("Q1", "Q2", "Q3", "Q4")
 - the other is an unordered factor from groups of a character value ("group A", "group B", "group C"). 
If I make a usual chi square test, I get the association between those variables.
Is there a way I can't take into account the ordering of my first variable ? If yes, which test is appropriate ?
 A: As illustrated by the R example below, given that the assumptions of the ordinal regression model are satisfied, you gain statistical power by testing for an effect of the factor group in an ordinal regression model (it's one line of code) as compared to testing for any kind of deviation from independence between your response (y below) and group via a chi-square test.
> # Simulated data
> n <- 30
> group <- factor(rep(c("A","B","C"),each=n))
> set.seed(1)
> z <- rnorm(3*n, mean=c(0,.5,1)[group],sd=1.5) # unobserved latent variable
> y <- rep(0,3*n)
> y[z>0] <- 1
> y[z>1] <- 2
> y[z>2] <- 3
> table(y,group)
   group
y    A  B  C
  0 13  9  6
  1  9  7  6
  2  6 10 12
  3  2  4  6
> 
> # Fit the model
> y <- ordered(y)
> library(MASS)
> anova(polr(y ~ group), polr(y ~ 1))
Likelihood ratio tests of ordinal regression models

Response: y
  Model Resid. df Resid. Dev   Test    Df LR stat.    Pr(Chi)
1     1        87   241.1152                                 
2 group        85   234.1001 1 vs 2     2 7.015068 0.02997073
> 
> # Compare to a chi-square test
> chisq.test(table(y, group))

    Pearson's Chi-squared test

data:  table(y, group)
X-squared = 7.2792, df = 6, p-value = 0.2958

