Chi square 2x3 table - Genotypes are related to disease? I want to conduct a Chi square test of independence.
I have three different genotypes (CC/CG/GG, independent variable) and "health conditions" (outcomes) which is basically a patient group with a certain disease and a control group without the disease.
Does it sound right if my null hypothesis states that "the distribution of these alleles in these "study groups" doesn't influence disease outcome"
Whereas the alternative hypothesis says that "the distribution of these alleles in these study groups does influence disease outcome".
Is i formulated in a right way? Because I can't state (with the Chi square) that there are a certain risk-allele that lies behind disease. 
And lastly, I have heard that you can only use odds ratio if it is a 2x2 table, but if I use a "dominant" model of Pearsons Chi-square then the result would no longer be significant and there should no longer be any point to perform a OR.
Thankful for comments!
 A: Regarding calculating odds ratios:
> tt
        dss
genotype sick healthy
      CC   14      34
      CG   14      24
      GG    8       3
> 
> oddsratio(tt, rev='col')
$data
        dss
genotype healthy sick Total
   CC         34   14    48
   CG         24   14    38
   GG          3    8    11
   Total      61   36    97

$measure
        odds ratio with 95% C.I.
genotype estimate     lower    upper
      CC 1.000000        NA       NA
      CG 1.409998 0.5628447  3.55030
      GG 6.087096 1.4813184 32.87432

$p.value
        two-sided
genotype midp.exact fisher.exact  chi.square
      CC         NA           NA          NA
      CG 0.46208267   0.49321142 0.450640195
      GG 0.01142108   0.01320433 0.007043333

$correction
[1] FALSE

attr(,"method")
[1] "median-unbiased estimate & mid-p exact CI"
Warning message:
In chisq.test(xx, correct = correction) :
  Chi-squared approximation may be incorrect

The odds ratios are calculated for second and third genotypes with respect to first genotype. 
Edit: I have edited the code above to have numbers as in comments. The odds ratio for GG (with respect to CC) being sick is 6.1 (95% CI 1.5,32.9; significant since it does not overlap 1). The odds of CG being sick (as compared with CC) is not significantly different 1. The P values are also shown in the output.
