Armitage's trend test for the 2x3 genotype table

Question

[GabrielMontenegro]

I would like to have an intuitive answer on why the Armitage trend test, commonly used for doing association analysis for a SNP with a trait, is equivalent to a chi square with 1 degree of freedom.

If the trend test usually uses a 2x3 contingency table isn't it more similar to a chi square with 2 degrees of freedom? What is the intuition there? Is it because you can also think of the Armitage trend test as similar to the allele count test where you are counting alleles and not genotypes? So it's actually a 2x2 table?

Answer 1

[Lemire]

The Armitage test for trend only has one parameter, hence one degree of freedom. If you code your genotypes 0,1 and 2, then implicitly the odds ratio for homozygous is assumed to be the square of the heterozygous one. Other codings of genotypes lead to different relationships between the odds ratios

In the 2x3 test that has 2df, all odds ratios are free to vary.

Note that this is not the same as collapsing the 2x3 table into a 2x2 table. You can read the paper by Sasieni, who describes the relation between these tests: http://www.ncbi.nlm.nih.gov/pubmed/9423247