In order to maximise the power to detect association due to linkage disequilibrium the cases should be as genetically homogenous as possible, since otherwise different associations present in different ethnic groups could mask each other.
In order to avoid spurious associations due to population stratifications the controls should be matched to the cases for relevant factors such as ethnicity and geographical origin.
Frequencies of alleles in cases and controls can be compared using a chi-squared test, or if some alleles are rare using a Monte Carlo approach.
Some studies compare also frequencies of genotypes, as well as alleles, between the two groups. There are a large number of possible genotypes, so an appropriate correction for multiple-testing must be included. Almost all biological mechanisms which would produce association with a genotype, especially a heterozygous genotype, would also produce detectable allelic association.