Genome-wide association studies (GWAS) examine a large number of genetic variants, e. g., single nucleotide polymorphisms (SNP), and associate them with a disease of interest. Traditional statistical methods for GWASs can produce spurious associations, due to limited information from individual SNPs and confounding effects. This paper develops two statistical methods to enhance data analysis of GWASs. The first is a multiple-SNP association test, which is a weighted chi-square test derived for big contingency tables. The test assesses combinatorial effects of multiple SNPs and improves conventional methods of single SNP analysis. The second is a method that corrects for confounding effects, which may come from population stratification as well as other ambiguous (unknown) factors. The proposed method identifies a latent confounding factor, using a profile of whole genome SNPs, and eliminates confounding effects through matching or stratified statistical analysis. Simulations and a GWAS of rheumatoid arthritis demonstrate that the proposed methods dramatically remove the number of significant tests, or false positives, and outperforms other available methods.