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Despite a strong genetic background in cognitive function only a limited number of single nucleotide polymorphisms (SNPs) have been found in genome-wide association studies (GWASs). We hypothesize that this is partially due to mis-specified modeling concerning phenotype distribution as well as the relationship between SNP dosage and the level of the phenotype. To overcome these issues, we introduced an assumption-free method based on generalized correlation coefficient (GCC) in a GWAS of cognitive function in Danish and Chinese twins t