There are four tests – the likelihood ratio (LR) test, Wald's test, the score test and the exact test – commonly employed in genetic association studies. On comparison of the four tests, we found that Wald's test, popular in genome-wide screens due to its low computational demands, exhibited a paradoxical behaviour in that the test statistic decreased as the effect size of the variant increased, resulting in a loss of power. The LR test always achieved the most significant P-values, followed by the exact test. We further examined the results in a real data set composed of high- and low-cholesterol subjects from the Dallas Heart Study (DHS). We also compared the single-variant LR test with two multi-variant analysis approaches – the burden test and the C-alpha test – in analysing the sequencing data by simulation. Our results call for caution in using Wald's test in genome-wide case-control association studies and suggest that the LR test is a better alternative in spite of its computational demands.