The kernel association test (KAT) is popular in biological studies for its ability to combine weak effects potentially of opposite direction. Its P-value is typically assessed via its (unconditional) asymptotic distribution. However, such an asymptotic distribution is known only for continuous traits and for dichotomous traits. Furthermore, the derived P-values are known to be conservative when sample size is small, especially for the important case of dichotomous traits. One alternative is the permutation test, a widely accepted approximation to the exact finite sample conditional inference. But it is time-consuming to use in practice due to stringent significance criteria commonly seen in these analyses.