Detecting genetic signatures of selection is of great interest for many research issues. Common approaches to separate selective from neutral processes focus on the variance of F(ST) across loci, as does the original Lewontin and Krakauer (LK) test. Modern developments aim to minimize the false positive rate and to increase the power, by accounting for complex demographic structures. Another stimulating goal is to develop straightforward parametric and computationally tractable tests to deal with massive SNP data sets. Here, we propose an extension of the original LK statistic (T(LK)), named T(F-LK), that uses a phylogenetic estimation of the population's kinship (F) matrix, thus accounting for historical branching and heterogeneity of genetic drift. Using forward simulations of single-nucleotide polymorphisms (SNPs) data under neutrality and selection, we confirm the relative robustness of the LK statistic (T(LK)) to complex demographic history but we show that T(F-LK) is more powerful in most cases. This new statistic outperforms also a multinomial-Dirichlet-based model [estimation with Markov chain Monte Carlo (MCMC)], when historical branching occurs. Overall, T(F-LK) detects 15-35% more selected SNPs than T(LK) for low type I errors (P < 0.001). Also, simulations show that T(LK) and T(F-LK) follow a chi-square distribution provided the ancestral allele frequencies are not too extreme, suggesting the possible use of the chi-square distribution for evaluating significance. The empirical distribution of T(F-LK) can be derived using simulations conditioned on the estimated F matrix. We apply this new test to pig breeds SNP data and pinpoint outliers using T(F-LK), otherwise undetected using the less powerful T(LK) statistic. This new test represents one solution for compromise between advanced SNP genetic data acquisition and outlier analyses.