In previous papers, see the references, the author introduced methods for estimating effects directly in samples of individuals whose genomes had be sequenced for the cases of one and two or more quantitative traits. In these papers, no attention was given to developing procedures of testing the statistical significance of the estimated effects. This paper is devoted to the development of statistical tests of significance of estimated effects for the simple case of one autosomal locus with two alleles, using Monte Carlo simulation methods. Because no real data was available to the author, artificial data for the three genotypes was simulated by using a Monte Carlo simulation procedures with fixed sample size for each genotypes as well as expectations and variances. In all cases considered, the null hypothesis was described in detail so as to inform a reader on the basic concepts underlying the proposed tests of statistical significance.