A novel statistical model was developed to test for linkage disequilibrium between a polymorphic genetic marker locus and a locus underlying a quantitative trait (QTL) in natural populations using principles of analysis of variance of unbalanced data and analysis of regression involving data of non-normal distribution. Powers of these statistical tests are formulated as functions of census population size, allelic frequencies at the marker locus and the trait locus, additive and dominance effects at the QTL as well as the coefficient of linkage disequilibrium. Theoretical predictions of the power are validated by extensive Monte Carlo simulations. Among all these factors examined, the amount of the disequilibrium and the size of effect of the QTL are of most importance in determining the power, and the dominance and the allele frequencies at the two loci have substantial effects on the power. Numerical analyses based upon the theoretical calculations and simulation studies favour use of regression of the number of marker alleles on the trait phenotypes as a measure of detection of linkage disequilibrium. Theoretical analysis is also performed to investigate robustness of the formula for predicting the variance of the regression coefficient, which requires normality of the regression variables, whereas normality may not be strictly warranted.