This paper concerns several important points when testing for Hardy-Weinberg equilibrium (HWE) and linkage disequilibrium (LD) in genetics. First, we challenge the necessity of using exclusively two-sided tests for LD. Next, we show that the exact 2-sided tests based on the most popular measures of LD are not equivalent, and neither are the standard statistical tests even though the 1-sided tests are equivalent. We show how this results in different inference about LD for two data sets consisting of small groups of markers. Finally, we advocate the use of the conditional p-value for both LD and HWE testing. An important advantage of this p-value is that equivalent 1-sided tests are transformed into equivalent 2-sided tests.