An important task in the genetic understanding of disease is determining whether there is a significant association between a phenotype and a set of markers. This task is sometimes referred to as a group test in a genome-wide association study. Examples of this task include determining whether a set of rare variants are associated with a phenotype, and whether a set of single nucleotide polymorphisms in a gene are associated with a phenotype. Another important task is determining whether a phenotype is significantly heritable (in the narrow sense) relative to a given set of genetic markers. We show that the two tasks can be formulated as the same statistical test. In addition, we show that the inclusion of extraneous markers in the set under consideration leads to substantial loss in power to detect heritability or association, a phenomenon we call dilution.