Genome-wide association studies are now shifting focus from an analysis of common to uncommon and rare variants with an anticipation to explain additional variation in complex traits. As power for association testing for individual rare variants may often be low, various aggregate level association tests have been proposed to detect genetic loci that may contain clusters of causal variants. First, we show that these methods can be divided into two classes: tests based on linear and composite statistics (e.g. variance-component tests). Typically, power calculations for such tests require specification of many parameters, making them difficult to use in practice. In this presentation, we approximate power of linear and quadratic tests to varying degree of accuracy using a smaller number of key parameters, including the total genetic variance explained by multiple variants within a locus. Using the simplified power calculation methods, we then develop a mathematical framework to obtain bounds on the genetic architecture of an underlying trait given results from a genome-wide study. By using proposed framework, we observe important implications for lack or a limited number of findings in many currently reported studies. Finally, we provide insights into the required quality of annotation/functional information for identification of likely causal variants to make meaningful improvement in power of subsequent association tests.