We provide a solution that avoids assuming the non-centrality parameter in power calculations. In GWA data analysis, some popular genetic models have one degree of freedom including the dominant model, the recessive model and the additive model. When these genetic models are assumed, the one-way ANOVA model (dominant and recessive models) and the simple linear regression model (additive models) are used in the majority of GWA data analyses for quantitative traits. In these studies, the F-statistic is related to Student's t statistic, i.e. if a random variable X has a t distribution with d degrees of freedom, then X2 has F distribution (1, d). This is true for central and non-central distributions [6]. This suggests that so long as the genetic model contains only one degree of freedom, then an F distribution can be used to perform the square root transformation to obtain the t statistics for the power calculation.
