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Chunk #7 — Results and Discussion — Methods for calculating power with heritability in one-degree-of-freedom models

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GWAPower: a statistical power calculation software for genome-wide association studies with quantitative traits.
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For dominant and recessive models, the one-way ANOVA table and the terminologies are described in Table 1. The heritability is defined as H = SSM/SST. Given H and the total sample size N, SSE = (1-H)SST, MSE = (1-H)SST/(N-2), and F = H(N-2)/(1-H), which is now independent of SSM and SSE. The F statistics can be converted into t statistics using the square root. The (relative) standard deviation of the t-test is std = square root (MSE). The (relative) numerator of the t-statistic is: Δm = std*t. For the additive model, assuming a linear regression model is used, the variance can be similarly decomposed. For all models, the F-statistic is a function only of H and N. The power under the two-sided t-test at level α is expressed as