Power for One-Way ANOVA Under the Falconer Model

Source: R/falconer_quantitative.R

Calculates power for a one-way ANOVA comparing the means of the three SNP genotype groups for one continuous quantitative trait.

qtl_anova_power(
  N,
  alpha,
  qtl_var,
  tau,
  pd,
  count_method = c("rounded", "expected"),
  verbose = TRUE
)

Arguments

N

Integer total sample size greater than 3.

alpha

Significance level in \((0,1)\).

qtl_var

Variance in the standardized trait attributable to the QTL. Must be in \((0,1)\).

tau

Finite dominance-to-additivity ratio \(\delta/a\).

pd

Frequency of the increaser allele. Must be in \((0,1)\).

count_method

Genotype count method. "rounded" rounds expected genotype counts to the nearest integer before computing the ANOVA quantities. "expected" uses expected genotype counts directly without rounding.

verbose

Logical. If TRUE, prints a concise summary.

Value

An object of class "qtl_anova_power" containing power, sample size, degrees of freedom, critical value, non-centrality parameter, genotype counts, genotype means, residual variance, and the complete Falconer parameter object.

Details

The three genotype groups have the means returned by qtl_falconer_parameters() and a common residual variance \(1-V_{QTL}\). Genotype group counts are either rounded Hardy–Weinberg expectations or unrounded expected counts according to count_method. The between-group effect gives the noncentrality parameter in textbook Eq. 6.8, and power is the upper tail of a noncentral F distribution with numerator degrees of freedom 2 and denominator degrees of freedom \(N-3\). Genotype counts follow Eq. 6.7 (Chapter 6, Section 6.1.1, p. 328).

References

Gordon, D., Finch, S. J., & Kim, W. (2020). Heterogeneity in Statistical Genetics: How to Assess, Address, and Account for Mixtures in Association Studies. Springer, Chapter 6, Section 6.1.1, Eqs. 6.7–6.8, p. 328. doi:10.1007/978-3-030-61121-7 .

Examples

qtl_anova_power(
  N = 996, alpha = 0.0001, qtl_var = 0.025,
  tau = 0.5, pd = 0.15, verbose = FALSE
)