Minimum Sample Size for One-Way ANOVA Under the Falconer Model

Source: R/falconer_quantitative.R

Finds the smallest sufficient integer total sample size for the three-group one-way ANOVA. Both denominator degrees of freedom and the non-centrality parameter are recalculated for every candidate sample size.

qtl_anova_mssn(
  power,
  alpha,
  qtl_var,
  tau,
  pd,
  count_method = c("rounded", "expected"),
  multiple_of_three = TRUE,
  verbose = TRUE
)

Arguments

power

Target power in \((0,1)\).

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.

multiple_of_three

Logical. If TRUE, searches sample sizes in multiples of three. If FALSE, searches every integer sample size.

verbose

Logical. If TRUE, prints a concise summary.

Value

An object of class "qtl_anova_mssn" containing the smallest sufficient N, achieved power, degrees of freedom, non-centrality parameter, genotype counts, and Falconer parameters.

Details

For every candidate integer N, the genotype counts, denominator degrees of freedom, noncentrality parameter, critical F value, and achieved power are recomputed. With count_method = "rounded", candidates for which any genotype group has zero members are excluded. The first candidate attaining power is returned; setting multiple_of_three = TRUE restricts the search grid rather than changing the ANOVA formula. The model and NCP follow textbook Eqs. 6.7–6.8 (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_mssn(
  power = 0.8, alpha = 0.0001, qtl_var = 0.025,
  tau = 0.5, pd = 0.15, verbose = FALSE
)