Standard error of the genetic correlation: how much data do we need to estimate a purebred-crossbred genetic correlation?

Table 1 Comparison of predicted $S E ({\hat{r}}_{p c})$ from Equation 1 to empirical estimates from ANOVA and to empirical and reported estimates from ASReml

For $σ_{c}^{2} = 0$ ; ¹results are the SD among 1000 replicates of ${\hat{r}}_{p c}$ ; ²results are the average of reported SE of 200 replicates; ³results are the SD among 200 replicates of ${\hat{r}}_{p c}$ ; ⁴four replicates were fixed at the boundary of ${\hat{r}}_{p c}$ 1; with these four estimates removed the SE equaled 0.216; ⁵Empirical SE from ASReml were based on 200 replicates only, and may therefore deviate from the true SE. With 200 replicates, the SE of the relative empirical SE, i.e. the SE of the ratio of the empirical SE over the true SE, equals $S E [\hat{S E} ({\hat{r}}_{p c}) / S E ({\hat{r}}_{p c})]$ = $1 / \sqrt{2 \times (200 - 1)}$ ≈0.05 [13]; thus a 5% error in predicted SE does not indicate a significant discrepancy between predictions and simulations, indicating that 200 replicates yield a limited accuracy of the empirical SE; when predicted $S E ({\hat{r}}_{p c})$ is unbiased, the expected absolute relative error equals ≈ 3.5%, and a relative error >9.8% indicates a significant difference between empirical and predicted $S E ({\hat{r}}_{p c})$ (P <0.05; two-sided, not accounting for multiple testing).

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