Type I error curve for the PP mean estimator
type1_error_curve_mean.RdComputes empirical and analytical Type I error estimates across a grid of
effect sizes using Monte Carlo via simulate_power(). When the null is true
(effect_size = 0), the curve reports the Type I error; for other effect
sizes the values coincide with the rejection probability (i.e., power).
Usage
type1_error_curve_mean(
effect_grid,
N,
n,
var_f,
var_res,
alpha = 0.05,
R = 10000,
seed = NULL
)Arguments
- effect_grid
Numeric vector of effect sizes \(\theta - \theta_0\) to evaluate.
- N
Unlabeled sample size.
- n
Labeled sample size.
- var_f
Variance of \(f(X)\).
- var_res
Variance of residuals \(Y - f(X)\).
- alpha
Two-sided significance level.
- R
Number of Monte Carlo replicates passed to
simulate_power().- seed
Optional RNG seed for reproducibility.
Value
Data frame with columns effect_size, type1_empirical,
type1_exact, N, n, alpha, var_f, and var_res.
Examples
type1_error_curve_mean(
effect_grid = seq(-0.4, 0.4, by = 0.05),
N = 4000,
n = 200,
var_f = 0.4,
var_res = 1.1,
R = 2000
)
#> effect_size type1_empirical type1_exact N n alpha var_f var_res
#> 1 -0.40 0.9995 0.9996444 4000 200 0.05 0.4 1.1
#> 2 -0.35 0.9965 0.9967072 4000 200 0.05 0.4 1.1
#> 3 -0.30 0.9800 0.9797667 4000 200 0.05 0.4 1.1
#> 4 -0.25 0.9165 0.9163301 4000 200 0.05 0.4 1.1
#> 5 -0.20 0.7620 0.7619701 4000 200 0.05 0.4 1.1
#> 6 -0.15 0.5175 0.5177820 4000 200 0.05 0.4 1.1
#> 7 -0.10 0.2670 0.2669161 4000 200 0.05 0.4 1.1
#> 8 -0.05 0.1025 0.1025043 4000 200 0.05 0.4 1.1
#> 9 0.00 0.0500 0.0500000 4000 200 0.05 0.4 1.1
#> 10 0.05 0.1025 0.1025043 4000 200 0.05 0.4 1.1
#> 11 0.10 0.2670 0.2669161 4000 200 0.05 0.4 1.1
#> 12 0.15 0.5175 0.5177820 4000 200 0.05 0.4 1.1
#> 13 0.20 0.7620 0.7619701 4000 200 0.05 0.4 1.1
#> 14 0.25 0.9165 0.9163301 4000 200 0.05 0.4 1.1
#> 15 0.30 0.9800 0.9797667 4000 200 0.05 0.4 1.1
#> 16 0.35 0.9965 0.9967072 4000 200 0.05 0.4 1.1
#> 17 0.40 0.9995 0.9996444 4000 200 0.05 0.4 1.1