Compute the frequentist power at an estimated type I error — compute_power_with_tie

Propagates the uncertainty of the equivalent type I error, and the Monte Carlo error of the power itself, into an interval for the power a separate frequentist analysis would reach at that type I error.

The reported bounds are quantiles of the resulting posterior for the power, not a frequentist confidence interval; they are stored under the existing conf_int_power name for continuity with the columns downstream.

Usage

compute_power_with_tie_ci(
  alpha,
  target_data,
  frequentist_test,
  theta_0,
  null_space,
  simulation_config,
  case_study = NULL,
  n_replicates = 1000,
  n_samples = 1000,
  p_values = NULL,
  null_p_values = NULL
)

Arguments

alpha: A list describing the estimated type I error: its mean, its exact interval bounds, and its mcse or n_replicates when available.
target_data: Target data object.
frequentist_test: Type of frequentist test to apply, either z-test or t-test.
theta_0: Boundary of the null hypothesis space.
null_space: Side of the null space, either left or right.
simulation_config: Simulation configuration.
case_study: Optional case-study name.
n_replicates: Number of Monte Carlo replicates for non-analytical power.
n_samples: Number of draws of the type I error.
p_values: Optional p-values of the separate analysis, already simulated for this design by simulate_test_p_values(). They depend on the design alone, not on the borrowing method, so a caller pricing many rows of one design simulates them once and passes them here. NULL simulates them. Ignored when the power has a closed form.
null_p_values: Optional p-values of the same test on the trials of the design's null scenario. When given, each sampled type I error is matched by the test's actual rejection rate there rather than by its nominal level - see calibrated_levels(). Ignored when the power has a closed form.

Value

A list with the power, its interval, and the number of draws used.