PPI++ Two-Sample t-Test — ppi

Performs a two-sample hypothesis test for the difference in means between two independent groups using PPI++ estimators.

Usage

ppi_ttest(
  Y_A,
  f_A_L,
  f_A_U,
  Y_B,
  f_B_L,
  f_B_U,
  delta0 = 0,
  alpha = 0.05,
  lambda_A = NULL,
  lambda_B = NULL
)

Arguments

Y_A: Numeric vector of labeled outcomes for group A.
f_A_L: Numeric vector of predictions for labeled samples in group A.
f_A_U: Numeric vector of predictions for unlabeled samples in group A.
Y_B: Numeric vector of labeled outcomes for group B.
f_B_L: Numeric vector of predictions for labeled samples in group B.
f_B_U: Numeric vector of predictions for unlabeled samples in group B.
delta0: Null hypothesis value for the difference (default 0).
alpha: Significance level (default 0.05).
lambda_A: Optional lambda for group A. If NULL, uses EIF-optimal.
lambda_B: Optional lambda for group B. If NULL, uses EIF-optimal.

Value

A list with components:

estimate: The PPI++ estimate of the difference (mean_A - mean_B).
se: Standard error of the difference estimate.
z_stat: Z test statistic.
p_value: Two-sided p-value.
reject: Logical indicating whether null is rejected at level alpha.
lambda_A: Lambda used for group A.
lambda_B: Lambda used for group B.
ci: Confidence interval at level 1-alpha.

Examples

set.seed(123)
n <- 50; N <- 500
# Group A (treatment)
Y_A <- rnorm(n, mean = 0.3)
f_A_L <- Y_A + rnorm(n, sd = 0.5)
f_A_U <- rnorm(N, mean = 0.3) + rnorm(N, sd = 0.5)
# Group B (control)
Y_B <- rnorm(n, mean = 0)
f_B_L <- Y_B + rnorm(n, sd = 0.5)
f_B_U <- rnorm(N, mean = 0) + rnorm(N, sd = 0.5)

ppi_ttest(Y_A, f_A_L, f_A_U, Y_B, f_B_L, f_B_U)
#> $estimate
#> [1] 0.2489567
#> 
#> $se
#> [1] 0.1016156
#> 
#> $z_stat
#> [1] 2.449985
#> 
#> $p_value
#> [1] 0.01428622
#> 
#> $reject
#> [1] TRUE
#> 
#> $lambda_A
#> [1] 0.741807
#> 
#> $lambda_B
#> [1] 0.766848
#> 
#> $ci
#> [1] 0.04979377 0.44811963
#>