16:T7d4, # Load the required package # Install if not already present if (!requireNamespace("BinomSamSize", quietly = TRUE)) { install.packages("BinomSamSize") } library(BinomSamSize) # Define the parameters acceptance_criterion <- 0.77 # p0: Null hypothesis proportion expected_performance <- 0.95 # p: Alternative hypothesis proportion confidence_level <- 0.80 # Corresponds to alpha = 1 - confidence_level power <- 0.80 # 1 - beta # Calculate alpha and beta alpha <- 1 - confidence_level beta <- 1 - power # Calculate the sample size using the exact binomial test (Clopper-Pearson related) # We use a one-sided test because we expect performance (0.95) to be greater than the criterion (0.77) # H0: p <= 0.77 vs H1: p > 0.77 sample_size_result <- ciss.binom( p0 = acceptance_criterion, p = expected_performance, alpha = alpha, beta = beta, side = 1 # One-sided test ) # Extract the minimum sample size min_sample_size <- sample_size_result$n # Print the result cat("Minimum Sample Size Calculation using Exact Binomial Test (Clopper-Pearson method):\n") cat("---------------------------------------------------------------------------------\n") cat("Acceptance Criterion (p0):", acceptance_criterion, "\n") cat("Expected Performance (p): ", expected_performance, "\n") cat("Confidence Level: ", confidence_level, "(alpha =", alpha, ")\n") cat("Desired Power: ", power, "(beta =", beta, ")\n") cat("Test Type: ", "One-sided (p > p0)\n") cat("---------------------------------------------------------------------------------\n") cat("Minimum Required Sample Size (n):", min_sample_size, "\n") cat("Critical Value (c): ", sample_size_result$c, "\n") # You can run this script directly in R using: source("calculate_sample_size.R") 17:T70e,# Load the required package