Intersection-Union Tests for Hierarchical Hypotheses

Implementation of proper intersection-union testing for hierarchical structures. This ensures that composite null hypotheses are tested appropriately and that the hierarchical structure is respected in hypothesis testing. Particularly useful for validating the logical structure of find_blocks() results.

Usage

intersection_union_tests(
  node_dat,
  tracker,
  alpha = 0.05,
  union_method = "max",
  intersection_method = "simes"
)

Arguments

node_dat

Node data with p-values and hierarchy

tracker

Node tracker with tree structure

alpha

Type I error rate

union_method

Method for testing union alternatives ("max", "simes", "fisher")

intersection_method

Method for testing intersection nulls ("min", "simes", "fisher")

Value

Updated node data with intersection-union test results

References

Berger, R. L. (1982). Multiparameter hypothesis testing and acceptance sampling. Technometrics, 24(4), 295-300.

Examples

if (FALSE) { # \dontrun{
# Apply intersection-union tests to find_blocks results
# Requires dplyr package
data(example_dat, package = "manytestsr")
library(data.table)
library(dplyr)

# Prepare data
idat <- as.data.table(example_dat)
bdat <- idat %>%
  group_by(blockF) %>%
  summarize(
    nb = n(),
    pb = mean(trt),
    hwt = (nb / nrow(idat)) * (pb * (1 - pb)),
    .groups = "drop"
  ) %>%
  as.data.table()

# Run find_blocks to get hierarchical structure
results <- find_blocks(
  idat = idat,
  bdat = bdat,
  blockid = "blockF",
  splitfn = splitCluster,
  pfn = pIndepDist,
  fmla = Y1 ~ trtF | blockF,
  splitby = "hwt",
  parallel = "no",
  maxtest = 15,
  trace = FALSE
)

# Apply intersection-union tests to validate hypothesis structure
iu_results <- intersection_union_tests(
  node_dat = results$node_dat,
  tracker = results$node_tracker, # Assuming tracker is available
  alpha = 0.05,
  union_method = "simes",
  intersection_method = "simes"
)

# Examine intersection-union test results
if ("iu_p_intersection" %in% names(iu_results$node_dat)) {
  iu_summary <- iu_results$node_dat[, .(
    nodenum,
    original_p = p,
    intersection_p = iu_p_intersection,
    union_p = iu_p_union,
    reject_intersection = iu_reject_intersection,
    reject_union = iu_reject_union
  )]

  cat("Intersection-Union Test Results:\n")
  print(head(iu_summary))

  # Count rejections by method
  cat("Intersection null rejections:", sum(iu_summary$reject_intersection, na.rm = TRUE), "\n")
  cat("Union alternative rejections:", sum(iu_summary$reject_union, na.rm = TRUE), "\n")
}

# Check consistency of intersection-union results
consistency_check <- check_iu_consistency(iu_results)
if (consistency_check$is_consistent) {
  cat("Intersection-union tests are logically consistent.\n")
} else {
  cat("Found inconsistencies:\n")
  print(consistency_check$inconsistencies)
}

# Visualize intersection-union results
if (requireNamespace("ggplot2", quietly = TRUE)) {
  iu_plot <- plot_intersection_union_results(iu_results)
  print(iu_plot)
}
} # }