test-aicpa-appendix-c.R
In jfa: Statistical Methods for Auditing

# Copyright (C) 2020-2023 Koen Derks

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# it under the terms of the GNU General Public License as published by
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context("Benchmark against Appendix C (AICPA 2017)")

# Audit Guide: Audit Sampling [https://future.aicpa.org/cpe-learning/publication/audit-sampling-audit-guide-OPL]
# Retrieved on 28-04-2021 from https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781119448617.app3

test_that(desc = "(id f10-v0.4.0-t1) Test Monetary Unit Sample Sizes for 5 percent risk of overreliance (AICPA 2017 - Appendix C: Table C-1)", {
  testthat::skip_on_cran()
  riskOfIncorrectAcceptance <- c(rep(5, 6), rep(10, 5), rep(15, 5), rep(20, 5), rep(25, 5), rep(30, 4), rep(35, 4), rep(50, 4)) / 100
  ratioExpectedTolerable <- c(seq(0, 0.5, 0.1), 0, seq(0.2, 0.5, 0.1), 0, seq(0.2, 0.5, 0.1), 0, seq(0.2, 0.5, 0.1), 0, seq(0.2, 0.5, 0.1), 0, seq(0.2, 0.6, 0.2), 0, seq(0.2, 0.6, 0.2), 0, seq(0.2, 0.6, 0.2))
  tolerableMisstatement <- c(0.5, 0.3, 0.1, 0.08, 0.06, 0.05, 0.04, 0.03, 0.02, 0.01, 0.005)
  sampleSizeMatrix <- matrix(NA, nrow = length(riskOfIncorrectAcceptance), ncol = length(tolerableMisstatement) + 3)
  colnames(sampleSizeMatrix) <- c("Risk", "Expected", tolerableMisstatement, "Taints")
  sampleSizeMatrix[, 1] <- riskOfIncorrectAcceptance
  sampleSizeMatrix[, 2] <- ratioExpectedTolerable
  for (i in seq_len(nrow(sampleSizeMatrix))) {
    for (j in seq_along(tolerableMisstatement)) {
      jfaRes <- planning(conf.level = (1 - sampleSizeMatrix[i, 1]), expected = tolerableMisstatement[j] * sampleSizeMatrix[i, 2], likelihood = "poisson", materiality = tolerableMisstatement[j])
      sampleSizeMatrix[i, j + 2] <- jfaRes[["n"]]
    }
    sampleSizeMatrix[i, 14] <- ceiling(jfaRes[["x"]] * 100) / 100
  }

  aicpaMatrix <- matrix(data = NA, nrow = length(riskOfIncorrectAcceptance), ncol = length(tolerableMisstatement) + 3, byrow = FALSE)
  colnames(aicpaMatrix) <- c("Risk", "Expected", tolerableMisstatement, "Taints")
  aicpaMatrix[, 1] <- riskOfIncorrectAcceptance
  aicpaMatrix[, 2] <- ratioExpectedTolerable
  aicpaMatrix[, 3:14] <- matrix(
    c(
      6, 10, 30, 38, 50, 60, 75, 100, 150, 300, 600, 0,
      8, 13, 37, 46, 62, 74, 92, 123, 184, 368, 736, 0.37,
      10, 16, 47, 58, 78, 93, 116, 155, 232, 463, 925, 0.93, # For taints of highest materiality percentage AICPA gives 0.93 but correct value is 0.92000000000000004
      12, 20, 60, 75, 100, 120, 150, 200, 300, 600, 1199, 1.80,
      17, 27, 81, 102, 135, 162, 203, 270, 405, 809, 1618, 3.24,
      24, 39, 116, 145, 193, 231, 289, 385, 577, 1154, 2308, 5.77,
      5, 8, 24, 29, 39, 47, 58, 77, 116, 231, 461, 0,
      7, 12, 35, 43, 57, 69, 86, 114, 171, 341, 682, 0.69, # For taints of highest materiality percentage AICPA gives 0.69 but correct value is 0.68000000000000005
      9, 15, 44, 55, 73, 87, 109, 145, 217, 433, 866, 1.30,
      12, 20, 58, 72, 96, 115, 143, 191, 286, 572, 1144, 2.29,
      16, 27, 80, 100, 134, 160, 200, 267, 400, 799, 1597, 4.00, # For taints of highest materiality percentage AICPA gives 4 but correct value is 3.9900000000000002
      4, 7, 19, 24, 32, 38, 48, 64, 95, 190, 380, 0,
      6, 10, 28, 35, 46, 55, 69, 91, 137, 273, 545, 0.55, # For taints of highest materiality percentage AICPA gives 0.55 but correct value is 0.55000000000000004
      7, 12, 35, 43, 57, 69, 86, 114, 171, 341, 681, 1.03, # For taints of highest materiality percentage AICPA gives 1.03 but correct value is 1.02
      9, 15, 45, 56, 74, 89, 111, 148, 221, 442, 883, 1.77,
      13, 21, 61, 76, 101, 121, 151, 202, 302, 604, 1208, 3.02,
      4, 6, 17, 21, 27, 33, 41, 54, 81, 161, 322, 0,
      5, 8, 23, 29, 38, 46, 57, 76, 113, 226, 451, 0.46, # For taints of highest materiality percentage AICPA gives 0.46 but correct value is 0.45000000000000001
      6, 10, 28, 35, 47, 56, 70, 93, 139, 277, 554, 0.84, # For taints AICPA gives 0.84 but correct value is 0.82999999999999996
      8, 12, 36, 45, 59, 71, 89, 118, 177, 354, 707, 1.42, # For taints of highest materiality percentage AICPA gives 1.42 but correct value is 1.4099999999999999
      10, 16, 48, 60, 80, 95, 119, 159, 238, 475, 949, 2.38, # For taints of highest materiality percentage AICPA gives 2.28 but correct value is 2.3700000000000001
      3, 5, 14, 18, 24, 28, 35, 47, 70, 139, 278, 0,
      4, 7, 19, 24, 32, 38, 48, 64, 95, 190, 380, 0.38,
      5, 8, 23, 29, 39, 46, 58, 77, 115, 230, 460, 0.69,
      6, 10, 29, 37, 49, 58, 73, 97, 145, 289, 578, 1.16,
      8, 13, 38, 48, 64, 76, 95, 127, 190, 380, 760, 1.90,
      3, 5, 13, 16, 21, 25, 31, 41, 61, 121, 241, 0,
      4, 6, 17, 21, 27, 33, 41, 54, 81, 162, 323, 0.33, # For taints of highest materiality percentage AICPA gives 0.33 but correct value is 0.32000000000000001
      5, 8, 24, 30, 40, 48, 60, 80, 120, 239, 477, 0.96, # For taints of highest materiality percentage AICPA gives 0.96 but correct value is 0.94999999999999996
      9, 15, 43, 54, 71, 85, 107, 142, 213, 425, 850, 2.55,
      3, 4, 11, 14, 18, 21, 27, 35, 53, 105, 210, 0,
      3, 5, 14, 18, 23, 28, 35, 46, 69, 138, 276, 0.28, # For taints of highest materiality percentage AICPA gives 0.28 but correct value is 0.28000000000000003
      4, 7, 20, 25, 34, 40, 50, 67, 100, 199, 397, 0.80, # For taints of highest materiality percentage AICPA gives 0.80 but correct value is 0.79000000000000004
      7, 12, 34, 43, 57, 68, 85, 113, 169, 338, 676, 2.03,
      2, 3, 7, 9, 12, 14, 18, 24, 35, 70, 139, 0,
      2, 3, 9, 11, 15, 18, 22, 29, 44, 87, 173, 0.18, # For taints of highest materiality percentage AICPA gives 0.18 but correct value is 0.17000000000000001
      3, 4, 12, 15, 19, 23, 29, 38, 57, 114, 228, 0.46,
      4, 6, 17, 22, 29, 34, 43, 57, 85, 170, 340, 1.02
    ),
    ncol = length(tolerableMisstatement) + 1, nrow = length(riskOfIncorrectAcceptance), byrow = TRUE
  )

  expect_equal(sampleSizeMatrix, aicpaMatrix, tolerance = 0.01)
})