R/commonClassicalAuditMethods.R
In koenderks/JASP-for-Audit: Audit Module for JASP
.calc.n.binomial <- function(options, alpha, jaspResults){
jaspResults$startProgressbar(5000)
for(n in 1:5000){
jaspResults$progressbarTick()
impk <- base::switch(options[["expectedErrors"]], "expectedRelative" = ceiling(n * options[["expectedPercentage"]]), "expectedAbsolute" = ceiling(options[["expectedNumber"]] / jaspResults[["total_data_value"]]$object * n))
if(impk >= n){ next }
x <- dbinom(0:impk, size = n, prob = jaspResults[["materiality"]]$object)
if(sum(x) < alpha){
return(n)
}
}
jaspResults[["errorInSampler"]] <- createJaspState(TRUE)
jaspResults[["errorInSampler"]]$dependOn(options = c("materiality", "materialityPercentage", "materialityValue", "expectedNumber", "expectedErrors", "populationValue", "populationSize"))
return(1)
}
.calc.n.hypergeometric <- function(options, alpha, jaspResults){
jaspResults$startProgressbar(5000)
K <- ceiling(jaspResults[["N"]]$object * jaspResults[["materiality"]]$object)
for(n in 1:5000){
jaspResults$progressbarTick()
impk <- base::switch(options[["expectedErrors"]], "expectedRelative" = ceiling(n * options[["expectedPercentage"]]), "expectedAbsolute" = ceiling(options[["expectedNumber"]] / jaspResults[["total_data_value"]]$object * n))
if(impk >= n) { next }
x <- dhyper(x = 0:impk, m = K, n = jaspResults[["N"]]$object - K, k = n)
if(sum(x) < alpha){
return(n)
}
}
jaspResults[["errorInSampler"]] <- createJaspState(TRUE)
jaspResults[["errorInSampler"]]$dependOn(options = c("materiality", "materialityPercentage", "materialityValue", "expectedNumber", "expectedErrors", "populationValue", "populationSize"))
return(1)
}
.calc.n.poisson <- function(options, alpha, jaspResults){
jaspResults$startProgressbar(5000)
for(n in 1:5000){
jaspResults$progressbarTick()
k <- base::switch(options[["expectedErrors"]], "expectedRelative" = (n * options[["expectedPercentage"]]), "expectedAbsolute" = (options[["expectedNumber"]] / jaspResults[["total_data_value"]]$object * n))
x <- pgamma(jaspResults[["materiality"]]$object, shape = 1 + k, scale = 1 / n)
#x <- dpois(x = 0:k, lambda = jaspResults[["materiality"]]$object * n)
if(x >= (1 - alpha)){
return(n)
}
}
jaspResults[["errorInSampler"]] <- createJaspState(TRUE)
jaspResults[["errorInSampler"]]$dependOn(options = c("materiality", "materialityPercentage", "materialityValue", "expectedNumber", "expectedErrors", "populationValue", "populationSize"))
return(1)
}
.classicalPlanningHelper <- function(options, jaspResults, planningContainer){
if(!is.null(jaspResults[["planningResult"]]$object)) return(jaspResults[["planningResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
k <- 0
if(jaspResults[["ready"]]$object && !planningContainer$getError()){
n <- base::switch(options[["planningModel"]],
"Poisson" = .calc.n.poisson(options, alpha, jaspResults),
"binomial" = .calc.n.binomial(options, alpha, jaspResults),
"hypergeometric" = .calc.n.hypergeometric(options, alpha, jaspResults))
k <- base::switch(options[["expectedErrors"]], "expectedRelative" = options[["expectedPercentage"]], "expectedAbsolute" = options[["expectedNumber"]] / n)
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- k
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["alpha"]] <- alpha
resultList[["confidence"]] <- options[["confidence"]]
jaspResults[["planningResult"]] <- createJaspState(resultList)
jaspResults[["planningResult"]]$dependOn(options = c("IR", "CR", "confidence", "expectedNumber", "materialityPercentage", "planningModel", "expectedPercentage", "expectedNumber",
"materialityValue", "materiality", "recordNumberVariable", "monetaryVariable"))
return(jaspResults[["planningResult"]]$object)
}
.classicalPlanningTable <- function(dataset, options, planningResult, jaspResults, position = 1, planningContainer){
if(!is.null(planningContainer[["planningSummary"]])) return() #The options for this table didn't change so we don't need to rebuild it
planningSummary <- createJaspTable("Planning Summary")
planningSummary$position <- position
planningSummary$dependOn(options = c("IR", "CR", "confidence", "materialityPercentage", "planningModel", "recordNumberVariable", "monetaryVariable",
"expectedErrors" , "expectedPercentage", "expectedNumber", "materialityValue", "materiality"))
planningSummary$addColumnInfo(name = 'materiality', title = "Materiality", type = 'string')
planningSummary$addColumnInfo(name = 'IR', title = "Inherent risk", type = 'string')
planningSummary$addColumnInfo(name = 'CR', title = "Control risk", type = 'string')
planningSummary$addColumnInfo(name = 'DR', title = "Detection risk", type = 'string')
planningSummary$addColumnInfo(name = 'k', title = "Expected errors", type = 'string')
planningSummary$addColumnInfo(name = 'n', title = "Required sample size", type = 'string')
if(!jaspResults[["ready"]]$object){
message <- base::switch(options[["planningModel"]],
"Poisson" = paste0("The required sample size is based on the <b>Poisson</b> distribution."),
"binomial" = paste0("The required sample size is based on the <b>binomial</b> distribution."),
"hypergeometric" = paste0("The required sample size is based on the <b>hypergeometric</b> distribution."))
planningSummary$addFootnote(message = message, symbol="<i>Note.</i>")
}
planningContainer[["planningSummary"]] <- planningSummary
if(!is.null(jaspResults[["errorInSampler"]])){
planningContainer$setError("There is no sample size (< 5000) large enough to prove the current materiality. Please try other values.")
return()
}
ktable <- base::switch(options[["expectedErrors"]], "expectedRelative" = round(planningResult[["k"]] * planningResult[["n"]], 2), "expectedAbsolute" = paste(jaspResults[["valutaTitle"]]$object, options[["expectedNumber"]]))
if(options[["planningModel"]] != "Poisson" && options[["expectedErrors"]] == "expectedRelative")
ktable <- ceiling(ktable)
DRtable <- paste0(round(planningResult[["alpha"]], 3) * 100, "%")
if(jaspResults[["materiality"]]$object == 0){
row <- data.frame(materiality = ".", IR = planningResult[["IR"]], CR = planningResult[["CR"]], DR = DRtable, k = 0, n = ".")
planningSummary$addRows(row)
planningSummary$addFootnote(message = "The materiality is defined as 0.", symbol="<b>ANALYSIS NOT READY.</b>")
return()
}
materialityTitle <- paste0(round(jaspResults[["materiality"]]$object * 100, 2), "%")
materialityValue <- base::switch(options[["materiality"]], "materialityRelative" = ceiling(jaspResults[["materiality"]]$object * sum(dataset[, .v(options[["monetaryVariable"]])])), "materialityAbsolute" = options[["materialityValue"]])
materiality <- base::switch(options[["materiality"]], "materialityRelative" = materialityTitle, "materialityAbsolute" = paste(jaspResults[["valutaTitle"]]$object, materialityValue))
if(!jaspResults[["ready"]]$object || planningContainer$getError()){
row <- data.frame(materiality = materiality, IR = planningResult[["IR"]], CR = planningResult[["CR"]], DR = DRtable, k = ktable, n = ".")
planningSummary$addRows(row)
return()
}
if(planningResult[["n"]] > jaspResults[["N"]]$object && jaspResults[["ready"]]$object){
planningContainer$setError("The required sample size is larger than the population size. You cannot audit this population with this materiality and this amount of confidence.")
return()
}
message <- base::switch(options[["planningModel"]],
"Poisson" = paste0("The required sample size is based on the <b>Poisson</b> distribution <i>(\u03BB = ", round(jaspResults[["materiality"]]$object * planningResult[["n"]], 4) , ")</i>."),
"binomial" = paste0("The required sample size is based on the <b>binomial</b> distribution <i>(p = ", round(jaspResults[["materiality"]]$object, 2) ,")</i>."),
"hypergeometric" = paste0("The required sample size is based on the <b>hypergeometric</b> distribution <i>(N = ", jaspResults[["N"]]$object ,", K = ", ceiling(jaspResults[["N"]]$object * jaspResults[["materiality"]]$object) ,")</i>."))
planningSummary$addFootnote(message = message, symbol="<i>Note.</i>")
row <- data.frame(materiality = materiality, IR = planningResult[["IR"]], CR = planningResult[["CR"]], DR = DRtable, k = ktable, n = planningResult[["n"]])
planningSummary$addRows(row)
}
.attributesBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
k <- 0
bound <- "."
if(jaspResults[["runEvaluation"]]$object){
if(options[["estimator"]] == "binomialBound"){
n <- jaspResults[["sampleSize"]]$object
kIndex <- which(dataset[,.v(options[["auditResult"]])] == 1)
if(options[["sampleFilter"]] != ""){
kNumber <- dataset[kIndex ,.v(options[["sampleFilter"]])]
k <- length(rep(kIndex, times = kNumber))
} else {
k <- length(kIndex)
}
binomResult <- binom.test(x = k,
n = n,
p = jaspResults[["materiality"]]$object,
alternative = "less",
conf.level = (1 - alpha))
bound <- binomResult$conf.int[2]
} else if(options[["estimator"]] == "hyperBound"){
N <- jaspResults[["N"]]$object
n <- jaspResults[["sampleSize"]]$object
kIndex <- which(dataset[,.v(options[["auditResult"]])] == 1)
if(options[["sampleFilter"]] != ""){
kNumber <- dataset[kIndex ,.v(options[["sampleFilter"]])]
k <- length(rep(kIndex, times = kNumber))
} else {
k <- length(kIndex)
}
for(K in 1000:1){
x <- phyper(k, K, N - K, n)
if(x >= 0.05)
break
}
bound <- K / N
} else if(options[["estimator"]] == "gammaBound"){
n <- jaspResults[["sampleSize"]]$object
kIndex <- which(dataset[,.v(options[["auditResult"]])] == 1)
kNumber <- dataset[kIndex ,.v(options[["sampleFilter"]])]
k <- length(rep(kIndex, times = kNumber))
bound <- qgamma(p = (1 - alpha), shape = 1 + k, scale = 1 / n)
}
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- k
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage", "materialityValue", "performAudit", "estimator"))
return(jaspResults[["evaluationResult"]]$object)
}
.attributesBoundTable <- function(options, evaluationResult, jaspResults, position = 1, evaluationContainer){
if(!is.null(evaluationContainer[["evaluationTable"]])) return() #The options for this table didn't change so we don't need to rebuild it
evaluationTable <- createJaspTable("Evaluation Summary")
evaluationTable$position <- position
evaluationTable$dependOn(options = c("IR", "CR", "confidence", "materialityPercentage", "auditResult", "sampleFilter", "planningModel",
"mostLikelyError", "materialityValue", "auditType", "valuta", "performAudit", "estimator"))
evaluationTable$addColumnInfo(name = 'materiality', title = "Materiality", type = 'string')
evaluationTable$addColumnInfo(name = 'n', title = "Sample size", type = 'string')
evaluationTable$addColumnInfo(name = 'k', title = "Errors", type = 'string')
if(options[["mostLikelyError"]])
evaluationTable$addColumnInfo(name = 'mle', title = "MLE", type = 'string')
evaluationTable$addColumnInfo(name = 'bound', title = paste0(options[["confidence"]] * 100,"% Confidence bound"), type = 'string')
if(options[["materiality"]] == "materialityAbsolute" || options[["monetaryVariable"]] != "")
evaluationTable$addColumnInfo(name = 'projm', title = "Maximum Misstatement", type = 'string')
message <- base::switch(options[["estimator"]],
"gammaBound" = "The confidence bound is calculated according to the <b>gamma</b> distributon.",
"binomialBound" = "The confidence bound is calculated according to the <b>binomial</b> distributon.",
"hyperBound" = "The confidence bound is calculated according to the <b>hypergeometric</b> distribution.")
evaluationTable$addFootnote(message = message, symbol="<i>Note.</i>")
evaluationContainer[["evaluationTable"]] <- evaluationTable
materialityTable <- ifelse(options[["materiality"]] == "materialityRelative", yes = paste0(round(jaspResults[["materiality"]]$object, 2) * 100, "%"), no = paste(jaspResults[["valutaTitle"]]$object, options[["materialityValue"]]))
# Return empty table
if(!jaspResults[["runEvaluation"]]$object){
row <- data.frame(materiality = materialityTable, n = ".", k = ".", bound = ".")
if(options[["materiality"]] == "materialityAbsolute" || options[["monetaryVariable"]] != "")
row <- cbind(row, projm = ".")
evaluationTable$addRows(row)
return()
}
mle <- 0
if(jaspResults[["N"]]$object != 0)
mle <- paste0(round(evaluationResult[["k"]] / evaluationResult[["n"]], 4) * 100, "%")
boundTable <- "."
if(evaluationResult[["bound"]] != ".")
boundTable <- paste0(round(evaluationResult[["bound"]], 4) * 100, "%")
row <- data.frame(materiality = materialityTable, n = evaluationResult[["n"]], k = evaluationResult[["k"]], bound = boundTable)
if(options[["materiality"]] == "materialityAbsolute" || options[["monetaryVariable"]] != "")
row <- cbind(row, projm = paste(jaspResults[["valutaTitle"]]$object, round(evaluationResult[["bound"]] * jaspResults[["total_data_value"]]$object, 2)))
if(options[["mostLikelyError"]])
row <- cbind(row, mle = mle)
evaluationTable$addRows(row)
}
.stringerBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
# Based on the paper:
# Stringer, K. W. (1963). Practical aspects of statistical sampling in auditing. In Proceedings of the Business and Economic Statistics Section (pp. 405-411). American Statistical Association.
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
NoOfErrors <- 0
z <- 0
bound <- "."
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
if(options[["sampleFilter"]] != ""){
z <- rep(z, times = dataset[ ,.v(options[["sampleFilter"]])])
}
n <- length(z)
zplus <- sort(subset(z, z > 0), decreasing = TRUE)
zmin <- sort(subset(z, z < 0), decreasing = TRUE)
M <- length(zplus)
NoOfErrors <- length(which(z != 0))
bound <- 1 - alpha^(1 / n)
if(M > 0){
prop.sum <- 0
for(i in 1:M){
prop.sum <- prop.sum + ((qbeta(1 - alpha, i + 1, n - i) - qbeta(1 - alpha, (i - 1) + 1, n - (i - 1) )) * zplus[i])
}
bound <- bound + prop.sum
}
if(options[["stringerBoundLtaAdjustment"]]){
bound <- bound - ( (1/n) * sum(abs(zmin)) )
}
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- NoOfErrors
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "variableType", "auditResult", "materiality", "estimator", "materialityValue", "materialityPercentage", "stringerBoundLtaAdjustment", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
.auditValueBoundTable <- function(options, evaluationResult, jaspResults, position = 1, evaluationContainer){
if(!is.null(evaluationContainer[["evaluationTable"]])) return() #The options for this table didn't change so we don't need to rebuild it
evaluationTable <- createJaspTable("Evaluation Summary")
evaluationTable$position <- position
evaluationTable$dependOn(options = c("IR", "CR", "confidence", "materialityPercentage", "auditResult", "planningModel", "mostLikelyError", "sampleFilter", "variableType",
"estimator", "monetaryVariable", "materialityValue", "valuta", "stringerBoundLtaAdjustment", "performAudit"))
evaluationTable$addColumnInfo(name = 'materiality', title = "Materiality", type = 'string')
evaluationTable$addColumnInfo(name = 'n', title = "Sample size", type = 'string')
evaluationTable$addColumnInfo(name = 'fk', title = "Errors", type = 'string')
evaluationTable$addColumnInfo(name = 'k', title = "Total tainting", type = 'string')
if(options[["mostLikelyError"]])
evaluationTable$addColumnInfo(name = 'mle', title = "MLE", type = 'string')
evaluationTable$addColumnInfo(name = 'bound', title = paste0(options[["confidence"]] * 100,"% Confidence bound"), type = 'string')
evaluationTable$addColumnInfo(name = 'projm', title = "Maximum Misstatement", type = 'string')
message <- base::switch(options[["estimator"]],
"stringerBound" = "The confidence bound is calculated according to the <b>Stringer</b> method.",
"regressionBound" = "The confidence bound is calculated according to the <b>regression</b> method.",
"directBound" = "The confidence bound is calculated according to the <b>direct</b> method.",
"differenceBound" = "The confidence bound is calculated according to the <b>difference</b> method.",
"ratioBound" = "The confidence bound is calculated according to the <b>ratio</b> method.")
evaluationTable$addFootnote(message = message, symbol="<i>Note.</i>")
evaluationContainer[["evaluationTable"]] <- evaluationTable
materialityTable <- ifelse(options[["materiality"]] == "materialityRelative", yes = paste0(round(jaspResults[["materiality"]]$object, 2) * 100, "%"), no = paste(jaspResults[["valutaTitle"]]$object, options[["materialityValue"]]))
# Return empty table with materiality
if(!jaspResults[["runEvaluation"]]$object){
row <- data.frame(materiality = materialityTable, n = ".", fk = ".", k = ".", bound = ".", projm = ".")
evaluationTable$addRows(row)
return()
}
total_data_value <- jaspResults[["total_data_value"]]$object
mle <- 0
if(options[["estimator"]] == "stringerBound"){
mle <- paste0(round(sum(evaluationResult[["z"]]) / evaluationResult[["n"]], 4) * 100, "%")
} else {
mle <- paste(jaspResults[["valutaTitle"]]$object, round(evaluationResult[["mleTable"]] * total_data_value, 2))
}
errors <- round(sum(evaluationResult[["z"]]), 2)
boundTable <- "."
projectedMisstatement <- "."
if(evaluationResult[["bound"]] != "."){
boundTable <- round(evaluationResult[["bound"]], 4)
projectedMisstatement <- paste(jaspResults[["valutaTitle"]]$object, ceiling(evaluationResult[["bound"]] * total_data_value))
boundTable <- paste0(boundTable * 100, "%")
}
row <- data.frame(materiality = materialityTable, n = evaluationResult[["n"]], fk = evaluationResult[["k"]], k = errors, bound = boundTable, projm = projectedMisstatement)
if(options[["mostLikelyError"]])
row <- cbind(row, mle = mle)
evaluationTable$addRows(row)
}
.directBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
M <- 0
z <- 0
bound <- "."
mle <- 0
mleTable <- 0
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
n <- nrow(sample)
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
M <- length(which(t != 0))
B <- jaspResults[["total_data_value"]]$object
N <- jaspResults[["N"]]$object
w <- sample[, .v(options[["auditResult"]])]
meanw <- mean(w)
mle <- N * meanw
stand.dev <- sd(w) * (N / sqrt(n)) * sqrt( (N-n) / (N-1) )
lowerValue <- mle - qt(p = 1 - alpha, df = n - 1) * stand.dev
bound <- (B - lowerValue) / B
mleTable <- (B - mle) / B
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- M
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
resultList[["mle"]] <- mle
resultList[["mleTable"]] <- mleTable
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage", "estimator", "monetaryVariable", "materialityValue", "variableType", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
.differenceBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
M <- 0
z <- 0
bound <- "."
mle <- 0
mleTable <- 0
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
n <- nrow(sample)
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
M <- length(which(t != 0))
B <- jaspResults[["total_data_value"]]$object
N <- jaspResults[["N"]]$object
w <- sample[, .v(options[["auditResult"]])]
meanw <- mean(w)
meant <- mean(t)
mle <- B - N * meant
stand.dev <- sd(t) * (N / sqrt(n)) * sqrt( (N-n) / (N-1) )
lowerValue <- mle - qt(p = 1 - alpha, df = n - 1) * stand.dev
if(lowerValue == 0){
bound <- 0
} else {
bound <- (B - lowerValue) / B
}
mleTable <- (B - mle) / B
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- M
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
resultList[["mle"]] <- mle
resultList[["mleTable"]] <- mleTable
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage", "estimator", "monetaryVariable", "materialityValue", "variableType", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
.ratioBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
M <- 0
z <- 0
bound <- "."
mle <- 0
mleTable <- 0
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
n <- nrow(sample)
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
M <- length(which(t != 0))
B <- jaspResults[["total_data_value"]]$object
N <- jaspResults[["N"]]$object
w <- sample[, .v(options[["auditResult"]])]
b <- sample[, .v(options[["monetaryVariable"]])]
meanw <- mean(w)
meanb <- mean(b)
sumw <- sum(w)
sumb <- sum(b)
q <- sumw / sumb
mle <- q * B
stand.dev <- sqrt( ( sum(t^2) - 2 * (1-q) * sum(b*t) + (1 - q)^2 * sum(b^2) ) / (n - 1)) * (N / sqrt(n)) * sqrt( (N-n) / (N-1) )
lowerValue <- mle - qt(p = 1 - alpha, df = n - 1) * stand.dev
if(lowerValue == 0){
bound <- 0
} else {
bound <- (B - lowerValue) / B
}
mleTable <- (B - mle) / B
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- M
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
resultList[["mle"]] <- mle
resultList[["mleTable"]] <- mleTable
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage", "estimator", "monetaryVariable", "materialityValue", "variableType", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
.regressionBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
M <- 0
z <- 0
bound <- "."
mleregression <- 0
mleTable <- 0
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
n <- nrow(sample)
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
M <- length(which(t != 0))
B <- jaspResults[["total_data_value"]]$object
N <- jaspResults[["N"]]$object
b <- sample[, .v(options[["monetaryVariable"]])]
w <- sample[, .v(options[["auditResult"]])]
b1 <- as.numeric(coef(lm(w ~ b))[2])
meanb <- mean(b)
meanw <- mean(w)
mleregression <- N * meanw + b1 * (B - N * meanb)
stand.dev <- sd(w) * sqrt(1 - cor(b, w)^2) * ( N / sqrt(n)) * sqrt( (N-n) / (N-1) )
lowerValue <- mleregression - qt(p = 1 - alpha, df = n - 1) * stand.dev
if(lowerValue == 0){
bound <- 0
} else {
bound <- (B - lowerValue) / B
}
mleTable <- (B - mleregression) / B
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- M
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
resultList[["mle"]] <- mleregression
resultList[["mleTable"]] <- mleTable
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage",
"estimator", "monetaryVariable", "materialityValue", "variableType", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
koenderks/JASP-for-Audit documentation built on June 22, 2019, 2:57 a.m.
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.calc.n.binomial <- function(options, alpha, jaspResults){
jaspResults$startProgressbar(5000)
for(n in 1:5000){
jaspResults$progressbarTick()
impk <- base::switch(options[["expectedErrors"]], "expectedRelative" = ceiling(n * options[["expectedPercentage"]]), "expectedAbsolute" = ceiling(options[["expectedNumber"]] / jaspResults[["total_data_value"]]$object * n))
if(impk >= n){ next }
x <- dbinom(0:impk, size = n, prob = jaspResults[["materiality"]]$object)
if(sum(x) < alpha){
return(n)
}
}
jaspResults[["errorInSampler"]] <- createJaspState(TRUE)
jaspResults[["errorInSampler"]]$dependOn(options = c("materiality", "materialityPercentage", "materialityValue", "expectedNumber", "expectedErrors", "populationValue", "populationSize"))
return(1)
}
.calc.n.hypergeometric <- function(options, alpha, jaspResults){
jaspResults$startProgressbar(5000)
K <- ceiling(jaspResults[["N"]]$object * jaspResults[["materiality"]]$object)
for(n in 1:5000){
jaspResults$progressbarTick()
impk <- base::switch(options[["expectedErrors"]], "expectedRelative" = ceiling(n * options[["expectedPercentage"]]), "expectedAbsolute" = ceiling(options[["expectedNumber"]] / jaspResults[["total_data_value"]]$object * n))
if(impk >= n) { next }
x <- dhyper(x = 0:impk, m = K, n = jaspResults[["N"]]$object - K, k = n)
if(sum(x) < alpha){
return(n)
}
}
jaspResults[["errorInSampler"]] <- createJaspState(TRUE)
jaspResults[["errorInSampler"]]$dependOn(options = c("materiality", "materialityPercentage", "materialityValue", "expectedNumber", "expectedErrors", "populationValue", "populationSize"))
return(1)
}
.calc.n.poisson <- function(options, alpha, jaspResults){
jaspResults$startProgressbar(5000)
for(n in 1:5000){
jaspResults$progressbarTick()
k <- base::switch(options[["expectedErrors"]], "expectedRelative" = (n * options[["expectedPercentage"]]), "expectedAbsolute" = (options[["expectedNumber"]] / jaspResults[["total_data_value"]]$object * n))
x <- pgamma(jaspResults[["materiality"]]$object, shape = 1 + k, scale = 1 / n)
#x <- dpois(x = 0:k, lambda = jaspResults[["materiality"]]$object * n)
if(x >= (1 - alpha)){
return(n)
}
}
jaspResults[["errorInSampler"]] <- createJaspState(TRUE)
jaspResults[["errorInSampler"]]$dependOn(options = c("materiality", "materialityPercentage", "materialityValue", "expectedNumber", "expectedErrors", "populationValue", "populationSize"))
return(1)
}
.classicalPlanningHelper <- function(options, jaspResults, planningContainer){
if(!is.null(jaspResults[["planningResult"]]$object)) return(jaspResults[["planningResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
k <- 0
if(jaspResults[["ready"]]$object && !planningContainer$getError()){
n <- base::switch(options[["planningModel"]],
"Poisson" = .calc.n.poisson(options, alpha, jaspResults),
"binomial" = .calc.n.binomial(options, alpha, jaspResults),
"hypergeometric" = .calc.n.hypergeometric(options, alpha, jaspResults))
k <- base::switch(options[["expectedErrors"]], "expectedRelative" = options[["expectedPercentage"]], "expectedAbsolute" = options[["expectedNumber"]] / n)
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- k
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["alpha"]] <- alpha
resultList[["confidence"]] <- options[["confidence"]]
jaspResults[["planningResult"]] <- createJaspState(resultList)
jaspResults[["planningResult"]]$dependOn(options = c("IR", "CR", "confidence", "expectedNumber", "materialityPercentage", "planningModel", "expectedPercentage", "expectedNumber",
"materialityValue", "materiality", "recordNumberVariable", "monetaryVariable"))
return(jaspResults[["planningResult"]]$object)
}
.classicalPlanningTable <- function(dataset, options, planningResult, jaspResults, position = 1, planningContainer){
if(!is.null(planningContainer[["planningSummary"]])) return() #The options for this table didn't change so we don't need to rebuild it
planningSummary <- createJaspTable("Planning Summary")
planningSummary$position <- position
planningSummary$dependOn(options = c("IR", "CR", "confidence", "materialityPercentage", "planningModel", "recordNumberVariable", "monetaryVariable",
"expectedErrors" , "expectedPercentage", "expectedNumber", "materialityValue", "materiality"))
planningSummary$addColumnInfo(name = 'materiality', title = "Materiality", type = 'string')
planningSummary$addColumnInfo(name = 'IR', title = "Inherent risk", type = 'string')
planningSummary$addColumnInfo(name = 'CR', title = "Control risk", type = 'string')
planningSummary$addColumnInfo(name = 'DR', title = "Detection risk", type = 'string')
planningSummary$addColumnInfo(name = 'k', title = "Expected errors", type = 'string')
planningSummary$addColumnInfo(name = 'n', title = "Required sample size", type = 'string')
if(!jaspResults[["ready"]]$object){
message <- base::switch(options[["planningModel"]],
"Poisson" = paste0("The required sample size is based on the <b>Poisson</b> distribution."),
"binomial" = paste0("The required sample size is based on the <b>binomial</b> distribution."),
"hypergeometric" = paste0("The required sample size is based on the <b>hypergeometric</b> distribution."))
planningSummary$addFootnote(message = message, symbol="<i>Note.</i>")
}
planningContainer[["planningSummary"]] <- planningSummary
if(!is.null(jaspResults[["errorInSampler"]])){
planningContainer$setError("There is no sample size (< 5000) large enough to prove the current materiality. Please try other values.")
return()
}
ktable <- base::switch(options[["expectedErrors"]], "expectedRelative" = round(planningResult[["k"]] * planningResult[["n"]], 2), "expectedAbsolute" = paste(jaspResults[["valutaTitle"]]$object, options[["expectedNumber"]]))
if(options[["planningModel"]] != "Poisson" && options[["expectedErrors"]] == "expectedRelative")
ktable <- ceiling(ktable)
DRtable <- paste0(round(planningResult[["alpha"]], 3) * 100, "%")
if(jaspResults[["materiality"]]$object == 0){
row <- data.frame(materiality = ".", IR = planningResult[["IR"]], CR = planningResult[["CR"]], DR = DRtable, k = 0, n = ".")
planningSummary$addRows(row)
planningSummary$addFootnote(message = "The materiality is defined as 0.", symbol="<b>ANALYSIS NOT READY.</b>")
return()
}
materialityTitle <- paste0(round(jaspResults[["materiality"]]$object * 100, 2), "%")
materialityValue <- base::switch(options[["materiality"]], "materialityRelative" = ceiling(jaspResults[["materiality"]]$object * sum(dataset[, .v(options[["monetaryVariable"]])])), "materialityAbsolute" = options[["materialityValue"]])
materiality <- base::switch(options[["materiality"]], "materialityRelative" = materialityTitle, "materialityAbsolute" = paste(jaspResults[["valutaTitle"]]$object, materialityValue))
if(!jaspResults[["ready"]]$object || planningContainer$getError()){
row <- data.frame(materiality = materiality, IR = planningResult[["IR"]], CR = planningResult[["CR"]], DR = DRtable, k = ktable, n = ".")
planningSummary$addRows(row)
return()
}
if(planningResult[["n"]] > jaspResults[["N"]]$object && jaspResults[["ready"]]$object){
planningContainer$setError("The required sample size is larger than the population size. You cannot audit this population with this materiality and this amount of confidence.")
return()
}
message <- base::switch(options[["planningModel"]],
"Poisson" = paste0("The required sample size is based on the <b>Poisson</b> distribution <i>(\u03BB = ", round(jaspResults[["materiality"]]$object * planningResult[["n"]], 4) , ")</i>."),
"binomial" = paste0("The required sample size is based on the <b>binomial</b> distribution <i>(p = ", round(jaspResults[["materiality"]]$object, 2) ,")</i>."),
"hypergeometric" = paste0("The required sample size is based on the <b>hypergeometric</b> distribution <i>(N = ", jaspResults[["N"]]$object ,", K = ", ceiling(jaspResults[["N"]]$object * jaspResults[["materiality"]]$object) ,")</i>."))
planningSummary$addFootnote(message = message, symbol="<i>Note.</i>")
row <- data.frame(materiality = materiality, IR = planningResult[["IR"]], CR = planningResult[["CR"]], DR = DRtable, k = ktable, n = planningResult[["n"]])
planningSummary$addRows(row)
}
.attributesBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
k <- 0
bound <- "."
if(jaspResults[["runEvaluation"]]$object){
if(options[["estimator"]] == "binomialBound"){
n <- jaspResults[["sampleSize"]]$object
kIndex <- which(dataset[,.v(options[["auditResult"]])] == 1)
if(options[["sampleFilter"]] != ""){
kNumber <- dataset[kIndex ,.v(options[["sampleFilter"]])]
k <- length(rep(kIndex, times = kNumber))
} else {
k <- length(kIndex)
}
binomResult <- binom.test(x = k,
n = n,
p = jaspResults[["materiality"]]$object,
alternative = "less",
conf.level = (1 - alpha))
bound <- binomResult$conf.int[2]
} else if(options[["estimator"]] == "hyperBound"){
N <- jaspResults[["N"]]$object
n <- jaspResults[["sampleSize"]]$object
kIndex <- which(dataset[,.v(options[["auditResult"]])] == 1)
if(options[["sampleFilter"]] != ""){
kNumber <- dataset[kIndex ,.v(options[["sampleFilter"]])]
k <- length(rep(kIndex, times = kNumber))
} else {
k <- length(kIndex)
}
for(K in 1000:1){
x <- phyper(k, K, N - K, n)
if(x >= 0.05)
break
}
bound <- K / N
} else if(options[["estimator"]] == "gammaBound"){
n <- jaspResults[["sampleSize"]]$object
kIndex <- which(dataset[,.v(options[["auditResult"]])] == 1)
kNumber <- dataset[kIndex ,.v(options[["sampleFilter"]])]
k <- length(rep(kIndex, times = kNumber))
bound <- qgamma(p = (1 - alpha), shape = 1 + k, scale = 1 / n)
}
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- k
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage", "materialityValue", "performAudit", "estimator"))
return(jaspResults[["evaluationResult"]]$object)
}
.attributesBoundTable <- function(options, evaluationResult, jaspResults, position = 1, evaluationContainer){
if(!is.null(evaluationContainer[["evaluationTable"]])) return() #The options for this table didn't change so we don't need to rebuild it
evaluationTable <- createJaspTable("Evaluation Summary")
evaluationTable$position <- position
evaluationTable$dependOn(options = c("IR", "CR", "confidence", "materialityPercentage", "auditResult", "sampleFilter", "planningModel",
"mostLikelyError", "materialityValue", "auditType", "valuta", "performAudit", "estimator"))
evaluationTable$addColumnInfo(name = 'materiality', title = "Materiality", type = 'string')
evaluationTable$addColumnInfo(name = 'n', title = "Sample size", type = 'string')
evaluationTable$addColumnInfo(name = 'k', title = "Errors", type = 'string')
if(options[["mostLikelyError"]])
evaluationTable$addColumnInfo(name = 'mle', title = "MLE", type = 'string')
evaluationTable$addColumnInfo(name = 'bound', title = paste0(options[["confidence"]] * 100,"% Confidence bound"), type = 'string')
if(options[["materiality"]] == "materialityAbsolute" || options[["monetaryVariable"]] != "")
evaluationTable$addColumnInfo(name = 'projm', title = "Maximum Misstatement", type = 'string')
message <- base::switch(options[["estimator"]],
"gammaBound" = "The confidence bound is calculated according to the <b>gamma</b> distributon.",
"binomialBound" = "The confidence bound is calculated according to the <b>binomial</b> distributon.",
"hyperBound" = "The confidence bound is calculated according to the <b>hypergeometric</b> distribution.")
evaluationTable$addFootnote(message = message, symbol="<i>Note.</i>")
evaluationContainer[["evaluationTable"]] <- evaluationTable
materialityTable <- ifelse(options[["materiality"]] == "materialityRelative", yes = paste0(round(jaspResults[["materiality"]]$object, 2) * 100, "%"), no = paste(jaspResults[["valutaTitle"]]$object, options[["materialityValue"]]))
# Return empty table
if(!jaspResults[["runEvaluation"]]$object){
row <- data.frame(materiality = materialityTable, n = ".", k = ".", bound = ".")
if(options[["materiality"]] == "materialityAbsolute" || options[["monetaryVariable"]] != "")
row <- cbind(row, projm = ".")
evaluationTable$addRows(row)
return()
}
mle <- 0
if(jaspResults[["N"]]$object != 0)
mle <- paste0(round(evaluationResult[["k"]] / evaluationResult[["n"]], 4) * 100, "%")
boundTable <- "."
if(evaluationResult[["bound"]] != ".")
boundTable <- paste0(round(evaluationResult[["bound"]], 4) * 100, "%")
row <- data.frame(materiality = materialityTable, n = evaluationResult[["n"]], k = evaluationResult[["k"]], bound = boundTable)
if(options[["materiality"]] == "materialityAbsolute" || options[["monetaryVariable"]] != "")
row <- cbind(row, projm = paste(jaspResults[["valutaTitle"]]$object, round(evaluationResult[["bound"]] * jaspResults[["total_data_value"]]$object, 2)))
if(options[["mostLikelyError"]])
row <- cbind(row, mle = mle)
evaluationTable$addRows(row)
}
.stringerBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
# Based on the paper:
# Stringer, K. W. (1963). Practical aspects of statistical sampling in auditing. In Proceedings of the Business and Economic Statistics Section (pp. 405-411). American Statistical Association.
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
NoOfErrors <- 0
z <- 0
bound <- "."
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
if(options[["sampleFilter"]] != ""){
z <- rep(z, times = dataset[ ,.v(options[["sampleFilter"]])])
}
n <- length(z)
zplus <- sort(subset(z, z > 0), decreasing = TRUE)
zmin <- sort(subset(z, z < 0), decreasing = TRUE)
M <- length(zplus)
NoOfErrors <- length(which(z != 0))
bound <- 1 - alpha^(1 / n)
if(M > 0){
prop.sum <- 0
for(i in 1:M){
prop.sum <- prop.sum + ((qbeta(1 - alpha, i + 1, n - i) - qbeta(1 - alpha, (i - 1) + 1, n - (i - 1) )) * zplus[i])
}
bound <- bound + prop.sum
}
if(options[["stringerBoundLtaAdjustment"]]){
bound <- bound - ( (1/n) * sum(abs(zmin)) )
}
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- NoOfErrors
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "variableType", "auditResult", "materiality", "estimator", "materialityValue", "materialityPercentage", "stringerBoundLtaAdjustment", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
.auditValueBoundTable <- function(options, evaluationResult, jaspResults, position = 1, evaluationContainer){
if(!is.null(evaluationContainer[["evaluationTable"]])) return() #The options for this table didn't change so we don't need to rebuild it
evaluationTable <- createJaspTable("Evaluation Summary")
evaluationTable$position <- position
evaluationTable$dependOn(options = c("IR", "CR", "confidence", "materialityPercentage", "auditResult", "planningModel", "mostLikelyError", "sampleFilter", "variableType",
"estimator", "monetaryVariable", "materialityValue", "valuta", "stringerBoundLtaAdjustment", "performAudit"))
evaluationTable$addColumnInfo(name = 'materiality', title = "Materiality", type = 'string')
evaluationTable$addColumnInfo(name = 'n', title = "Sample size", type = 'string')
evaluationTable$addColumnInfo(name = 'fk', title = "Errors", type = 'string')
evaluationTable$addColumnInfo(name = 'k', title = "Total tainting", type = 'string')
if(options[["mostLikelyError"]])
evaluationTable$addColumnInfo(name = 'mle', title = "MLE", type = 'string')
evaluationTable$addColumnInfo(name = 'bound', title = paste0(options[["confidence"]] * 100,"% Confidence bound"), type = 'string')
evaluationTable$addColumnInfo(name = 'projm', title = "Maximum Misstatement", type = 'string')
message <- base::switch(options[["estimator"]],
"stringerBound" = "The confidence bound is calculated according to the <b>Stringer</b> method.",
"regressionBound" = "The confidence bound is calculated according to the <b>regression</b> method.",
"directBound" = "The confidence bound is calculated according to the <b>direct</b> method.",
"differenceBound" = "The confidence bound is calculated according to the <b>difference</b> method.",
"ratioBound" = "The confidence bound is calculated according to the <b>ratio</b> method.")
evaluationTable$addFootnote(message = message, symbol="<i>Note.</i>")
evaluationContainer[["evaluationTable"]] <- evaluationTable
materialityTable <- ifelse(options[["materiality"]] == "materialityRelative", yes = paste0(round(jaspResults[["materiality"]]$object, 2) * 100, "%"), no = paste(jaspResults[["valutaTitle"]]$object, options[["materialityValue"]]))
# Return empty table with materiality
if(!jaspResults[["runEvaluation"]]$object){
row <- data.frame(materiality = materialityTable, n = ".", fk = ".", k = ".", bound = ".", projm = ".")
evaluationTable$addRows(row)
return()
}
total_data_value <- jaspResults[["total_data_value"]]$object
mle <- 0
if(options[["estimator"]] == "stringerBound"){
mle <- paste0(round(sum(evaluationResult[["z"]]) / evaluationResult[["n"]], 4) * 100, "%")
} else {
mle <- paste(jaspResults[["valutaTitle"]]$object, round(evaluationResult[["mleTable"]] * total_data_value, 2))
}
errors <- round(sum(evaluationResult[["z"]]), 2)
boundTable <- "."
projectedMisstatement <- "."
if(evaluationResult[["bound"]] != "."){
boundTable <- round(evaluationResult[["bound"]], 4)
projectedMisstatement <- paste(jaspResults[["valutaTitle"]]$object, ceiling(evaluationResult[["bound"]] * total_data_value))
boundTable <- paste0(boundTable * 100, "%")
}
row <- data.frame(materiality = materialityTable, n = evaluationResult[["n"]], fk = evaluationResult[["k"]], k = errors, bound = boundTable, projm = projectedMisstatement)
if(options[["mostLikelyError"]])
row <- cbind(row, mle = mle)
evaluationTable$addRows(row)
}
.directBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
M <- 0
z <- 0
bound <- "."
mle <- 0
mleTable <- 0
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
n <- nrow(sample)
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
M <- length(which(t != 0))
B <- jaspResults[["total_data_value"]]$object
N <- jaspResults[["N"]]$object
w <- sample[, .v(options[["auditResult"]])]
meanw <- mean(w)
mle <- N * meanw
stand.dev <- sd(w) * (N / sqrt(n)) * sqrt( (N-n) / (N-1) )
lowerValue <- mle - qt(p = 1 - alpha, df = n - 1) * stand.dev
bound <- (B - lowerValue) / B
mleTable <- (B - mle) / B
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- M
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
resultList[["mle"]] <- mle
resultList[["mleTable"]] <- mleTable
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage", "estimator", "monetaryVariable", "materialityValue", "variableType", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
.differenceBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
M <- 0
z <- 0
bound <- "."
mle <- 0
mleTable <- 0
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
n <- nrow(sample)
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
M <- length(which(t != 0))
B <- jaspResults[["total_data_value"]]$object
N <- jaspResults[["N"]]$object
w <- sample[, .v(options[["auditResult"]])]
meanw <- mean(w)
meant <- mean(t)
mle <- B - N * meant
stand.dev <- sd(t) * (N / sqrt(n)) * sqrt( (N-n) / (N-1) )
lowerValue <- mle - qt(p = 1 - alpha, df = n - 1) * stand.dev
if(lowerValue == 0){
bound <- 0
} else {
bound <- (B - lowerValue) / B
}
mleTable <- (B - mle) / B
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- M
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
resultList[["mle"]] <- mle
resultList[["mleTable"]] <- mleTable
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage", "estimator", "monetaryVariable", "materialityValue", "variableType", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
.ratioBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
M <- 0
z <- 0
bound <- "."
mle <- 0
mleTable <- 0
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
n <- nrow(sample)
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
M <- length(which(t != 0))
B <- jaspResults[["total_data_value"]]$object
N <- jaspResults[["N"]]$object
w <- sample[, .v(options[["auditResult"]])]
b <- sample[, .v(options[["monetaryVariable"]])]
meanw <- mean(w)
meanb <- mean(b)
sumw <- sum(w)
sumb <- sum(b)
q <- sumw / sumb
mle <- q * B
stand.dev <- sqrt( ( sum(t^2) - 2 * (1-q) * sum(b*t) + (1 - q)^2 * sum(b^2) ) / (n - 1)) * (N / sqrt(n)) * sqrt( (N-n) / (N-1) )
lowerValue <- mle - qt(p = 1 - alpha, df = n - 1) * stand.dev
if(lowerValue == 0){
bound <- 0
} else {
bound <- (B - lowerValue) / B
}
mleTable <- (B - mle) / B
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- M
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
resultList[["mle"]] <- mle
resultList[["mleTable"]] <- mleTable
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage", "estimator", "monetaryVariable", "materialityValue", "variableType", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
.regressionBound <- function(dataset, options, jaspResults){
if(!is.null(jaspResults[["evaluationResult"]]$object))
return(jaspResults[["evaluationResult"]]$object)
ar <- 1 - options[["confidence"]]
ir <- base::switch(options[["IR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
cr <- base::switch(options[["CR"]], "Low" = 0.50, "Medium" = 0.60, "High" = 1)
alpha <- ar / ir / cr
n <- 0
M <- 0
z <- 0
bound <- "."
mleregression <- 0
mleTable <- 0
if(jaspResults[["runEvaluation"]]$object){
sample <- dataset[, c(.v(options[["monetaryVariable"]]), .v(options[["auditResult"]]))]
n <- nrow(sample)
t <- sample[, .v(options[["monetaryVariable"]])] - sample[, .v(options[["auditResult"]])]
z <- t / sample[, .v(options[["monetaryVariable"]])]
M <- length(which(t != 0))
B <- jaspResults[["total_data_value"]]$object
N <- jaspResults[["N"]]$object
b <- sample[, .v(options[["monetaryVariable"]])]
w <- sample[, .v(options[["auditResult"]])]
b1 <- as.numeric(coef(lm(w ~ b))[2])
meanb <- mean(b)
meanw <- mean(w)
mleregression <- N * meanw + b1 * (B - N * meanb)
stand.dev <- sd(w) * sqrt(1 - cor(b, w)^2) * ( N / sqrt(n)) * sqrt( (N-n) / (N-1) )
lowerValue <- mleregression - qt(p = 1 - alpha, df = n - 1) * stand.dev
if(lowerValue == 0){
bound <- 0
} else {
bound <- (B - lowerValue) / B
}
mleTable <- (B - mleregression) / B
}
resultList <- list()
resultList[["n"]] <- n
resultList[["k"]] <- M
resultList[["z"]] <- z
resultList[["IR"]] <- options[["IR"]]
resultList[["CR"]] <- options[["CR"]]
resultList[["confidence"]] <- options[["confidence"]]
resultList[["bound"]] <- bound
resultList[["alpha"]] <- alpha
resultList[["mle"]] <- mleregression
resultList[["mleTable"]] <- mleTable
jaspResults[["evaluationResult"]] <- createJaspState(resultList)
jaspResults[["evaluationResult"]]$dependOn(options = c("IR", "CR", "confidence", "auditResult", "sampleFilter", "materialityPercentage",
"estimator", "monetaryVariable", "materialityValue", "variableType", "performAudit"))
return(jaspResults[["evaluationResult"]]$object)
}
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