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CONTENTS
1 Definitions and Conventions ...................................................................................................1
2 Theory and Algorithms ...........................................................................................................3
2.1 The Hypergeometric Probability Distribution ............................................................................................. 3
2.1.1 Attributes Sample Sizes Using the Hypergeometric Distribution .................................................. 5
2.1.2 Practical Limitations of the Hypergeometric Distribution ............................................................ 5
2.2 The Binomial Probability Distribution ........................................................................................................ 5
2.2.1 Attributes Sample Sizes Using the Binomial Distribution ............................................................. 6
2.2.2 The Beta Distribution and its Relationship to the Binomial .......................................................... 7
2.2.3 Calculating the Upper Error Rate Limit ....................................................................................... 8
2.3 The Poisson Probability Distribution ........................................................................................................... 8
2.3.1 The Gamma Distribution and its Relationship to the Poisson ..................................................... 10
2.3.2 Evaluating MUS Samples ............................................................................................................ 11
2.3.3 MUS Sample Sizes ....................................................................................................................... 12
2.4 Conservatism of Binomial- and Poisson-Based Sample Design and Evaluation ....................................... 13
2.5 Precision and Tolerable Misstatement in Classical Variables Sampling (Table D.1 of the Guide) ........... 15
3 Statistical Functions in Excel ................................................................................................19
3.1 Built-in Excel Functions ............................................................................................................................ 19
3.2 Special-Purpose Functions in VBA ........................................................................................................... 20
3.2.1 Binomial Sample Sizes................................................................................................................. 20
3.2.2 Poisson Sample Sizes .................................................................................................................. 21
3.2.3 MUS Sample Design Factors ...................................................................................................... 22
4 Computation of Tables with Examples ................................................................................25
4.1 Table 3.1: Effect on Sample Size of Different Levels of Risk of Overreliance and Tolerable Deviation
Rate ............................................................................................................................................................ 25
4.2 Table 3.2: Effect of Tolerable Rate on Sample Size .................................................................................. 25
4.3 Table 3.3: Relative Effect of the Expected Population Deviation Rate on Sample Size ........................... 25
4.4 Table 3.4: Limited Effect of Population Size on Sample Size ................................................................... 26
4.5 Table 4.2: Table Relating RMM, Analytical Procedures (AP) Risk, and Test of Details (TD) Risk ........ 26
4.6 Table 4.5: Illustrative Sample Sizes .......................................................................................................... 27
4.7 Table 4.6: Confidence (Reliability) Factors............................................................................................... 27
4.8 Table 6.1: Confidence (Reliability) Factors............................................................................................... 27
4.9 Table 6.2: 5% of Incorrect Acceptance ..................................................................................................... 27
4.10 Table A.1: Statistical Sample Sizes for Tests of Controls—5% Risk of Overreliance .............................. 28
4.11 Table A.2: Statistical Sample Sizes for Tests of Controls—10% Risk of Overreliance ............................ 28
4.12 Table A.3: Statistical Sampling Results Evaluation Table for Tests of Controls—Upper Limits at 5%
Risk of Overreliance .................................................................................................................................. 28
4.13 Table A.4: Statistical Sampling Results Evaluation Table for Tests of Controls—Upper Limits at 10%
Risk of Overreliance .................................................................................................................................. 28
4.14 Table C.1: Monetary Unit Sample Size Determination Tables.................................................................. 28
4.15 Table C.2: Confidence Factors for Monetary Unit Sample Size Design ................................................... 29
4.16 Table C.3: Monetary Unit Sampling—Confidence Factors for Sample Evaluation .................................. 29
4.17 Table D.1: Ratio of Desired Allowance for Sampling Risk to Tolerable Misstatement ............................ 29
4.18 Tables Not Described ................................................................................................................................ 30
References .....................................................................................................................................31