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“There are three kinds of lies: lies, damned lies, and statistics” Anonymous

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“There are three kinds of lies: lies, damned lies, and statistics” Anonymous

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  1. “Statistics is a science which ought to be honorable, the basis of many most important sciences; but it is not to be carried on by steam, this science, any more than others are: a wise head is requisite for carrying it on. Conclusive facts are inseparable from inconclusive except by a head that already understands and knows”. • Thomas Carlyle, 1839

  2. “There are three kinds of lies: lies, damned lies, and statistics” • Anonymous

  3. Statistical Sampling for Controls

  4. Audit Objectives Changed from “guaranteeing accuracy of accounts” to “providing reasonable assurance as to the overall fairness of financial statement” Audit Procedures Changed from “detailed examination of all transactions” to“testing” Statistical Sampling

  5. Types of Sampling • Non-statistical: sample size, sample selection, and evaluation of results are based upon professional judgment instead of mathematical techniques • smaller populations • non-homogeneous • OLRT populations not conducive to random selection • Statistical: mathematical calculation of sample size, population values, ranges of reliability & precision, does not replace judgment • larger homogeneous populations • mathematical inference

  6. Types of Sampling • Attribute Sampling: testing controls • Estimating frequency of events, error percentages, & assessing control risk • Variables Sampling: substantive testing • Estimating $ value of accounts (or errors)

  7. Audit Effectiveness, Efficiency, & Risk

  8. Basic Terminology & Notation • Population size = N • Sample size = n • y (or x) = sample mean • y (or x) = estimated population mean • Y (or X) = actual (true) population mean • Standard Deviation (S.D.) = measure of dispersion

  9. Basic Terminology & Notation • Random Selection - each item in the population has an equal chance of selection • random number tables (p. 368) • systematic or interval sampling • random start + each successive N/n th item • Stratified Random Sampling • stratify larger non-homogeneous populations into smaller, more homogeneous ones

  10. Steps in Sampling Controls • Select the attribute to be sampled • Determine the relevant population • Set risk of underassessing control risk • Determine the sample size (pp. 366-7) • Select the sample (p. 368) • Test the control / evaluate the sampled attribute (p.371) • Evaluate the results (p.373-4)

  11. Attribute Sampling Terminology • Population size, assumed large :N is GT 1K • Risk of Underassessing Control Risk/Risk of Assessing Control Risk Too Low • Expected Occurrence Rate (EOR) or Expected Deviation Rate (EDR) • Tolerable Occurrence Rate (TOR) or Tolerable Deviation Rate (TDR) • Upper Occurrence Limit (UOL) or Upper Deviation Limit (UDL) • Precision = TOR - EOR

  12. Evaluating the Sample Results • Determine the number of errors • Calculate the UOL (pp. 373-4) • Compare UOL & TOR • If UOL is GT TOR, use higher level of control risk • If TOR is GT UOL, consider lowering assessed level of control risk • If EDR is GT SDR, then UOL is GT TOL & vice versa

  13. Quantifying Control Risk

  14. Quantifying Detection Risk AR = IR x CR x DR DR = AR IR x CR See Table 9-8 (p. 379)

  15. Evidence, Materiality, & Detection Risk Evidence = 1 DR Materiality = 1 Evidence

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