CMA Intermediate · Corporate Accounting and Auditing

Audit Sampling, Audit Techniques and Analytical Procedure: formula sheet

Full chapter guide

Key formulas

Audit sampling: Procedures on < 100% of items, with every sampling unit having a chance of selection; Purpose: a reasonable basis for conclusions about the whole population (SA 530, para 5(a)).
Statistical sampling: Random selection + probability theory to evaluate results; If either feature is missing, it is non-statistical sampling.
Evaluation of tests of details: Projected misstatement + anomalous misstatement (if any) compared with tolerable misstatement; If the total exceeds tolerable misstatement, the sample does not give a reasonable basis for conclusions about the population. The closer it is to tolerable misstatement, the more likely actual misstatement exceeds it (para A22).
Tolerable misstatement: Tolerable misstatement ≤ performance materiality; It may be equal to or lower than performance materiality (para A3).
Sample size factors (tests of details): Increase: assessed risk of material misstatement, desired assurance, expected misstatement. Decrease: tolerable misstatement, other substantive procedures on the same assertion, stratification. Population size: negligible effect; From Appendix 3. For large populations, size has little effect.
Sample size factors (tests of controls): Increase: reliance on controls, expected deviation rate, desired assurance. Decrease: tolerable deviation rate. Population size: negligible effect; From Appendix 2.
Sampling interval (systematic selection): Sampling interval = Population size ÷ Sample size; Pick a random starting point within the first interval, then take every item at that interval. Example: 2,000 items and a sample of 40 give an interval of 50.
Statistical sampling test: Statistical sampling = Random selection + Probability theory to evaluate results; Both conditions are needed. Random selection with judgmental evaluation is non-statistical.
Stratified sample coverage: Items per stratum = Sample size × (Stratum size ÷ Population size), when sampling in proportion; Proportional allocation is one option. Auditors often test all high-value items and sample the rest.
Sampling risk: Sampling risk = risk that the conclusion from the sample differs from the conclusion if the whole population were tested; It arises in both approaches but can be quantified only in statistical sampling.
Simple projection of misstatement (ratio method): Projected misstatement = (Misstatement found in sample ÷ Value of sample) × Value of population; A common way to apply the para 14 requirement when the misstatement is proportional to value. Use it for the population from which the sample was drawn.
Projection by average error (difference method): Projected misstatement = (Misstatement found ÷ Number of items in sample) × Number of items in population; Useful when errors do not depend on the size of the item. State clearly which method you used.
Sample deviation rate (tests of controls): Sample deviation rate = Number of deviations found ÷ Sample size; Compare with the tolerable rate you set. The sample rate is the auditor's best estimate for the population rate.
SA 530 requirement on size: Sample size must reduce sampling risk to an acceptably low level; Para 7. Size comes from a statistical formula or professional judgment.
SA 530 requirement on selection: Every sampling unit in the population must have a chance of selection; Para 8.
Techniques to remember: Inspection, Observation, External confirmation, Recalculation, Reperformance, Analytical procedures, Inquiry; These are the procedures SA 500 describes for obtaining evidence. Write them in this order to avoid missing any.
Strength of evidence: External and auditor-generated evidence > internal evidence; documents > oral statements; Evidence from independent sources and obtained directly by the auditor is more reliable. Use this to explain why inquiry alone is not enough.
Choice of testing approach: Strong internal control → smaller test checks; weak internal control → larger tests or complete checking; Complete checking is also used for small populations or high-risk items.
Difference to investigate: Difference = Recorded amount − Expected amount; Investigate if the difference is larger than the threshold you set. A small difference may still matter if the area is high risk.
Gross profit ratio: Gross profit ratio = (Gross profit ÷ Net sales) × 100; A sudden change may signal sales or closing stock errors, or a change in pricing or product mix.
Current ratio: Current ratio = Current assets ÷ Current liabilities; Useful for going concern and liquidity concerns.
Debtors turnover period: Average collection period (days) = (Trade receivables ÷ Credit sales) × 365; A rising period may point to overstated receivables or weak recoveries.
Trend (percentage change): Change % = (Current year − Previous year) ÷ Previous year × 100; Compare with the change you expect from business facts.
Choice of procedure (SA 520, A4): Tests of details, substantive analytical procedures, or both; Chosen by judgment on expected effectiveness and efficiency in reducing audit risk to an acceptably low level.
When analytical procedures are less suitable (SA 520, A9): Weak controls → rely more on tests of details; Example in SA 520: weak controls over sales order processing mean more reliance on tests of details for receivables.
Audit software: Auditor's program + client's real data → exceptions, totals, samples; Tests the data. Used for substantive tests such as recalculation, ageing, duplicates, gaps and sample selection.
Test data: Auditor's dummy transactions + client's program → compare actual output with expected output; Tests the program controls. Include both valid and invalid transactions. Run it on a copy or under controlled conditions so live records are not corrupted.
Core difference: Audit software = tests data; Test data = tests processing logic; This is the usual one-line answer for the comparison question.
Other CAAT forms: Integrated test facility; parallel simulation; embedded audit module; data analytics; Name these for completeness, with one line on each.

Quick revision

Audit sampling means applying procedures to fewer than 100% of items so every unit has a chance of selection.
Sampling risk is the risk that the conclusion from the sample differs from testing the whole population.
Non-sampling risk arises from causes unrelated to sample size, such as wrong procedures or misreading evidence.
Tolerable error is the maximum error the auditor accepts in the population.
An anomaly is an error shown to be not representative of the population.
Statistical sampling uses random selection and probability theory to evaluate results; otherwise it is non-statistical.
A larger sample is needed when risk is higher or tolerable error is lower.
Project the errors found in the sample to the population before drawing a conclusion.
Selective testing checks chosen items, but unlike sampling its results are not projected statistically to the whole population.
Analytical procedures are used in risk assessment, as substantive procedures and in the overall final review.
Unusual fluctuations found by analytical procedures need investigation and corroborating evidence.
CAATs use software to test data, and they depend on reliable data and proper controls.

Common mistakes

Saying sampling means testing a random selection only Fix: Random selection is needed for statistical sampling only. Audit sampling requires that every unit has a chance of selection. Non-statistical sampling is also valid sampling.
Treating non-sampling risk as controllable by a bigger sample Fix: Non-sampling risk comes from inappropriate procedures, misinterpreting evidence or failing to recognise errors. Training, supervision and good procedures reduce it, not a larger sample.
Calling any random selection statistical sampling. Fix: Remember both features: random selection and probability-based evaluation. Missing either one makes it non-statistical.
Treating haphazard selection as random selection. Fix: Random uses a method such as random numbers, giving every item a known chance. Haphazard has no structure and relies on the auditor avoiding bias, so it is non-statistical.
Counting every difference found as a misstatement. Fix: Define the misstatement first. In a receivables existence test, a payment received just after the confirmation date is not a misstatement.
Saying the projected misstatement is the amount the client must book. Fix: State that projection gives a broad view of the scale of misstatement and may not be sufficient to determine an amount to be recorded.
Confusing recalculation with reperformance. Fix: Recalculation checks arithmetic accuracy. Reperformance redoes a procedure or control, such as a reconciliation or an approval check.
Treating observation as proof of year-round operation. Fix: State the limitation and say the auditor supports it with other procedures.
Treating analytical procedures as only a ratio calculation. Fix: Always add the expectation, the investigation of differences and the audit conclusion.
Forgetting that analytical procedures are used at three stages. Fix: List risk assessment, substantive procedures and final review whenever the question asks about use.

Exam tips

Learn the SA 530 definitions word for word in your own plain phrasing; short notes questions reward them.
For sampling risk versus non-sampling risk, give a definition, two examples each and one line on whether sample size affects it.
In sums, show the line: projected plus anomalous misstatement versus tolerable misstatement, then state the conclusion.
Remember the direction of each sample-size factor; MCQs often ask whether a factor increases or decreases sample size.
There is no negative marking in Section A, so attempt every MCQ.
For difference questions, set out a two-column comparison: selection method, evaluation method, sampling risk measurement, cost and skill needed.
In numerical questions, always show the sampling interval formula and the random start before listing items.
For suitability questions, link the method to the population: stratified for varied values, systematic for numbered uniform items, block only with caution.