Audit Sampling Techniques Explained: Methods & Application

Your auditor selected only 60 invoices out of your 4,200 sales transactions to test—but how did they choose those specific 60, why didn't they test all 4,200, how can they be confident their conclusions are valid for the entire population, and most importantly, what can you do to ensure your transactions are "audit-ready" when they select their sample? Audit sampling is the application of audit procedures to less than 100% of a population to obtain sufficient appropriate audit evidence about the entire population—but many UAE business owners don't understand the difference between statistical and non-statistical sampling, how auditors determine sample sizes (and why certain balances require larger samples), the mathematics behind projecting errors from samples to populations, and critically, how poor transaction quality can force auditors to increase sample sizes (and therefore audit fees).

With 37 years performing audit sampling across 28,000+ UAE businesses (testing everything from 50 invoices for AED 2M startups to 2,500 transactions for AED 800M corporations), Farahat & Co has applied every sampling technique across all industries and transaction types. Our experience shows that well-organized, high-quality transactions allow smaller sample sizes (reducing audit time by 15-30%), while disorganized or error-prone populations require significantly larger samples and increase audit costs.

This comprehensive audit sampling guide explains:

• ISA 530 framework: International Standard on Auditing requirements for sampling
• Statistical vs. non-statistical sampling: When each method is appropriate and cost-effective
• Sample size determination: The 5 key factors that determine how many items auditors must test
• Sampling methods: Monetary Unit Sampling (MUS), random sampling, stratified sampling, systematic sampling
• Real UAE examples: Detailed walkthroughs of sampling for receivables, inventory, payroll, expenses
• Error projection: How auditors extrapolate sample errors to evaluate the entire population
• Practical tips: How to prepare your records to enable smaller samples and lower audit fees

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What Is Audit Sampling? (ISA 530 Definition)

Audit Sampling is the application of audit procedures to less than 100% of items within a population of audit relevance such that all sampling units have a chance of selection, allowing the auditor to obtain and evaluate audit evidence about some characteristic of the items selected to form or assist in forming a conclusion concerning the population from which the sample is drawn.

Key Concepts:

1. Population: The entire set of data from which the sample is selected (e.g., all 4,200 sales invoices for 2024)
2. Sampling Unit: Individual items in the population (e.g., one invoice, one inventory item, one payment)
3. Sample: The items actually selected and tested (e.g., 60 out of 4,200 invoices)
4. Sampling Risk: The risk that the auditor's conclusion based on the sample differs from the conclusion if the entire population were tested
5. Non-Sampling Risk: The risk that the auditor reaches an erroneous conclusion for reasons unrelated to sampling (e.g., auditor fails to recognize an error)

Why Auditors Use Sampling (Instead of Testing 100%):

Cost-Effectiveness: Testing all 4,200 invoices would cost ~AED 84,000 in audit fees (4,200 × AED 20/invoice). Testing 60 invoices costs ~AED 1,200. Client saves AED 82,800 while still obtaining sufficient audit evidence.

Efficiency: Testing 100% is impractical for large populations. A properly designed sample provides reliable conclusions at a fraction of the time and cost.

ISA 530 Permits It: International auditing standards explicitly allow sampling when it provides sufficient appropriate audit evidence.

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Statistical vs. Non-Statistical (Judgmental) Sampling

Statistical Sampling

Definition: Any approach to sampling that uses:

1. Random selection of the sample
2. Probability theory to evaluate sample results

Advantages:

• Objective sample selection: No auditor bias in choosing items
• Measurable sampling risk: Can quantify confidence level (e.g., 95% confidence)
• Defensible conclusions: Mathematical support for extrapolations
• Efficient for large populations: Formulas optimize sample size

Disadvantages:

• More complex: Requires statistical knowledge and software
• Time to set up: Stratification and random number generation take time
• Less flexibility: Can't easily adjust sample once selected

When to Use:

• Large populations (1,000+ items)
• Homogeneous populations (similar transaction types)
• High-risk areas requiring defensible conclusions
• Situations where you need to quantify precision

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Non-Statistical (Judgmental) Sampling

Definition: Auditor uses professional judgment to:

1. Select sample items
2. Evaluate results

Advantages:

• Flexibility: Can focus on high-risk items, unusual transactions, large amounts
• Simpler: No complex calculations or software needed
• Practical for small populations: When population is <100 items, judgment often better
• Can combine testing approaches: e.g., test all items >AED 50K + sample smaller items

Disadvantages:

• Auditor bias risk: Might unconsciously select "easy" or "clean" items
• Cannot quantify sampling risk: Can't say "95% confident"
• Less defensible: Hard to justify why 60 items is "enough"

When to Use:

• Small populations (<100 items)
• Heterogeneous populations (many different transaction types)
• Low-risk areas where qualitative judgment is sufficient
• Situations where you're testing specific characteristics (e.g., all cash disbursements >AED 100K)

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Sample Size Determination: The 5 Key Factors

Sample size for statistical sampling is determined by:

Factor #1: Tolerable Misstatement (Performance Materiality)

What It Is: Maximum error in the population the auditor is willing to accept

Impact on Sample Size: Lower tolerable misstatement = larger sample needed

Example:

• Population: AED 50M trade receivables
• Overall materiality: AED 1.5M
• Performance materiality for receivables: AED 1.1M (tolerable misstatement)
• If tolerable misstatement reduced to AED 550K → sample size increases ~50%

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Factor #2: Expected Misstatement

What It Is: Amount of error the auditor expects to find in the population (based on prior years, interim testing, control effectiveness)

Impact on Sample Size: Higher expected misstatement = larger sample needed

Example:

• Prior year: Found AED 180K of errors in receivables
• Current year expected misstatement: AED 200K
• If controls have weakened and expected misstatement rises to AED 400K → sample size increases ~40%

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Factor #3: Assessed Risk of Material Misstatement

What It Is: Combined assessment of inherent risk and control risk

Impact on Sample Size: Higher risk = larger sample needed

Risk Levels & Typical Sample Sizes (for AED 50M receivables population):

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Key Insight: Strong internal controls allow lower sample sizes. This is why control testing comes first—effective controls reduce substantive testing.

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Factor #4: Population Size

Impact: Surprisingly, population size has minimal impact on sample size once populations exceed ~2,000 items.

Example:

• Population of 2,000 items: Sample size = 88
• Population of 20,000 items: Sample size = 92 (only 5% increase!)
• Population of 200,000 items: Sample size = 93 (only 6% increase!)

Why? Statistical formulas reach a "plateau" where increasing population adds negligible sampling risk.

Practical Implication: Don't assume "we have 50,000 transactions so the auditor needs to test thousands." Sample sizes plateau around 80-120 for most large populations.

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Factor #5: Population Variability (Standard Deviation)

What It Is: How much individual amounts differ from the mean

Impact on Sample Size: Higher variability = larger sample needed

Example - AED 10M Inventory (500 items):

Scenario A: Low Variability (homogeneous inventory)

• Items range from AED 15K to AED 25K
• Standard deviation: AED 2,500
• Sample size needed: 42 items

Scenario B: High Variability (mixed inventory)

• Items range from AED 500 to AED 250K
• Standard deviation: AED 35,000
• Sample size needed: 88 items (110% more!)

Solution for High Variability: Stratification - divide population into subgroups (strata) and sample each separately. This dramatically reduces required sample size.

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Sampling Methods Explained with UAE Examples

Method #1: Monetary Unit Sampling (MUS) - Most Common for Substantive Testing

What It Is: Each AED 1 in the population has an equal chance of selection. Items with larger values have proportionally higher probability of being selected.

How It Works:

Step 1: Calculate sampling interval

• Sampling interval = Population value ÷ Desired sample size
• Example: AED 50M receivables ÷ 80 sample size = AED 625K interval

Step 2: Select random starting point

• Random number between AED 1 and AED 625K
• Example: AED 142,580

Step 3: Select items at each interval

• First item: Contains AED 142,580 (cumulative)
• Second item: Contains AED 767,580 (AED 142,580 + AED 625K)
• Third item: Contains AED 1,392,580 (AED 767,580 + AED 625K)
• Continue until 80 items selected

Real UAE Example: Trade Receivables Testing

Population:

• 1,450 customer balances
• Total: AED 52.3M
• Range: AED 850 to AED 2.4M

Sampling Plan:

• Desired sample size: 75 items
• Sampling interval: AED 52.3M ÷ 75 = AED 697,333
• Random start: AED 234,891

Results:

• Selected 75 balances totaling AED 38.2M (73% of population value)
• All 12 balances >AED 1M automatically selected (systematic bias toward large items - this is a FEATURE, not a bug!)
• Found 3 errors: AED 15K overstatement, AED 8.5K overstatement, AED 22K understatement

Advantages of MUS:

• Automatically focuses on larger amounts: High-value items more likely selected
• Efficient for overstatement testing: Effective at finding inflated balances
• Easy to apply: Software or Excel can automate selection
• Sample size not affected by population variability: Unlike classical variables sampling

Disadvantages:

• Less efficient for understatement testing: Zero or small balances have low selection probability
• Requires more evaluation if errors found: Error projection is complex

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Method #2: Random Sampling

What It Is: Every item in the population has an equal and independent chance of selection (like drawing names from a hat)

How It Works:

Step 1: Assign sequential numbers to all population items (1, 2, 3... 4,200)

Step 2: Use random number generator to select sample

Real UAE Example: Expense Testing

Population:

• 4,200 expense transactions
• Total: AED 8.6M
• Expense types: Travel (1,200), Utilities (850), Office supplies (920), Professional fees (480), Marketing (450), Other (300)

Sampling Plan:

• Desired sample size: 60 transactions
• Use Excel RANDBETWEEN(1, 4,200) to generate 60 unique random numbers

Sample Selected (first 10 shown):

1. Transaction #142 - AED 3,200 (travel)
2. Transaction #891 - AED 850 (utilities)
3. Transaction #1,455 - AED 420 (office supplies)
4. Transaction #2,876 - AED 18,500 (professional fees)
5. Transaction #3,201 - AED 1,240 (marketing) ...

Results:

• Tested 60 transactions totaling AED 184K (2.1% of population value - note this is MUCH lower than MUS which would have captured ~73%)
• Found 2 errors: Missing approval on AED 18.5K payment, duplicate invoice AED 1.2K

When to Use Random Sampling:

• Testing controls (where you care about error RATE, not error AMOUNT)
• Homogeneous populations where value doesn't indicate risk
• When you want truly representative sample of ALL transaction sizes

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Method #3: Systematic Sampling

What It Is: Select every "nth" item after a random start

How It Works:

Step 1: Calculate sampling interval

• Sampling interval = Population size ÷ Desired sample size
• Example: 2,500 items ÷ 50 sample = Every 50th item

Step 2: Select random starting point between 1 and 50

• Example: Random start = 23

Step 3: Select items at intervals

• Item #23, #73, #123, #173, #223... (until 50 items selected)

Real UAE Example: Payroll Testing

Population:

• 240 employees
• 12 monthly payrolls
• Total population: 2,880 payslips (240 employees × 12 months)

Sampling Plan:

• Desired sample size: 48 payslips
• Sampling interval: 2,880 ÷ 48 = Every 60th payslip
• Random start: Payslip #37

Sample: Payslips #37, #97, #157, #217, #277... (total 48)

Testing Performed:

• Recalculate gross pay, deductions, net pay
• Verify approval by HR Manager
• Trace to bank transfer
• Check employee still employed

Results:

• All 48 payslips calculated correctly
• 1 missing approval signature (employee terminated, final payslip processed urgently)
• Conclusion: Payroll control operating effectively (1 exception due to unusual circumstance)

Advantages:

• Simple to apply: Easy to understand and execute
• Spreads sample across population: Ensures coverage of entire period

Disadvantages:

• Risk of pattern bias: If population has systematic patterns (e.g., every 50th invoice is month-end accrual), sample may be biased

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Method #4: Stratified Sampling

What It Is: Divide population into subgroups (strata) based on a characteristic (usually value), then sample each stratum separately

Why Use It: Dramatically reduces required sample size for populations with high variability

Real UAE Example: Inventory Testing

Population:

• 3,800 inventory items
• Total value: AED 15.2M
• Highly variable: Small spare parts (AED 50-500) to heavy machinery (AED 10K-350K)

Without Stratification:

• High variability requires sample size of ~180 items to achieve desired precision

With Stratification:

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Benefits of Stratification:

• Reduced total sample from 180 to 103 items (43% reduction!)
• Greater assurance on high-value items (tested 100%)
• Efficient allocation of audit effort where it matters most
• Lower audit fees: ~12 hours saved = AED 3,000 savings

Testing Performed:

• Physical inspection and count verification
• Valuation testing (cost vs. NRV)
• Obsolescence assessment
• Cutoff testing

Results:

• Found AED 85K of obsolete items in Stratum C (slow-moving parts >5 years old, not written down)
• Projected error to full Stratum C: AED 85K ÷ AED 90K (sample value) × AED 3.6M (stratum value) = AED 3.4M potential obsolescence
• Recommendation: Full obsolescence review required, potentially material adjustment

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Evaluating Sample Results: Error Projection

When auditors find errors in the sample, they must project those errors to the entire population to determine if material misstatement likely exists.

Projection Method #1: Ratio Estimation (Classical Variables)

Formula: Projected Misstatement = (Sample Misstatement ÷ Sample Value) × Population Value

Example:

• Population: AED 50M receivables
• Sample: 80 balances, AED 36.8M (sampled value)
• Errors found: AED 15K overstatement + AED 22K understatement = AED 7K net overstatement
• Projected Misstatement: (AED 7K ÷ AED 36.8M) × AED 50M = AED 9,511

Auditor's Evaluation:

• Materiality for receivables: AED 1.1M
• Projected misstatement: AED 9,511 (0.9% of tolerable misstatement)
• Conclusion: Population NOT materially misstated (well below threshold)

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Projection Method #2: Tainting Percentage (MUS)

Concept: Calculate the percentage error ("tainting") for each error found, then project to sampling interval

Example:

Error #1:

• Selected balance: AED 84,500
• Correct balance: AED 62,300
• Overstatement: AED 22,200
• Tainting: AED 22,200 ÷ AED 84,500 = 26.3%

Error #2:

• Selected balance: AED 45,200
• Correct balance: AED 37,800
• Overstatement: AED 7,400
• Tainting: AED 7,400 ÷ AED 45,200 = 16.4%

Projected Misstatement:

• Sampling interval: AED 697,333
• Error #1 projection: 26.3% × AED 697,333 = AED 183K
• Error #2 projection: 16.4% × AED 697,333 = AED 114K
• Total Projected Misstatement: AED 297K

Plus Sampling Uncertainty (Precision): Statistical software calculates "upper limit on misstatement" considering sampling risk

• Basic precision: ~AED 420K (depends on confidence level)
• Upper Limit on Misstatement: AED 297K + AED 420K = AED 717K

Auditor's Evaluation:

• Tolerable misstatement: AED 1.1M
• Upper limit on misstatement: AED 717K (65% of tolerable)
• Conclusion: Acceptable, but approaching threshold. Consider:
  • Requesting client investigate and correct known errors
  • Expanding sample if upper limit exceeds 80% of tolerable misstatement

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Sampling for Tests of Controls vs. Substantive Testing

Tests of Controls: Attribute Sampling

Purpose: Determine if control operates effectively (e.g., "Are all purchase orders approved by authorized personnel?")

Focus: Error RATE (how many exceptions), not error AMOUNT

Sample Size Guidance:

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Real UAE Example: Purchase Order Approval Control

Control: All purchase orders >AED 5,000 require CFO approval signature

Population: 850 purchase orders >AED 5,000 during the year

Sample: 40 purchase orders (moderate reliance planned)

Testing: Inspect each PO for CFO signature

Results:

• 38 POs properly approved
• 2 POs missing approval (both emergency IT equipment purchases, AED 8,200 and AED 6,500)
• Deviation rate: 2 ÷ 40 = 5%

Evaluation:

• Tolerable deviation rate: 10%
• Sample deviation rate: 5%
• Conclusion: Control operating effectively (below tolerable rate). Note the 2 exceptions for follow-up, but can still rely on control.

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Substantive Testing: Variables Sampling

Purpose: Determine if account balance is materially misstated (e.g., "Are receivables fairly stated?")

Focus: Error AMOUNT (AED value of misstatements)

Methods: MUS, ratio estimation, difference estimation

Sample sizes: Typically 60-120 for large populations (depends on 5 factors discussed earlier)

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Frequently Asked Questions

1. Our auditor wants to test 80 invoices out of 5,000 (only 1.6%). How can they be confident about the other 98.4%?

Answer: This is the mathematics of sampling. When properly designed using statistical methods:

The Math:

• With 80 properly selected items from a population of 5,000
• At 95% confidence level
• The auditor can conclude that IF the error in the sample is <X, THEN the error in the population is <Y (within a calculable range)

Example:

• Sample 80 invoices from AED 42M population
• Find AED 12K of errors in the sample
• Statistical projection: 95% confident that population error is between AED 95K and AED 285K
• If materiality is AED 1.2M, the auditor concludes population is NOT materially misstated

Key Insight: The confidence comes from probability theory, not from testing a high percentage. A random sample of 80 from 5,000 provides nearly the same confidence as 80 from 50,000.

How to Reduce Sample Size (and therefore audit fees):

1. Strengthen internal controls: Effective controls reduce assessed risk → smaller samples
2. Improve record quality: Clean, well-organized transactions reduce expected errors → smaller samples
3. Stratify populations: Provide a separate listing of high-value items (>AED 50K) so auditor can test those 100% and sample the smaller items
4. Fix prior-year errors: Low errors in prior years reduce expected misstatement → smaller samples

ROI: Spending AED 15K to improve controls can reduce audit sampling time by 25% = AED 8-12K annual audit fee savings

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2. The auditor found 2 errors in their sample of 60 expenses (total AED 142K) and projected an error of AED 650K to the full AED 8.6M population. How is this possible from just 2 errors?

Answer: This is error projection with sampling uncertainty. Here's how it works:

Scenario:

• Population: 4,200 expenses, AED 8.6M
• Sample: 60 expenses, AED 142K
• Errors found:
  • Missing receipt AED 8,400 (claimed as business expense, actually personal)
  • Duplicate payment AED 3,200

Calculation:

Step 1: Project known errors

• Sample misstatement: AED 8,400 + AED 3,200 = AED 11,600
• Projection ratio: AED 11,600 ÷ AED 142K = 8.17%
• Projected misstatement: 8.17% × AED 8.6M = AED 703K

Wait, that's AED 703K from just 2 errors!

Step 2: Consider sampling uncertainty

• Because auditor only tested 60 of 4,200 (1.4%), there's "precision" range
• Statistical calculation (depends on confidence level): Precision = ±AED 180K
• Range: AED 523K to AED 883K (95% confident true error is in this range)

Why so high?

• Small sample value: AED 142K out of AED 8.6M is only 1.7% of population
• Relatively high error rate: 2 out of 60 = 3.3% error rate
• Projection multiplier: Errors get multiplied by ~60× (AED 8.6M ÷ AED 142K)

What happens next:

IF projected error exceeds tolerable misstatement (say materiality is AED 600K):

1. Auditor requests client investigate: Review all 4,200 expenses to find and correct errors
2. Client can perform detailed review: If client finds only AED 85K of actual errors across all 4,200, auditor can re-evaluate
3. Auditor might expand sample: Test additional 60 expenses. If no further errors found, projection decreases significantly
4. Potential audit adjustment: If client can't resolve, may require AED 650K expense reduction (audit adjustment)

Key Insight: This is why clean, well-controlled expense processes matter. Two sloppy errors in the sample can project to material misstatement and trigger extensive additional work (and fees).

Prevention:

• Implement expense approval workflow (no payment without approval + receipt)
• Monthly expense reviews by managers
• Duplicate payment detection (accounting system flags)
• These controls reduce expected errors → smaller samples → lower projections even if 1-2 errors found

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3. Can we just give the auditor the "clean" transactions to sample from, so they don't find errors and we avoid adjustments?

Short Answer: No. This is fraud (misrepresentation) and will be detected.

Why This Doesn't Work:

Detection Method #1: Completeness Testing

• Auditors test completeness BEFORE sampling
• They'll trace from source documents (bank statements, goods received notes, shipping logs) TO your accounting records
• If you excluded 200 problematic invoices from the population, auditors will discover this when they trace bank deposits and find invoices missing from your list

Detection Method #2: Sequence Gap Analysis

• Auditors check invoice/PO/payment numbering sequences for gaps
• If your invoice numbers go 1001, 1002, 1003, 1005, 1006... where's 1004?
• Missing numbers trigger investigation

Detection Method #3: Analytical Procedures

• If you excluded AED 2.4M of problematic transactions, your revenue/expenses will look unusual
• Example: Monthly revenue averaging AED 4.2M for 11 months, but only AED 1.8M in December (because you hid problematic December transactions)

Detection Method #4: Third-Party Confirmations

• Auditors send confirmations directly to customers/suppliers
• If customer confirms AED 85K balance but you only showed AED 42K (excluded problematic AED 43K invoice), discrepancy is discovered

Consequences:

1. Scope limitation: Auditor may be unable to issue unqualified opinion
2. Expanded procedures: Auditor will expand testing significantly (doubling or tripling audit fees)
3. Loss of trust: Future audits will be planned with "high fraud risk" - meaning maximum sample sizes, extensive procedures, highest fees
4. Legal consequences: Intentional misrepresentation can lead to criminal charges under UAE Commercial Companies Law
5. Regulatory action: Ministry of Economy can impose penalties, ban from operating

The Right Approach:

1. Identify problematic transactions BEFORE the audit
2. Investigate and correct them (adjust accounting records)
3. Inform the auditor proactively ("We found AED 340K of errors during our pre-audit review and have corrected them")
4. Result: Auditor sees strong control environment and management integrity, may reduce sample sizes due to lower assessed risk

Real Example:

• Client found AED 420K of revenue recognition errors during year-end close (before audit)
• Corrected the errors and documented the review process
• Informed auditor proactively
• Outcome: Auditor assessed control risk as LOWER (because management has effective review process), reduced substantive testing by 20%, audit fee decreased by AED 6,500

Key Insight: Honesty reduces audit fees. Attempting to hide problems increases them (and risks your business).

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Best Practices: Preparing for Audit Sampling

For Your Team:

1. Organize records before the audit:

   • Complete population listings (all invoices, all inventory items, all employees)
   • Sequential numbering (check for gaps)
   • Supporting documentation readily available

2. Stratify high-value items proactively:

   • Provide auditor with separate listings of items >AED 50K
   • Allows efficient stratified sampling approach

3. Run your own pre-audit sample:

   • Test 20-30 transactions before auditor arrives
   • If you find errors, investigate and correct across full population
   • Demonstrate to auditor that you have effective review process

4. Fix prior-year issues:

   • If prior audit found errors in payroll, improve payroll controls THIS year
   • Low expected error rate reduces required sample size

What to Expect from Your Auditor:

1. Sampling plan documentation: Auditor should document methodology, sample size rationale
2. Random selection: For statistical samples, auditor should use random number generator (not "I picked these 60")
3. Testing consistency: All selected items should be tested (auditor can't skip difficult items)
4. Clear communication: Auditor should explain how they'll project errors if found

Red Flags (Poor Sampling):

• Auditor says "I just grabbed 50 invoices from the file" (not random)
• Auditor only tests transactions from one month (not representative)
• Sample includes only small transactions (ignores high-value items)
• Auditor can't explain how sample size was determined

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Understanding audit sampling helps you prepare better records, anticipate audit procedures, and implement controls that reduce sample sizes (and audit fees). With 37 years sampling across 28,000+ UAE businesses, Farahat & Co applies statistically sound, efficient sampling methods that provide reliable conclusions at optimal cost—typically reducing audit hours by 15-25% compared to firms using inefficient "rule of thumb" approaches.