## Audit Sampling – Sample Design, Population Characteristics, and Stratification (SA 530)

### 1. The Sampling Process (Four Steps)

Step	Activity
1. Sample Design	Define objective, assertion, and relevant audit procedure
2. Sample Size	Determine how many items to select
3. Sampling Method	Choose how to select items (random, systematic, etc.)
4. Perform Audit Procedures	Execute the procedure on selected items and evaluate results

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### 2. Step 1 – Sample Design in Detail

The auditor must define three things before designing the sample:

1. Specific objective – Which assertion is being tested? (e.g., existence, completeness, valuation)

2. Relevant audit procedure – What procedure will be applied to the sample?

3. Definition of error – What will be treated as an error?

For Test of Controls: define what constitutes a deviation from the control
For Substantive Testing: define what constitutes a misstatement

> The conclusion drawn from the sample is extrapolated to the whole population – so the sample design must precisely match the population and objective.

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### 3. Impact of Expected Errors on Sample Design

Scenario	Action
Auditor expects a higher rate of deviation after initial control testing	Expand substantive procedures (do not rely on controls)
Auditor expects high misstatement in the population	Increase sample size for substantive testing

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### 4. Characteristics of Population – Stratification

Problem: A heterogeneous population (e.g., debtors ranging from ₹500 to ₹13,00,000) cannot be sampled uniformly – high-value items carry far greater audit risk.

Solution – Stratification: Divide the population into homogeneous sub-groups (strata) based on a characteristic (usually value), then sample each stratum separately.

#### Example – Debtor Population Stratified by Balance:

Stratum	Balance Range	Sampling Approach
1	₹500 – ₹2,50,000	Fewer samples (lower risk)
2	₹2,50,000 – ₹5,00,000	Moderate samples
3	₹5,00,000 – ₹8,00,000	More samples
4	₹8,00,000 – ₹15,00,000	Highest samples
5	> ₹13,00,000	May test 100%

Process:

1. Auditor applies audit procedures to each stratum separately

2. Draws a conclusion for each stratum

3. Combines stratum conclusions to form a conclusion on the overall population

#### Analogy:

Think of a school divided into Commerce, Science, and Arts streams (strata). The principal draws conclusions about each stream separately before concluding on the whole school.

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### 5. Value-Weighted Selection

Another approach where items are selected with probability proportional to their monetary value – larger-value items have a higher chance of being selected. This is often used in monetary unit sampling (MUS).

Worked example

### Example 1

Sample design for accounts payable completeness: Assertion = completeness. Population = all purchase orders raised in the year. Auditor defines a misstatement as any purchase order for which no liability has been recorded. Procedure = trace PO to creditor ledger. Sample size is increased because management indicated some cut-off issues (expected high misstatement).

### Example 2

Stratification of debtors – numerical illustration: Total debtors = 2,000 accounts, total balance = ₹80 lakh. After stratification: Stratum A (< ₹10,000) = 1,200 accounts → sample 30; Stratum B (₹10,000–₹1,00,000) = 600 accounts → sample 50; Stratum C (> ₹1,00,000) = 200 accounts → sample 80 (or 100%). Auditor tests each stratum, finds 2 misstatements in Stratum C, projects this to Stratum C only, then aggregates to form a total population misstatement estimate.

### Example 3

Control testing – defining deviation: Auditor tests the 'purchase order approval' control. Deviation is defined as: any purchase order above ₹50,000 that does not bear the CFO's signature. From a sample of 50 POs, 3 lack the signature → deviation rate = 6%. If tolerable deviation rate was 5%, the control cannot be relied upon → auditor increases substantive testing.

⚠️ Common exam mistakes

Forgetting to define what constitutes a 'deviation' or 'misstatement' before sampling – without a clear definition, results cannot be evaluated consistently.
Applying a single sampling approach to a heterogeneous population without stratification – this produces an unrepresentative sample weighted toward low-value, low-risk items.
Projecting misstatements from one stratum to the entire population – errors found in a stratum must only be projected within that stratum.
Confusing 'deviation rate' (relevant to control testing) with 'misstatement' (relevant to substantive testing) – they are evaluated against different tolerable thresholds.
Not increasing sample size when high misstatements are expected – expected errors must be factored into sample size calculation, not treated as a reason to abandon the procedure.

Reference: — SA 530 – Audit Sampling (ICAI)

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SA 530 – Audit Sampling: Sample Design, Population Stratification, and Value-Weighted Selection

Worked example

⚠️ Common exam mistakes