## SA 530 — Audit Sampling

### Definition

Audit Sampling = Application of an audit procedure to less than 100% of items within a population of audit relevance, such that all sampling units have a chance of selection, and the auditor can draw conclusions about the entire population.

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### Characteristics of a Valid Population

For sampling to produce valid conclusions, the population must be:

Complete — all items that should be in the population are included.
Appropriate — the population matches the audit objective.
Reliable — the data constituting the population is accurate.

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### Sampling Unit

The individual items that make up the population (e.g., each invoice, each journal entry, each customer balance).

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### Sampling Selection Methods

#### 1. Simple Random Sampling

Every unit has an equal probability of selection.
Uses random number tables or computer-generated random numbers.
Suitable for homogeneous populations with similar items in a reasonable range.

#### 2. Stratified Sampling

Population is divided into strata (sub-groups) based on a characteristic (e.g., value ranges).
Each stratum is treated as a separate population.
Proportionate samples drawn from each stratum.
Example: Debtors split into ₹10L–₹100L, ₹100L–₹200L, ₹200L–₹300L bands.

#### 3. Systematic Sampling

Population size ÷ sample size = Sampling Interval (SI).
A random start is chosen within the first interval; then every nth item is selected.
Formula: SI = Total Population Units ÷ Sample Size
Example: SI = 1,00,000 ÷ 1,000 = every 100th item.

#### 4. Haphazard Selection

No structured technique; auditor selects without a formal method.
Must still avoid conscious bias or predictability (e.g., not always skipping difficult-to-locate items or always picking the first entry on a page).
Not the same as random selection — cannot be used for statistical sampling.

#### 5. Monetary Unit Sampling (MUS)

A value-weighted method where each monetary unit (e.g., ₹1) is a sampling unit.
Larger-value items have a proportionately higher chance of selection.
Results expressed in monetary amounts.
Example: All transactions above ₹10,000 treated as individual sampling units.

#### 6. Block Selection

Selects a block of contiguous items (sequential items) from the population.
Generally NOT suitable for audit sampling because items in sequence tend to have similar characteristics — the block does not represent the diversity of the population.

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### Quick Comparison Table

Method	Statistical?	Best For	Watch Out
Simple Random	Yes	Homogeneous populations	Not efficient for skewed distributions
Stratified	Yes	Heterogeneous populations	Strata must be properly defined
Systematic	Yes	Large sequential populations	Risk if population has a periodic pattern
Haphazard	No	Supplementary use only	Cannot extrapolate statistically
MUS	Yes	Overstatement risk in monetary values	Less effective for detecting understatements
Block	No	Rarely appropriate	Fails representativeness requirement

Worked example

### Example 1

Example 1 — Systematic Sampling:

An auditor needs to sample 200 sales invoices from a population of 10,000.

Sampling Interval = 10,000 ÷ 200 = 50.

Random start selected: Invoice #23.

Subsequent selections: #73, #123, #173, #223 … and so on.

If the company sequentially numbers invoices, this method efficiently covers the entire range.

### Example 2

Example 2 — Stratified Sampling for Debtors:

A debtor population of ₹5 crore is divided into three strata:

Stratum A: Balances ₹0–₹1 lakh (800 debtors) — sample 5% = 40
Stratum B: Balances ₹1–₹5 lakh (150 debtors) — sample 20% = 30
Stratum C: Balances > ₹5 lakh (50 debtors) — sample 100% = 50 (100% check)

Total sample = 120. This concentrates effort on high-value items while maintaining coverage of the full population.

### Example 3

Example 3 — Why Block Selection fails:

An auditor selects invoices #501–#600 (a block of 100 consecutive invoices) from a population of 5,000. All 100 invoices relate to a single week in October and were processed by the same operator. They share common characteristics and do not represent the rest of the year. The sample cannot support conclusions about the full population.

⚠️ Common exam mistakes

Treating haphazard selection as equivalent to random selection — haphazard selection cannot be used for statistical sampling; random number-based selection is required for statistical inference.
Forgetting to verify population completeness before drawing a sample — if the population extract from the system is incomplete, the sample will not represent the true population (violates the 'completeness' characteristic).
Using block selection and claiming it represents the population — blocks are almost always inappropriate because sequential items share similar characteristics.
Confusing Monetary Unit Sampling with value-based judgmental selection — MUS is a formal statistical technique; selecting 'all items above a threshold' is judgmental selection, not MUS.
Setting a random start outside the first interval in systematic sampling — the random start must be within the first interval (1 to SI) to ensure every item in the population has an equal chance of selection.

Reference:

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SA 530 Audit Sampling — Basics and Selection Methods

Worked example

⚠️ Common exam mistakes