## SA 530 – Methods of Sample Selection

### Overview of Approaches

```

Methods of Sample Selection

├── Statistical Approach

│ ├── Random Sampling

│ │ ├── Simple Random

│ │ └── Stratified Random

│ ├── Systematic / Interval Sampling

│ └── Value Weighted Sampling

└── Non-Statistical Approach

├── Haphazard Sampling

└── Block Sampling

```

---

### Statistical Sampling Methods

#### 1. Random Sampling

Simple Random: Every item has an equal probability of selection; typically done via random number tables or computer generation.
Stratified Random: Population is divided into sub-groups (strata) with similar characteristics (e.g., by value), then random sampling is applied within each stratum. Improves efficiency when population is heterogeneous.

#### 2. Systematic / Interval Sampling

Select every nth item after a random start.
Example: Population of 1,000 invoices, sample size 50 → interval = 20. Start at invoice #7, then pick #27, #47, …

#### 3. Value Weighted (Monetary Unit Sampling – MUS)

Each rupee in the population has an equal chance of selection.
Higher-value items have a proportionally higher chance of being picked.
Useful for detecting overstatement in monetary balances.

---

### Non-Statistical Sampling Methods

#### 4. Haphazard Sampling

Items selected without a structured technique but without conscious bias.
Not truly random — relies on the auditor's judgement.
Acceptable only if the auditor ensures no deliberate bias.

#### 5. Block Sampling

Selecting a continuous sequence of items (e.g., all transactions in October).
Least preferred — the block may not represent the full population.

---

### Statistical vs Non-Statistical Sampling: Key Differences

Basis	Statistical	Non-Statistical
Probability	Based on probability theory	Not based on probability
Bias	Eliminates bias	Prone to auditor bias
Accuracy	More accurate	Less accurate
Scientific Evaluation	Possible	Not possible
Population Size	Suitable for large populations	Suitable for small populations
Representation	More representative	Less representative

---

### Advantages of Statistical Sampling

1. Sample selection is more objective

2. Allows estimating the minimum sample size for a specified risk and precision

3. Provides a better description of large data sets

4. Widely accepted methodology

5. Enables derivation of a calculated (quantified) risk

Worked example

### Example 1

Example – Systematic Sampling:

Population: 500 sales invoices. Required sample size: 25. Interval = 500 ÷ 25 = 20. Random start: invoice #9. Selected invoices: 9, 29, 49, 69 … 489. This is efficient and removes bias as long as there is no pattern every 20th invoice.

### Example 2

Example – Value Weighted / MUS:

A creditor ledger has 200 accounts totalling ₹10 crore. Using MUS, each rupee has an equal selection probability. A ₹20 lakh account has 20× more chance of selection than a ₹1 lakh account. This naturally focuses audit effort on material balances.

### Example 3

Example – Block Sampling (why it's risky):

An auditor selects all 80 purchase transactions from December. If the client front-loads fake purchases in Q1 to inflate expenses, the December block will miss this entirely. Block sampling creates blind spots across the population.

⚠️ Common exam mistakes

Treating 'haphazard' as equivalent to 'random' — haphazard lacks the mathematical randomness that statistical sampling requires.
Using block sampling and believing it is representative — it covers only a period/sequence and can miss systematic fraud in other periods.
Forgetting that statistical sampling requires both random selection AND statistical evaluation of results — just using random numbers for selection without statistical analysis does not make it 'statistical sampling.'
Confusing stratified sampling with block sampling — stratification divides the population by characteristic and then randomly samples within each stratum; block sampling takes a consecutive sequence.

Reference:

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SA 530 – Methods of Sample Selection: Statistical vs Non-Statistical

Worked example

⚠️ Common exam mistakes