## **Learning Outcomes**

By reading this article, you will understand how sampling enables conclusions about populations without examining every item. You will learn to distinguish between random, systematic, and stratified sampling. You will be able to identify situations where each technique is suitable, outline their steps, and recognise potential sources of bias or error. You will also be able to evaluate the appropriateness of a sampling method for a given scenario, an essential skill for ACCA BT exams.

## **ACCA Management Accounting (MA) Syllabus**

For ACCA Management Accounting (MA), you are required to understand the principles and application of basic sampling methods in data collection. This article covers the following relevant syllabus areas:

- Explain the concept and purpose of sampling in data collection
- Describe key sampling techniques: random, systematic, and stratified sampling
- Recognise advantages and disadvantages of each method
- Identify appropriate sampling methods for different business scenarios

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. Which sampling method gives each item in the population an equal chance of being selected?
   a) Random sampling
   b) Systematic sampling
   c) Stratified sampling
   d) Quota sampling

2. A factory wants to audit 50 invoices out of 1,000. If every 20th invoice is selected after starting from a random point, which sampling method is this?

3. In which scenario would a stratified sample be more representative than a simple random sample?

4. True or false? Systematic sampling cannot introduce bias even if the population has a hidden pattern matching the sampling interval.

## **Introduction**

Sampling is often used when analysing an entire population is impractical due to size, cost, or time constraints. By selecting a smaller group—the sample—statisticians can draw conclusions about the wider population. The accuracy of these conclusions depends on the sampling method used. Three core sampling strategies relevant to management accounting and business studies are random sampling, systematic sampling, and stratified sampling. Understanding their methodology, advantages, and limitations is essential for ACCA students.

## Why Use Sampling?

Sampling allows organisations to make cost-effective, timely decisions without reviewing every data item. This is critical when examining transactions, production output, or employee surveys. However, inappropriate sampling can give misleading results, jeopardising decisions. Selection of the correct sampling technique depends on the nature of the population and the objectives of the analysis.

> **Key Term: population**
> The complete set of items or individuals relevant to the subject of investigation, from which a sample is drawn.
>
> **Key Term: sample**
> A subset selected from a population, intended to represent the population’s characteristics.

## RANDOM SAMPLING

Random sampling is the simplest probability sampling method. Every member of the population has an equal chance of being selected. This approach minimises selection bias and is a common reference point for other sampling methods.

### Steps in Random Sampling

1. Define the population clearly.
2. Assign a unique identifier to each population member.
3. Use a random mechanism (e.g., random number table, software RNG) to select the required number of sample items.
4. Collect data from the chosen items.

> **Key Term: random sampling**
> A technique where each population member has an equal and independent chance of being selected for the sample.

### Advantages and Disadvantages

- **Advantages:**
  - Minimises bias in selection.
  - Allows use of statistical tools to estimate error and make inferences.

- **Disadvantages:**
  - Can be impractical for large or inaccessible populations.
  - May require a complete population list, which can be expensive or unavailable.

### **Worked Example 1.1**

**A company has 500 employees and wishes to survey 25 about job satisfaction. Describe an appropriate sampling procedure.**

> **Answer:** Assign a unique number to each employee (1–500). Use a software random number generator to select 25 unique numbers. Survey those employees corresponding to the selected numbers.

## SYSTEMATIC SAMPLING

Systematic sampling provides an efficient, structured way to select a sample from a list. After choosing the first item at random within the first interval, subsequent items are picked at a regular interval throughout the population.

### Procedure for Systematic Sampling

1. Calculate the sampling interval: divide the population size by the required sample size.
2. Choose a random starting point between 1 and the interval.
3. Select every nth item thereafter until the sample is complete.

> **Key Term: systematic sampling**
> A technique where sample items are selected at fixed intervals from an ordered population, with the first item chosen randomly.

### Practical Example

Suppose you want a sample of 50 from a population of 1,000. The interval is 1,000 ÷ 50 = 20. Pick a random start between 1 and 20 (e.g., 7), then select items numbered 7, 27, 47, etc., up to 1,000.

### Advantages and Disadvantages of Systematic Sampling

- **Advantages:**
  - Easy to apply and time-efficient.
  - Ensures even coverage throughout the population.

- **Disadvantages:**
  - Can introduce bias if the population list has a periodic pattern matching the interval (e.g., production shifts, alternating supplier invoices).

### **Exam Warning**

> If the population list is ordered in a way that matches the sampling interval (e.g., alternating types), systematic sampling may miss or over-represent certain types, creating bias. Always verify the absence of hidden patterns before applying this method.

### **Worked Example 1.2**

**A factory logs 8,000 deliveries per year and wants to sample 400 for audit. Describe a systematic sampling process.**

> **Answer:** The interval is 8,000 ÷ 400 = 20. Randomly select a starting point between 1 and 20, then select every 20th delivery (e.g., if start = 13, select deliveries 13, 33, 53, ..., 7,993).

## STRATIFIED SAMPLING

Stratified sampling is designed to ensure that distinct sub-groups within a population are proportionally represented in the sample. This improves the reliability and relevance of results, especially when the population is diverse.

### Procedure for Stratified Sampling

1. Identify relevant strata (sub-groups), such as department, region, or product type.
2. Determine the proportion of each stratum in the population.
3. Randomly sample within each stratum, using quantities proportional to their size in the population.
4. Combine the results from all strata into the overall sample.

> **Key Term: stratified sampling**
> A sampling method where the population is divided into sub-groups (strata), and random samples are taken independently from each, proportionate to their sizes.

### When Is Stratified Sampling Appropriate?

Use stratified sampling when the population can be logically split into non-overlapping groups with different characteristics, and accurate representation of these groups is important for analysis.

### Advantages and Disadvantages of Stratified Sampling

- **Advantages:**
  - Increases representativeness for heterogeneous populations.
  - Improves precision compared to simple random sampling of the same size.

- **Disadvantages:**
  - Requires population breakdown into strata and accurate data on group sizes.
  - More complex to plan and execute.

### **Worked Example 1.3**

**An insurance firm’s workforce consists of 200 clerks, 50 managers, and 250 sales staff. To survey 50 employees, how should stratified sampling be used?**

> **Answer:** Clerks: 200/500 = 40% → sample 20.  
>
> Managers: 50/500 = 10% → sample 5.  
> Sales staff: 250/500 = 50% → sample 25.  
> Randomly sample within each group to reach these numbers.

## Comparing the Methods

| **Aspect**            | **Random Sampling**    | **Systematic Sampling**  | **Stratified Sampling**        |
| --------------------- | ---------------------- | ------------------------ | ------------------------------ |
| Equal chance per item | Yes                    | Yes (if no list pattern) | Yes (within strata)            |
| Needs complete list   | Yes                    | Yes                      | Yes plus group breakdown       |
| Handles sub-groups    | May exclude small ones | May exclude small ones   | Ensures all groups represented |
| Complexity            | Simple                 | Simple to moderate       | Moderate to complex            |
| Risk of bias          | Low                    | Medium if pattern exists | Low if strata accurate         |

### **Revision Tip**

> Before choosing a sampling method, consider: the diversity of the population, whether sub-groups exist, the availability of a comprehensive and up-to-date list, and any patterns in that list.

## **Summary**

Sampling methods help organisations obtain reliable conclusions without exhaustive analysis. Random sampling is the most basic and unbiased but can be impractical for large groups. Systematic sampling offers efficiency but may risk bias if the list is patterned. Stratified sampling delivers better representation when sub-groups exist and vary in size or relevance. Understanding when and how to use each method is key for both the exam and real-world applications.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain why sampling is used and its benefits in business data collection
- Describe random sampling and its use of equal probability
- Outline systematic sampling and fixed-interval selection process
- Identify the potential bias risk in systematic sampling
- Explain stratified sampling and proportional representation of sub-groups
- Evaluate the appropriateness of sampling methods for different scenarios

## **Key Terms and Concepts**

- population
- sample
- random sampling
- systematic sampling
- stratified sampling


Sampling methods - Random, systematic, and stratified sampling