Audit sampling and other means of testing

Introduction: Why We Can’t Check Everything

Welcome to one of the most practical chapters in Audit and Assurance! Think about it: if a massive company like Amazon has millions of sales transactions every day, could an auditor possibly check every single invoice? Of course not! It would take years, and the audit fee would be astronomical.

In this chapter, we will learn how auditors use sampling and other methods to gather enough evidence to form an opinion without looking at every single piece of paper. Don't worry if this seems a bit "maths-heavy" at first—it’s actually more about logic and professional judgment than complex calculations.

1. Three Ways to Select Items for Testing

Auditors have three main tools in their toolkit when deciding what to look at:

A. 100% Examination
This means checking every single item in a population. This is rare but used when the population is small, or the items are high-value and high-risk (e.g., five very expensive pieces of machinery).

B. Selecting Specific Items
The auditor chooses items based on a specific characteristic, such as:
- High value: All invoices over \( \$10,000 \).
\n- Key items: Items that look suspicious or have a history of errors.
\nNote: This is not sampling because not every item has a chance of being selected!

C. Audit Sampling
\nThis involves applying audit procedures to less than 100% of items within a population so that every "sampling unit" has a chance of being selected. The goal is to reach a conclusion about the entire population.

Key Takeaway:

Audit sampling is about using a part to represent the whole. If the sample is "clean," we assume the rest of the records are likely clean too.

2. Understanding Audit Sampling (ISA 530)

To understand sampling, you need to know two important terms:

1. The Population: The entire set of data from which the sample is selected (e.g., all sales invoices for the year).
\n2. Sampling Unit: The individual items that make up the population (e.g., one single invoice).

Statistical vs. Non-Statistical Sampling

There are two "styles" of sampling:

Statistical Sampling: This uses random selection and probability theory to evaluate results. It involves math and removes human bias.
\nNon-Statistical Sampling: This is often called "judgmental sampling." The auditor uses their professional judgment to pick items they think are important.

Quick Review: Which is better? Neither! ISA 530 says both are acceptable as long as the auditor gathers sufficient appropriate evidence.

3. Sampling Risk and Non-Sampling Risk

Even the best auditor can get it wrong. We categorize these "wrong" results into two risks:

1. Sampling Risk: This is the risk that the sample you picked does not represent the population. Imagine you have a bag of 100 marbles (90 blue, 10 red). If you pick 5 marbles and they all happen to be red, you would wrongly conclude the whole bag is red. That's sampling risk!

2. Non-Sampling Risk: This is the risk that the auditor reaches a wrong conclusion for any other reason. For example, the auditor picks the right sample but uses the wrong audit procedure, or they look at a document but fail to notice it's a forgery. This is basically "human error."

Memory Aid:

Sampling Risk = Sample is the problem.
\nNon-Sampling Risk = Not the sample (it's the auditor's mistake!).

4. How to Select Your Sample (Methods)

How do we actually pick the items? Here are the most common methods:

1. Random Selection: Every item has an equal chance of being picked. Usually done using a computer random number generator.

2. Systematic Selection: Picking items at a constant interval.
\nExample: You decide to check every 20th invoice. You pick a random starting point (e.g., invoice #5) and then check #25, #45, #65, and so on.

3. Haphazard Selection: The auditor picks items without following a structured technique but tries to avoid any conscious bias.
\nCommon Mistake: Students often think "haphazard" means "lazy." It actually requires effort to ensure you aren't just picking the "easy" files at the top of the pile!

4. Monetary Unit Sampling (MUS): A type of value-weighted selection. Every dollar (or £) in the population has an equal chance of being selected. This ensures that larger balances are more likely to be tested.

5. Block Selection: Picking a "block" of items (e.g., all sales in the month of March).
\nWarning: This is generally not a good sampling method because transactions in one month might not represent the whole year.

5. Designing and Evaluating the Sample

Before you start, you must define what a "misstatement" or "deviation" is. If you are testing a control (e.g., a manager must sign every invoice), a deviation is any invoice without a signature.

Tolerable vs. Expected

Tolerable Misstatement: The maximum error the auditor is willing to accept in the population and still say the accounts are "fair." This is related to Materiality.
\nExpected Misstatement: What the auditor thinks they will find based on previous years or their risk assessment.

Rule of Thumb: If the Expected error is too close to the Tolerable error, the auditor will need to pick a larger sample size to be sure.

Projecting Errors

If you find an error in your sample, you can't just ignore it! You must project it to the whole population.

The Formula:
\n\( \text{Projected Error} = \left( \frac{\text{Error found in sample}}{\text{Total value of sample}} \right) \times \text{Total value of population} \)

Example: You test \( \$1,000 \) worth of stock and find a \( \$50 \) error. If the total stock is worth \( \$100,000 \), your projected error is \( \$5,000 \).

Key Takeaway:

If the projected error (plus any "anomalous" or one-off errors) is higher than the Tolerable Misstatement, the auditor cannot rely on that population and must perform more work.

Summary Checklist for Students

When you are sitting in your exam, remember these points:

- Did you know? Sampling is only used when the auditor wants to draw a conclusion about the whole population.
- Don't mix them up: Statistical sampling uses math; non-statistical uses judgment.
- The Gold Standard: Random and Systematic selection are the most common statistical methods.
- The Goal: If the projected error is higher than what we can "tolerate," the audit evidence suggests the accounts might be materially misstated.

Final Encouragement: Audit sampling is just like tasting a small piece of cake to see if the whole cake is delicious. As long as your bite (the sample) includes a bit of everything, you can be pretty confident in your opinion!