What it means
Suppose a company processed 4,000 supplier invoices last year and an auditor wants to know whether they were recorded correctly. Checking all 4,000 would take weeks, so the auditor picks a sample of, say, 100 and tests those instead.
If the sample is chosen well, what is found in the 100 gives a reliable indication of what is true across the 4,000. The key word is representative.
A sample is only useful if each item in the population had a fair chance of being picked, so that it mirrors the whole group rather than a convenient slice. Choosing only the largest invoices, or only the ones that were easy to find, produces a biased sample and misleading conclusions.
In finance and accounting, samples appear in audits, internal control testing, credit reviews, market research and quality checks. A bank might sample loan files to test underwriting standards, while a marketing team samples customers to estimate satisfaction.
In each case the results are scaled up to estimate the whole. Size matters, but not in the way many people expect.
A larger sample reduces uncertainty, yet the improvement slows as the sample grows, and a well-chosen sample of 100 can be far more reliable than a poorly chosen sample of 1,000. The population's variability, the confidence level wanted and the acceptable margin of error all influence how big the sample needs to be.
It also helps to separate a sample from a census. A census examines every item, which gives certainty but costs time and money, whereas a sample trades a little certainty for speed.
Knowing which to use is a judgement about risk and materiality. Documentation is part of good practice.
Auditors record how the population was defined, how items were chosen and what was found, so that another reviewer could repeat the work and reach the same conclusion.
In practice
Real-world examples.
Example
An auditor of a logistics company selects 60 delivery invoices from 3,000 and finds two with pricing errors. The sample suggests an error rate of about 3.3%, which she reports to the finance director for follow-up.
Example
A bank's credit risk team pulls a sample of 200 small-business loan files from a portfolio of 8,000 to test whether underwriters followed the lending policy. The results guide the next round of staff training, and the team plans to repeat the test the following year to see whether error rates have fallen.
Example
A consumer brand surveys 500 customers out of a customer base of 250,000 to estimate satisfaction before deciding whether to redesign its packaging.
Formula
Calculation
Sample Mean = Sum of the Sampled Values / Number of Items in the Sample
Estimated Population Total = Sample Mean x Population Size
Worked example: an auditor takes a sample of 5 invoices from a population of 4,000. The invoice values are $1,200, $1,500, $900, $1,800 and $1,100.
Sum = $1,200 + $1,500 + $900 + $1,800 + $1,100 = $6,500
Sample Mean = $6,500 / 5 = $1,300
Estimated Population Total = $1,300 x 4,000 = $5,200,000
The tiny sample of 5 is used only to keep the arithmetic clear. A real audit would use a much larger sample.Case study
Seen in the real world.
Meridian Auto Parts is an illustrative, fictional distributor whose internal audit team wanted to test 12,000 expense claims. A full review would have taken three months, so the team agreed to test a random sample of 150 claims.
The team numbered every claim, used a random number generator to pick the 150, and checked each against receipts and policy. Six of the 150 had missing receipts, an error rate of 4%.
Applied to the whole population, a 4% rate suggested about 480 claims with problems, and in the illustrative story management tightened its receipt rules. The team noted that the figure was an estimate rather than a count and reported it with a margin of error.
Watch out
Common mistakes.
- Picking the easiest or most convenient items and calling it a sample, which builds in bias.
- Assuming a bigger sample always fixes a badly chosen one, when the selection method matters more than the size.
- Reporting sample results as exact facts about the whole population without mentioning uncertainty.
Questions
People also ask.
What is the difference between a sample and a population?
The population is the entire group you care about, while the sample is the smaller part of it that you actually examine.
How big should a sample be?
It depends on how variable the population is, how confident you need to be and how much error you can tolerate, and statistical formulas can calculate a suitable size.
When is it better to check everything instead?
When the population is small, when every item is highly material or when a single error would be unacceptable, a full review is the safer choice.
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