What it means
Checking every invoice, customer or product is often too slow or costly. A sample gives a reasonable picture at a fraction of the effort, provided it is chosen fairly.
Systematic sampling is one of the simplest ways to do that. The method starts with a list of all the items, called the population.
You decide how many you want to check, which is the sample size, and divide the population by this to find the interval k. You then choose a random number between 1 and k as your starting point and select that item and every kth item after it.
The main advantage is that the sample is spread evenly across the list. If the list is in date order, the sample covers the whole year rather than bunching in one month.
It is also easy to explain and repeat, which suits audit documentation. The main risk is a hidden pattern in the list.
If every 50th item happens to be a certain type, such as the first invoice of each batch, the sample will be biased. Auditors check for this before relying on the method, and they may shuffle the list or use a different approach if a pattern is suspected.
Systematic sampling is not always as statistically pure as simple random sampling, in which every item has an equal and independent chance of being picked. For many business tasks, though, the difference is small, and the convenience outweighs it.
Where the results matter a great deal, the sample size should be set using the required confidence level and acceptable error. Documentation is a big part of using the method properly.
An auditor records the population, the interval, the random start and how the random number was generated, so that another reviewer could repeat the selection exactly. If errors are found, the same record makes it clear how many items were tested, how many failed and how far the findings can safely be extended to the rest of the population.
In practice
Real-world examples.
Example
An internal auditor tests expense claims by selecting every 25th claim from a list of 2,500 after a random start. Of the 100 claims checked, six lack receipts, which she reports with the sample size.
Example
A factory quality inspector takes every 200th bottle off the line to check the fill level. The method catches drift in the machine during the shift because the sample is spread over the whole run.
Example
A retailer surveys every 10th customer who leaves a store. The marketing team notes that results may be biased if busy periods have a pattern that matches the interval.
Formula
Calculation
Sampling interval k = Population size N / Sample size n
Suppose an auditor has 5,000 invoices and wants a sample of 100.
k = 5,000 / 100 = 50
She picks a random starting number between 1 and 50, for example 17.
The sample is invoice 17, 67, 117, 167 and so on, adding 50 each time.
The last item is 17 + (99 x 50) = 17 + 4,950 = 4,967, which is within the list of 5,000 invoices.
In total she checks 100 invoices, and every part of the year is covered because invoices are in date order.Case study
Seen in the real world.
Brookfield Logistics is an illustrative, fictional freight company with 12,000 delivery receipts a quarter. The finance team wanted to check that each receipt matched an invoice but could not review them all.
They decided on a sample of 240 receipts, giving an interval of 12,000 / 240 = 50. A random start of 33 meant selecting receipts 33, 83, 133 and so on through the list.
In the illustrative review, 12 of the 240 sampled receipts, or 5%, had mismatches. The team estimated that around 5% of the whole population, about 600 receipts, might have mismatches, and recommended a full review of one depot where the errors were concentrated.
Watch out
Common mistakes.
- Starting at the first item every time instead of choosing a random start, which makes the sample predictable.
- Using the method on a list with a repeating pattern that matches the interval.
- Treating results from a sample as exact facts about the whole group, when they are estimates with some margin of error.
Questions
People also ask.
How is systematic sampling different from random sampling?
Random sampling picks items by chance each time, while systematic sampling picks them at fixed intervals after one random start.
How do I choose the sample size?
It depends on the confidence you need, the error you can accept and how variable the population is.
When should I avoid systematic sampling?
When the list is ordered in a way that repeats at the same interval, because the sample would then give a misleading picture.
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