What it means
Imagine estimating the average invoice value across 4,000 invoices by checking 100. A different random 100 would give a slightly different average, and neither would match the true figure exactly, even though both samples were chosen fairly.
That natural wobble is sampling error. The good news is that it can be measured and managed.
The larger the sample, the smaller the error tends to be, and the more varied the population, the larger it tends to be. Analysts express it through the standard error and the margin of error, which put a range around the estimate.
It is vital to separate sampling error from non-sampling error. Non-sampling errors come from things such as badly worded questions, wrong data entry, biased selection or auditors misreading evidence, and no increase in sample size will cure them.
Sampling error, by contrast, is the unavoidable price of looking at only part of the group. For decision makers the practical question is whether the margin of error is small enough to act on.
If an audit sample suggests overstated receivables of $50,000 plus or minus $10,000, the conclusion is firm, but a result of $50,000 plus or minus $80,000 may not even prove there is a problem. Knowing the range prevents false confidence.
Finance teams reduce sampling error by increasing sample size, stratifying the population or using better selection methods. Each option costs time, so the aim is a tolerable error rather than none at all.
Sampling error is usually reported alongside a confidence level, such as 95%. That means that if the same sampling process were repeated many times, about 95 out of 100 of the resulting ranges would contain the true population value.
In practice
Real-world examples.
Example
A polling team surveys 1,000 customers of a bank and reports that 62% are satisfied, give or take 3 percentage points. The 3 points is the sampling error allowance.
Example
An internal auditor tests 80 inventory items and finds the sample overstated by $2,000. She extrapolates this to the full stock list and reports a range, because the true overstatement could be higher or lower than the point estimate.
Example
A subscription software firm samples 300 accounts to estimate average monthly usage. A wide margin of error leads the analyst to pull another 700 accounts before setting pricing tiers. The extra data narrowed the range enough to support a sensible decision.
Formula
Calculation
Standard Error = Sample Standard Deviation / Square Root of Sample Size
Margin of Error = Z x Standard Error
Worked example: an auditor samples 100 invoices and finds a mean of $1,300 with a sample standard deviation of $400. Using a Z value of 2 for roughly 95% confidence:
Standard Error = $400 / square root of 100 = $400 / 10 = $40
Margin of Error = 2 x $40 = $80
The estimated range for the true average is $1,300 - $80 to $1,300 + $80, which is $1,220 to $1,380.
To halve the standard error the auditor would need four times as many invoices, because the square root of 400 is 20 and $400 / 20 = $20.Case study
Seen in the real world.
Cobalt Foods is an illustrative, fictional manufacturer whose finance team estimated the average shelf life of returned goods from a sample of 30 returns. The sample average suggested write-offs of $12 per unit, and the team nearly built that figure into next year's provision.
A senior analyst calculated the margin of error and found it was plus or minus $6 per unit, so the true figure could easily be anywhere from $6 to $18. The sample was simply too small to support a precise provision.
The team increased the sample to 120 returns, which roughly halved the margin of error. In this fictional story the provision was set with a sensible range, and no one treated the first number as certain. The controller also added a line to the policy requiring a stated margin of error on every estimate that feeds into a provision.
Watch out
Common mistakes.
- Believing a well-chosen sample should match the population exactly, when some difference is statistically normal.
- Confusing sampling error with mistakes such as typing errors or biased question wording, which are non-sampling errors.
- Reporting a single number from a sample without any margin of error, which hides how uncertain it is.
Questions
People also ask.
How can sampling error be reduced?
By taking a larger sample, using stratification to cover the key segments or improving how items are selected.
Does a larger sample remove sampling error completely?
No, it shrinks it, but only a full census removes it entirely, and the benefit slows as the sample grows.
Is a margin of error the same as sampling error?
They are closely linked: the margin of error is the range, at a chosen confidence level, that expresses the likely size of the sampling error.
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