What it means
Imagine you must test 1,000 invoices but cannot read them all. A plain random sample could, by chance, miss the few very large invoices that matter most.
Stratified sampling avoids that risk by first sorting the invoices into groups, such as small, medium and large, and then sampling within each group. The word random is important.
Inside each stratum, items are chosen by chance so that every item has a known probability of selection and the personal judgement of the person sampling cannot bias the result. The word stratified means the population is split by a characteristic that matters, such as invoice size, region, customer type or product line.
The usual approach is proportional allocation, where each stratum receives a share of the sample equal to its share of the population. If large invoices are 10% of all invoices, they are 10% of the sample.
Some analysts prefer disproportionate allocation, which deliberately over-samples a small but important or highly variable stratum, and then they weight the results back so the final estimate remains fair. Finance and audit teams use the technique for testing transactions, estimating inventory values, reviewing customer receivables and checking expense claims.
Market researchers use the same idea in customer surveys, so that results reflect each age group or region properly. In each case, the benefit is a more precise estimate from the same sample size.
The method needs a good list of the population and a clear rule for assigning each item to exactly one stratum. If the strata are poorly defined, or the list is out of date, the sample will not represent the population, however carefully it is drawn.
Strata should also be meaningfully different from one another, otherwise the extra effort adds nothing over a simple random sample.
In practice
Real-world examples.
Example
An external auditor reviews a retailer's receivables of 5,000 customer balances. She splits them into balances under $1,000, between $1,000 and $10,000, and above $10,000, then draws a random sample from each group. This ensures the handful of large balances, which carry most of the financial risk, are tested.
Example
A consumer goods company surveys 2,000 customers about a new product. Because its customers are 50% in cities, 30% in towns and 20% in rural areas, it samples 1,000, 600 and 400 respectively. The survey results therefore mirror the real customer base.
Example
A human resources team wants to estimate average overtime across a 1,200-person company. It stratifies employees by department, samples within each, and reports a more accurate company-wide figure than a simple random sample would have given.
Formula
Calculation
Sample size for a stratum = (stratum size / total population size) x total sample size
Suppose an internal auditor will test 100 invoices out of a population of 1,000, split into small invoices (600), medium invoices (300) and large invoices (100). For the small stratum the sample is (600 / 1,000) x 100 = 60 invoices. For the medium stratum it is (300 / 1,000) x 100 = 30 invoices, and for the large stratum it is (100 / 1,000) x 100 = 10 invoices. The total is 60 + 30 + 10 = 100 invoices, and within each group the specific invoices are picked at random.Case study
Seen in the real world.
Bluefin Wholesale is an illustrative, fictional distributor that holds about 40,000 stock items in a single warehouse. At year end the finance director needed a reliable inventory value without counting every item. A simple random sample of 400 items had produced a wide range of estimates in earlier years because a small number of high-value machines dominated the total.
This year the team stratified the stock into three groups by unit value: low-value consumables, mid-value parts and high-value machines. They counted every one of the few hundred high-value machines and took random samples from the other two groups in proportion to their size.
The resulting estimate was far tighter and the auditors accepted it with minimal further work. The illustrative lesson is that stratifying around value concentrates effort where errors would matter most.
Watch out
Common mistakes.
- Confusing stratified sampling with quota sampling, where interviewers choose people to fill quotas by hand instead of drawing at random.
- Creating overlapping strata so that some items could belong to more than one group, which breaks the probability logic.
- Over-sampling a stratum on purpose and then forgetting to apply weights, which skews the final estimate.
Questions
People also ask.
When is stratified sampling better than simple random sampling?
It is better when the population contains distinct subgroups that differ in size or behaviour, because it guarantees each is represented and usually gives more precise results.
Does each stratum need the same sample size?
No, proportional allocation gives larger strata more items, though a small but critical stratum may be deliberately over-sampled.
Can stratified sampling still be wrong?
Yes, if the population list is incomplete or the strata are poorly chosen, the sample will not reflect reality.
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