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Lekhya.in

Explainer2 min readPublished

Why there's no fixed sample size per population, however big it is

"25 items for a population this size" is a firm habit, not a statistical result — the actual sample size moves with tolerable error, expected error and confidence level, not population size alone. A free way to calculate your own.

A fixed sample size like "25 for any population over 500 items" is a firm habit, not a statistical result — the actual drivers are the confidence level wanted, the tolerable error or deviation rate, and the error or deviation rate already expected, and population size barely moves the answer once a population is reasonably large. Two populations of 2,000 and 20,000 items, tested at the same confidence and tolerable error, produce almost the same sample size; what actually changes the number is tightening the tolerable error or raising the confidence level.

What actually drives the number

What moves a sample size, and by how much
InputEffect of tightening itEffect of loosening it
Confidence level (90% → 99%)Sample size roughly doublesSample size roughly halves
Tolerable error (relative to population value)Smaller tolerable error inflates the sample sharplyLarger tolerable error shrinks it sharply
Expected error rateAny expected error inflates the required sample above the basic calculationZero expected error gives the smallest sample the other inputs allow
Population size (once reasonably large)Negligible effect past a few thousand itemsNegligible effect past a few thousand items
What moves a sample size, and by how much

Treating population size as the main driver is the most common sampling mistake in practice — it feels intuitive ("bigger population, bigger sample") but for populations past a few thousand items, it's close to the least important input in the calculation.

Why a firm-wide fixed number persists anyway

A standard sample size is easy to apply consistently across files and easy for a reviewer to recognise — which is exactly why many firms default to one. The cost shows up on the populations where it's wrong: a low-risk, low-tolerable-error-sensitivity population gets over-tested, and a population where the real tolerable error is tight gets under-tested, with nobody noticing because the number matched what every other working paper in the file used.

Running the actual calculation — confidence level, tolerable error or deviation rate, expected error rate — takes the same five minutes a fixed-number lookup does, and produces a number that's actually defensible against the specific population being tested, rather than against "what we always use."

This is practical guidance written for audit teams, not an authoritative statement of any standard or statute. Standards, forms and timelines change. Check the current text issued by the ICAI and the relevant authority before relying on anything here in an audit file.

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