Formula
Sample size is n = ((Zrejection + Zacceptance) × SD × N ÷ TM)², rounded up, where N is the population count, SD the estimated standard deviation and TM tolerable misstatement. With the finite-population correction it becomes n ÷ (1 + n ÷ N). The projection uses N times the sample mean (mean-per-unit), book value plus N times the mean difference (difference), or the sample audited-to-book ratio times book value (ratio). The standard error is N × SD ÷ √n × √(1 − n ÷ N), and precision is Z times that. The interval is the estimate plus or minus precision. The balance passes this test when the projected misstatement plus precision stays within tolerable misstatement.
Source
Audit sampling is governed by AU-C 530 for AICPA engagements and PCAOB AS 2315 for issuers. The calculations are the standard classical estimators described in the AICPA Audit Sampling guide and in Cochran, Sampling Techniques (3rd ed., 1977). The standards do not prescribe one formula, so your firm's methodology decides the risk levels and the method.
When to use it
Use it to plan a substantive test of a balance made of many items, such as receivables, inventory or a population of invoices, when you expect errors in both directions. Pair it with materiality to set tolerable misstatement and with the random number generator to select the items.
Limits
The interval rests on a normal approximation, which is weaker for small samples and for populations with many zero-error items and a few large errors. The planning formula assumes no expected misstatement. Misstatements found in a sample are projected, and the qualitative side of each error still needs evaluation. Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
When do I use variables sampling instead of attribute sampling or MUS?
Attribute sampling counts how often a control or a transaction deviates. Variables sampling estimates a dollar amount for a population, such as the audited value of an inventory listing or a receivables ledger. Monetary unit sampling also estimates dollars but weights selection by book value and suits populations where you expect few misstatements. Classical variables sampling can handle both overstatements and understatements and works when errors are common, but it needs an estimate of the population standard deviation and is weaker when the sample turns up few or no differences.
Which estimation method should I pick?
Mean-per-unit ignores book values and projects the audited mean, so it does not use the link between book and audited amounts and needs a larger sample than difference or ratio estimation when those amounts track each other. Difference estimation projects the average error per item and works best when errors are about the same size regardless of the item amount. Ratio estimation projects the audited-to-book ratio and works best when errors scale with item size. The tool computes whichever you select from the same pasted pairs, so you can compare them.
Where does the standard deviation for planning come from?
A pilot sample, last year's result for the same population, or a judgment based on how widely book values vary. For difference and ratio estimation the relevant figure is the standard deviation of the differences or of the audited minus ratio times book amounts, which is smaller than the spread of the values themselves when book and audited values track each other. Using the spread of the values themselves is the conservative choice.
What do the two risks mean?
The risk of incorrect rejection is the chance the sample points to a misstated balance when the balance is fairly stated. The risk of incorrect acceptance is the chance the sample supports a balance that is materially misstated. The auditor sets both. The risk of incorrect acceptance is the one that bears on whether the audit reaches the wrong conclusion. The tool uses a two-sided factor for rejection and a one-sided factor for acceptance.
What if the sample is bigger than the population allows?
The tool caps the sample at the population size and says so. At that point test every item, or stratify so large items are tested individually and sampling applies only to the rest.
Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.