The formulas
Planning: n = (N × (Ua + Ub) × SD ÷ (TM − E))². Evaluation: the point estimate is N × mean audited value (mean-per-unit), the book total less N × mean difference (difference), or the sample audited-to-book ratio times the book total (ratio). Precision is the normal coefficient times the standard error. These are the standard textbook estimators for classical variables sampling, the same ones taught in university auditing texts and AICPA audit sampling guidance.
When to use it
Use classical variables sampling for substantive tests of a balance made of many items, such as receivables or inventory, when the population standard deviation can be estimated and misstatements are expected to be frequent enough for the estimators to work. When misstatements are rare, monetary unit sampling usually behaves better.
Limits
The planning standard deviation is an estimate, so recompute it from the actual sample. Normal-theory intervals are approximate for small samples or skewed populations, and the tool does not stratify. Items must be selected so that every item has a known chance of selection, which the random sample tools on this site can help with. Under AU-C 530 the auditor also investigates the nature and cause of every misstatement.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
What is classical variables sampling?
It applies the normal distribution to a sample of recorded items to estimate the population's audited amount or its misstatement. The three common estimators are mean-per-unit, difference and ratio. AU-C 530 covers statistical and nonstatistical sampling generally and does not prescribe one formula.
How is the sample size calculated?
This tool uses n = (N × (Ua + Ub) × SD ÷ (TM − E))², where Ua is the one-tailed normal coefficient for the risk of incorrect acceptance, Ub is the two-tailed coefficient for the risk of incorrect rejection, SD is the estimated standard deviation, TM is tolerable misstatement and E is expected misstatement. The result is rounded up and capped at the population count.
Which estimator should I use?
Mean-per-unit needs only audited values. Difference and ratio use each item's book value as well and usually need fewer items when book and audited values move together. Difference suits misstatements of similar size across items, ratio suits misstatements that scale with item size. Neither works well when the sample has few or no misstatements, because the standard error then collapses.
What does the standard error include?
It is N × s ÷ √n × √(1 − n ÷ N). Here s is the sample standard deviation of audited values for mean-per-unit, of the book-minus-audited differences for difference estimation, or of the residuals audited − ratio × book for ratio estimation. The last factor is the finite population correction.
How do I read the result against tolerable misstatement?
The tool compares the projected misstatement plus the precision to tolerable misstatement. If the larger end of the interval is inside it, the sample supports the balance on its own terms. Known misstatements found outside the sample, qualitative factors and the aggregate across accounts still need evaluation under AU-C 450.
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.