The Wisdom of Statistics

“America's poverty problem is not one of material scarcities but of abundant bad behavior. There are three simple behavioral rules for avoiding poverty: finish high school, produce no child before marrying, and no child before age 20. Only 8% of families who follow these rules are poor; 79% of those who do not are.” -- George Will

Audit Effectiveness, Efficiency, & Risk Lowers Audit Lowers Audit

Effectiveness Efficiency

BETA RISK

ROOR X

ROIA X

ALPHA RISK

ROUR X

ROIR X

Substantive Test SamplingTWO COMMON METHODS

Probability Proportionate to Size– sample overstatements & extend results to population– Stats based on 1 tailed test of attribute sampling

Variables sampling– sample account $ values& extend result to population– Mean-per-unit (sample mean x N)– Difference estimation (ave.AV-ave.BV x N)

PPS Sampling Advantages

No Standard Deviation calculation required Automatic stratification Smaller sample size

Sample Size DeterminantsAs theseincrease

Sample Sizeincreases

Sample Sizedecreases

Pop. size X

Standard dev. X

Precision X

Reliability X

Materiality X

Beta risk (ROIA) X

Alpha risk (ROIR) X

Steps in PPS Sampling

Determine the relevant population Calculate the sample size (p. 413) Draw the sample (p. 413) Evaluate the results (p.414)

– Projected Error– Precision – Upper error limit

Steps in Variables Sampling

Determine the relevant population Determine the sample size (p. 402-4) Select the sample Evaluate the results

– Precision (p. 403-4)– Reliability/Confidence level (p.403-5)