A3-M8-Sampling, Part 2

Describe variables sampling.

Variables sampling is a statistical sampling method used to estimate the numerical measurement of a population. Variable sampling is used primarily in substantive testing.

Define tolerable deviation rate (for attribute sampling) and tolerable misstatement (for variables sampling).

Tolerable deviation rate: the maximum rate (%) of deviation from a control procedure the auditor is willing to accept while still relying on the control.

Tolerable misstatement: the largest amount of misstatement the auditor believes can exist in a balance or class of transactions w/o causing the F/S to be MM.

What is stratification and why would an auditor stratify a population?

Stratification separates the sample into relatively homogenous groups. Each group is treated as a separate population. Stratification is typically used when a population has highly variable amounts. Stratification usually results in a smaller sample size.

What are the sampling plans commonly used for variables estimation?

• Mean-per-unit: the sample mean is multiplied by the number of items in the population to estimate population value.

• Ratio estimation: the ratio between BV and audited value (from a sample) is used to estimate population value.

  • Difference estimation: the difference between BV and audited value (from a sample) is used to estimate population value. Commonly used plans include mean-per-unit, ratio estimation, and difference estimation.

What factors affect sample size for a variables sampling application?

• standard deviation or population variability (direct relationship)

• tolerable misstatement (inverse relationship)

• acceptable level of risk (inverse relationship)

• expected size and frequency of misstatements (direct relationship)

• assessed level of risk (direct relationship)

What amounts are compared in drawing a conclusion about a variables sampling application?

The auditor compares the client’s BV to the calculated range in a variables sampling application. If the recorded BC is within the acceptable range, the BV is considered fairly stated. (The calculated range is the point estimate, as determined from the sample, plus/ minus an allowance for sampling risk). The amounts compared are the client's book value (BV) and the calculated range derived from the sample estimation.

Define probability-proportional-to-size (PPS) sampling.

PPS sampling is a hybrid sampling technique that uses attribute sampling theory to express a conclusion in dollar amounts rather than as a rate of occurrence. The sampling unit is defined as an individual dollar in a population, which creates the effect of stratified sampling (the unit’s chance of being selected increases as its amount increases).

What are the advantages and disadvantages of PPS?

Advantages:

• automatic stratification

• efficient (smaller sample)

Disadvantages:

• may require special considerations for negative, zero, and understated balances

How is the sampling interval determined in a PPS sampling application?

Sampling interval = tolerable misstatement/ reliability factor

(The reliability factor comes from a table and is based on the risk of incorrect acceptance.)

How is the sample size determined in a PPS sampling application?

Sample size = recorded amount of the population/ sampling interval