# Audit Sampling

Attributes of statistical sampling

1) design an efficient sample, 2) measure sufficiency of evidential matter obtained, and 3) evaluate sample results. This provides an objective basis for quantitatively evaluating sample risk. Uses table to determine the sample size, and considers accepta

nonsampling risk

error unrelated to sampling risk that the auditor might commit when performing an audit sampling task, such as failing to recognize a misstatement or otherwise misinterpreting the audit evidence.

Type 1 error

False rejection, related to efficiency. Related to Internal control it is the risk of under reliance - risk of assessing control risk too high. Auditor may decide to increase risk if cost and effort to select additional sample items are low.

type 2 error

False acceptance, over reliance. related to effectiveness. For IC, this is the risk of over-reliance on internal controls, or assessing control risk too low. For substantive testing, it refers to the risk of incorrect acceptance.

Attributes Sampling steps

1) Identify objective, 2) Define what constitutes an occurrence, 3) Identify relevant population, 4) Determine sampling method, 5) Determine sample size, 6) select the sample, 7) evaluate results, 8) document sampling process

Allowance for sampling risk, attributes sampling

achieved upper precision limit less the sample rate

Attributes Sampling

Statistical sampling for the purpose of identifying the percentage frequency of a hit or miss characteristic in a population; usually used to refer to audit sampling to ascertain the operating effectiveness of internal control

Factors affecting Sample size for attributes sampling

1) Risk of over reliance - Inverse; 2) Expected error rate - direct; 3) Tolerable error rate - inverse; 4) Risk of under reliance - inverse; 5) population size (implicit) direct.

Computed Upper deviation error rate

sample error rate + allowance for sampling risk. Sample error rate = # errors found / over sample size

Sample size test of controls - inverse relationship

inverse relationship to tolerable rate and risk of over reliance. Increase in tolerable rate = decrease in sample size. Increase in control risk = increase sample size

Deviations from specific internal control procedures at a given rate

ordinarily result in misstatements at a lower rate because each failure to apply a control does not necessarily result in a misstatement.

sample size for a test of controls

considers the tolerable deviation rate, the allowable risk of assessing control risk too low, and the expected deviation rate. The auditor also considers the relationship of the sample to the objective for the test of controls.

Sampling for variables

classical variables sampling, is used to calculate a best estimate of a population value with confidence intervals around the estimate. methods as mean per unit, used to provide a numerical estimate of a population.

Effectiveness of ratio estimation

most efficient when the differences are proportional to book values. The existence of a relatively small number of differences in the population does not ensure that the differences will be proportional to book values.

Precision

The width of the confidence interval of the estimate, or the possible error in either direction.

reliability

pertains to the confidence level achieved in statistical sampling application

projected error

the estimate of the total amount of over- or understatement in a population, usually an account balance. It is determined by projecting the sample results to the population as a whole.

Standard deviation

measures the amount of variability in the population.

Stratification mean per unit of a population

enables the auditor to separate the population into size-related classes to produces a higher level of precision than a smaller sample size. Could be used for specific audit objectives and substantive procedures more efficiently. I.e., all transactions ov

Allowance for sampling risk, variables sampling

A = (coefficient reliability x population size x estimated population standard deviation) / sample size.

PPS Sampling

groups the population into individual dollar-items for sampling. Extreme degree of stratification, efficient when there are few differences between audit and book values. Does not require an estimate of the standard deviation, nor special design for the i

tainting percentage for projected misstatement

used when PPS Sampling items have BV less than sample interval. (BV-AV)/BV = tainting. projected misstatement = tainting x sample interval.

Projected misstatement for PPS, BV >=Sample

actual misstatement identified, no further "projection" BV - Audit value.

Sample Size Calculation PPS

(reliability factor x BV) / Tolerable misstatement, net of expected misstatements. OR BV/Sampling interval.

5 categories of IT General Controls

1) Organization and operation, 2) Systems development and documentation, 3) hardware and software built-in controls, 4) Access, 5) Data procedures

Haphazard sampling

Arbitrary selection, with no conscious biases. Nonstatistical sampling approach.

factors relating to sample size

1. Expected error rate - the more errors, the larger the sample

block sampling

Sampling methodology where a group of contiguous items are selected; (e.g., selecting all transaction for the month of June). nonstatistical sampling method.

observed deviation rate

number errors in the sample / sample size

Upper error limit, attributes sampling

sample error rate plus allowance for sampling risk. If this sum exceeds the tolerable rate, the planned assessed level of control risk must be modified.

Ratio estimation sampling technique

sampling method used when calculated audit amounts are approximately proportional to the client's book amounts. A correlation between book amounts and individual differences would exist.

Sampling interval PPS

Population book value / sample size.