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Advanced Audit
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Gravity
Key Concepts:
Terms in this set (47)
Sampling
process of making a statement about a population of interest by examining only a subset (or a sample) of that population
o When to use- when there is a large population or the need for exact info is less important
o Population- group of items we are trying to make a statement about
Sampling Risk
likelihood that the decision based on the sample differs from the decision that would've been made if entire population were sampled
o Caused by a selecting a non-representative sample
o Controlled by:
Determining an appropriate sample size
Ensuring that all items have an equal likelihood of selection
Evaluating sample results to control risk
Non-sampling risk
likelihood that an incorrect conclusion is drawn for reasons unrelated to the sample
o Caused by mistakes in evaluating the sample items (Ex: counting red beads as clear beads)
Statistical Sampling
applies laws of probability in selecting sample items and evaluating sample results
o Allows audit team to control exposure to sampling risk
Quantitative statements about the results
Measure the sufficiency of evidence gathered
o Sample selection methods:
Unrestricted random selection- select items based on random numbers matched to items in population
Systematic random selection- bypass a fixed number of items in the population, by selecting every nth item
Weighted random selection- select items based on random numbers; each item has a probability of being selected in proportion to a known characteristic
Non-statistical sampling
made subjectively and relies on professional judgment
o Does not allow audit team to control exposure to sampling risk
o Use statistical sampling to guide judgment on sample size
o Sample selection methods:
Haphazard- select items in a nonsystematic, yet not fully random, manner
Block selection- select contiguous units
Precision (allowance for sampling risk)
distance from the estimate population value in which the true (but unknown) population value may lie within a given probability
Allowance for sampling risk
used to adjust the sample estimate to control exposure to sampling risk
Reliability (confidence)
likelihood of achieving a given level of precision; true population lies within the precision interval
Attribute sampling
used to estimate the extent to which a characteristic exists within a population
- Used in auditor's study of internal control
o Estimate the rate at which internal control policies or procedures are not functioning as intended
Sampling risk (Risk of overreliance)
risk that, based on the sample, the auditor concludes that the control is effective when in fact it is not
Establish based on desired level of control risk
Lower control risk = lower risk of overreliance
Inverse relationship with sample size; as the sample size increases, the risk of overreliance decreases; therefore, you are less likely to make an incorrect judgment about the population.
If 95% confidence- 5% risk of overreliance
Tolerable rate of deviation
percent of the population that could have a deviation and you would still call the control effective
Establish based on desired level of control risk
Lower control risk = lower tolerable rate of deviation
Inverse relationship with sample size; if the auditor is okay with having more deviations, they don't have to test as many controls (smaller sample size)
Expected population deviation rate
the deviation rate you expect in the population
Established based on past audits
Direct relationship with sample size; if the expected population deviation rate increases, sample size should increase as well.
Population size
number of items in the population
Direct relationship to sample size
Upper limit rate of deviation
The highest rate of deviation that could exist in the population and still produce the observed sample with a certain probability
Upper limit on deviation is the sample rate of deviation plus an allowance for sampling risk.
Upper limit rate of deviation
o ULRD= sample rate of deviation + allowance for sampling risk
Deviation rate= number of deviations/sample size
Confidence= 1-risk of overreliance
Making the decision
o If UL rate of deviation is LESS THAN tolerable rate of deviation- rely on controls as planned
o If UL rate of deviation is GREATER THAN tolerable rate of deviation- reduce planned reliance on controls
Discovery sampling
type of sampling used when deviations at a very low rate, but are critical in nature
o If one deviation is identified, audit team immediately concludes controls are ineffective
Sequential sampling-
auditor takes an initially small sample and then decides, based on the results of the initial sample, whether to expand the sample or make a conclusion
o Selects sample which is generally smaller than would otherwise be
o Advantage is that the sample may be more efficient (smaller) than a fixed sampling plan
Variables Sampling
form of sampling where the objective is to estimate some (continuous) value for the population.
Variables sampling in auditing is used mainly estimate misstatement amounts for the population (a.k.a., the projected misstatement) whereas attributes sampling is for determining if a population has a certain characteristic (i.e. there is a binary response yes or no, red or blue, effective or not effective).
Sampling risk (risk of incorrect acceptance)
accepting an account as being fairly presented when there is actually a material misstatement
Inversely related to sample size
Risk of incorrect rejection
auditor concluding that the account is misstated when in fact it is fairly presented
Tolerable misstatement
the max amount by which an account balance or class of transactions can be misstated and be accepted by the audit team as being fairly presented
Performance materiality applied to particular sampling application; often set equal to the performance materiality
Inverse relationship to sample size
Expected population misstatement
Based on prior audits
Direct relationship to sample size
Upper limit on misstatement
amount that has a "high" (1-risk of incorrect acceptance) probability of equaling or exceeding the true amount of the misstatement
o ULM= projected misstatement + allowance for sampling risk
Making the decision:
o If ULM is LESS THAN tolerable misstatement- account is NOT materially misstated- unqualified
o If ULM is GREATER THAN tolerable misstatement- account is materially misstated
Monetary Unit Sampling (MUS)
Defines the sampling unit as an individual dollar (or other monetary unit) in an account balance
Auditor will select individual dollars (or monetary units) for examination
Auditor will verify the entire "logical unit" containing the selected dollar (or monetary unit)
Accounts receivable: Customer account
Inventory: Inventory item
Advantages of MUS
Results in more efficient (smaller) sample sizes
Selects transactions or components reflecting larger dollar amounts
Effective in identifying overstatement errors
Asset and revenue accounts
Generally simpler to use than classical variables sampling
Disadvantages of MUS
Provides a conservative (higher) estimate of misstatement
Not effective for understatement or omission errors
Liabilities and expenses
Expanding sample is difficult if initial conclusion is to reject the account balance
Requires special consideration for accounts with zero or negative balances
Inputs
Risk of incorrect acceptance
Expected misstatement
Tolerable misstatement
Population size
Sampling interval
Population size ÷ Sample size (Dollars)
Sampling Interval Cont.
- If a sub account is larger than the sampling interval, then the entire misstatement is included in the projected misstatement
o Recorded balance> sample interval; difference= projected misstatement
- If the sub account is smaller than the sampling interval, then the tainting percentage is multiplied by the sampling interval to reach the projected misstatement
o Tainting %= difference (recorded balance-audited value) / recorded balance
o Sample interval * tainting % = projected misstatement
upper limit on misstatements
total projected misstatement + basic allowance for sampling risk + incremental allowance for sampling risk
Basic allowance for sampling risk
sample interval * confidence factor for zero misstatements
Making the decision
- compare the upper limit on misstatement to tolerable misstatement
o If ULM > TM then reject account as being fairly stated
o If ULM < TM then accept account as being fairly stated
Differences from classical variable
MUS is more efficient, more conservative, generally more simple to use
Classical Variables Sampling
Uses normal distribution theory and the central limit theorem to provide an estimated range of
Recorded account balance or class of transactions
Misstatement in an account balance or class of transactions
Basic methodology
Determine estimated range of account balance or misstatement
Evaluate using tolerable misstatement
Additional Considerations in Classical Variables Sampling
Consider the following additional factors in determining sample size
Risk of incorrect rejection
Population variability
To reduce population variability, auditors may choose to stratify the population
Advantages of CVS
Can handle both overstatement and understatement
Considers both risk of incorrect acceptance and risk of incorrect rejection
Handles large number of exceptions well
Disadvantages of CVS
Need to estimate more parameters
No guarantee that large accounts will be selected
Meanings
Population = (N)
Sample Size: (n)
Population Recorded Amount: (Pr)
Sample Recorded Amount (Sr)
Sample Audited Amount: (Sa)
Want to find the Population Audited Amount (Pa)
Ratio estimation
Assumes a constant percentage misstatement in population
Estimates recorded balance by multiplying recorded balance by ratio of audited value to recorded balance
Ratio estimation Calculation
Pa = (Sa/Sr) * Pr
Mean-per-unit
Assumes each item in population (component of account) has similar balance
Estimates recorded balance by multiplying number of components by average audited value
Mean-per-unit Calculation
Pa = (Sa/n) * N
Difference estimation
Assumes each item in population (component of account) has similar difference between recorded and audited value
Estimates the amount of misstatement by multiplying number of components by average misstatement
Estimates recorded balance using estimated misstatement
Difference estimation Calculation
Pa = Pr - ((Sr - Sa))/n) * N
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