Term
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Definition
| applies an audit procedure to fewer than 100% of the items under audit for the purpose of drawing a conclusion about a characteristic of a balance or transaction class (the population sampled). Sampling may be statistical or nonstatistical. |
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Term
| judgment (nonstatistical) sampling |
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Definition
uses the auditor's subjective judgment to determine the sample size and sample selection.
This subjectivity is not always a weakness. |
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Term
| statistical (probability or random) sampling |
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Definition
| provides an objective method of determining sample size and selecting the items to be examined. |
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Term
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Definition
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Term
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Definition
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Term
| effects of judgment sampling |
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Definition
| The auditor, based on other audit work, may be able to test the most material and risky transactions and emphasize the types of transactions subject to high RMM. |
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Term
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Definition
| how closely the sample represents the population |
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Term
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Definition
| confidence level, which is the % of times the sample will adequately reflect the population |
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Term
| effects of statistical sampling |
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Definition
| Unlike judgment sampling, it also provides a means of quantitatively assessing precision and reliability. |
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Term
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Definition
| primary characteristic of statistical sampling. |
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Term
| types of random-based selection |
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Definition
1. random sampling
2. stratified sampling
3. monetary-unit sampling
4. systematic sampling |
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Term
| Why do auditors do statistical sampling? |
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Definition
| It helps the auditor design an efficient sample, measure the sufficiency of the evidence obtained, and evaluate the sample results. |
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Term
| third standard of field work |
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Definition
| requires auditors to obtain sufficient appropriate evidence. |
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Term
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Definition
| measure of the quantity of evidence. Thus, it relates to the design and size of the sample. |
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Term
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Definition
| Statistical sampling permits the auditor to measure sampling risk and therefore to design more efficient samples. |
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Term
| Is statistical sampling applicable to tests of controls? Or substantive testing? |
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Definition
| It is applicable to both. |
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Term
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Definition
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Term
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Definition
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Term
| Is audit risk the same as sampling risk? |
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Definition
| Audit risk includes both uncertainties due to sampling and those due to nonsampling factors. |
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Term
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Definition
| probability that a properly drawn sample may not be representative of the population. The conclusions from the sample may differ from those made if all the items in the population are examined. |
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Term
| How is sampling risk related to sample size? |
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Definition
| Inversely related. As the sample increases, sampling risk decreases. |
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Term
| How does the auditor control sampling risk? |
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Definition
| By specifying the acceptable level when developing the sampling plan. |
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Term
| risk of assessing control risk too low (tests of controls) |
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Definition
risk that actual control risk is greater than that indicated by the sample.
This risk relates to audit effectiveness and could cause audit failure.. This risk also is termed a Type II error or Beta risk.
risk that the assessed level of control risk based on the sample is less than the true operating effectiveness of internal control. |
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Term
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Definition
| risk that controls do not prevent or detect material misstatements on a timely basis. |
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Term
| risk of assessing control risk too high (tests of controls) |
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Definition
risk that actual control risk is less than that indicated by the sample.
This risk relates to audit efficiency and is likely to result in greater audit effort; could lead to an auditor's overassessment of control risk may lead to an unnecessary extension of substantive procedures. |
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Term
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Definition
| risk of assessing control risk too high or risk of incorrect acceptance |
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Term
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Definition
| risk of assessing control risk too low or risk of incorrect rejection |
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Term
| risk of incorrect acceptance (substantive tests) |
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Definition
risk that the sample supports the conclusion that the recorded account balance is not materially misstated when it is materially misstated.
This risk relates to audit effectiveness and could cause audit failure. |
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Term
| risk of incorrect rejection (substantive tests) |
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Definition
risk that the sample supports the conclusion that the recorded account balance is materially misstated when it is not materially misstated.
This risk relates to audit efficiency and is likely to result in greater audit effort. |
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Term
| After an incorrect rejection, what will likely happen? |
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Definition
1. The client will assert the fairness of the balance.
2. The auditor will perform additional procedures.
3. The fairness of the balance will be affirmed. |
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Term
| When is a high risk of incorrect rejection acceptable? |
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Definition
| When the cost an effort of selecting additional sample items is low. |
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Term
| confidence/reliability level |
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Definition
complement of the applicable sampling risk factor.
If the allowable risk of assessing control risk too low is 5%, the auditor's desired confidence level is 95%. |
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Term
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Definition
| concerns all aspects of audit risk not caused by sampling, such as the auditor's application of inappropriate procedures or his/her inability to recognize misstatements or control deviations. |
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Term
| adequate planning and supervision |
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Definition
| used to decrease nonsampling risk. |
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Term
| basic steps in a statistical plan |
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Definition
1. Determine the objectives of the plan.
2. Define the population.
3. Determine acceptable levels of sampling risk.
4. Calculate the sample size.
5. Select the sampling approach.
6. Take the sample.
7. Evaluate the sample results.
8. Document the sampling procedures. |
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Term
| determine the objectives of the plan |
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Definition
1. Test of Controls (ToC)- example is to conclude that a control is reasonably effective.
2. Substantive procedure (Sp)- conclude that a balance is not misstated by more than an immaterial amount. |
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Term
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Definition
defining the sampling unit and considering the completeness of the population.
ToC- defining the period covered.
Sp- identifying individually significant items. |
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Term
| determine acceptable levels of sampling risk |
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Definition
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Term
| calculate the sample size |
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Definition
| using tables or sample-size formulas. |
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Term
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Definition
In some cases, it is efficient to divide the population into subpopulations or strata.
The primary objective of stratification is to minimize variability.
B/c variance w/in each subpopulation or stratum is lower than in the population as a whole, the auditor may sample a smaller number of items while holding the allowance for sampling risk and the confidence level constant. |
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Term
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Definition
each item in the population has an equal and nonzero probability of selection.
Random selection is usually accomplished by generating random numbers from a random number table or computer program and tracing them to associated documents or items in the population. |
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Term
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Definition
| begins w/selecting a random start and then taking every nth item in the population. |
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Term
| How do you compute the value of n? (systematic sampling) |
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Definition
| By dividing the population by the number of sampling units. |
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Term
| systematic sampling (card 2) |
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Definition
| The random start should be in the first interval. B/c the sampling technique only requires counting in the population, no correspondence btwn. random numbers and the items in the population is necessary as in random number sampling. |
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Term
| assumption of systematic sampling plan |
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Definition
| assumes that the items are arranged randomly in the population. If this is not true, a random selection method should be used. |
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Term
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Definition
| randomly selects groups of items as the sampling units rather than individual items |
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Term
| advantage of block sampling |
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Definition
| avoids the needs to assign random numbers to individual items in the population. |
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Term
| disadvantage of block sampling |
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Definition
| Variability of items within the blocks may not be representative of the variability within the population. |
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Term
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Definition
| Select items to be evaluated. |
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Term
| evaluate the sample results |
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Definition
| Draw conclusions about population. |
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Term
| document the sampling procedures |
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Definition
| Prepare appropriate working papers. |
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Term
| In general, the sample size is dependent upon... |
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Definition
1. The population size.
2. The acceptable risk.
3. The variability in the population.
4. The tolerable misstatement for variables sampling or the tolerable deviation rate for attribute sampling. |
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Term
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Definition
| As population size increases, the sample increases but at a decreasing rate. |
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Term
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Definition
| (1 - confidence level). The smaller the acceptable risk, the larger the sample size. |
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Term
| variability in the population |
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Definition
More variability = larger sample size.
more variability in the population, measured by the standard deviation for variables sampling or the expected deviation rate for attribute sampling, the larger the sample size. |
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Term
| tolerable misstatement for variables sampling or the tolerable deviation rate for attribute sampling |
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Definition
| Smaller acceptable misstatement = larger sample size. |
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Term
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Definition
| tests binary, Y/N, error/nonerror questions; used to test the effectiveness of controls (tests of controls) because it can estimate a rate of occurrence of control deviations in a population. |
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Term
| failure (deviation) rate in the application of the control |
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Definition
| used to project the failure rate to the whole population. |
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Term
| By specifying a tolerable deviation rate... |
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Definition
| a preliminary estimate of the population failure rate, and the risk of assessing control risk too low, the auditor can determine the appropriate sample size by consulting a table. |
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Term
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Definition
| applies to $ values or other quantities in contrast with the binary propositions tested by attribute sampling |
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Term
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Definition
averages the audit amounts of the sample items and multiplies the average by the # of items in the population to estimate the population amount.
An allowance for sampling risk is then calculated. |
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Term
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Definition
| achieved precision at the desired level of confidence based on the normal distribution |
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Term
| difference estimation (of population misstatement) |
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Definition
1. Determines differences between the audit and recorded amounts of items in the sample.
2. Adds the differences.
3. Calculates the mean difference.
4. Multiplies the mean by the number of items in the population.
An allowance for sampling risk is then calculated. |
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Term
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Definition
| similar to difference estimation except that it estimates the population misstatement by multiplying the recorded amount of the population by the ratio of the total audit amount of the sample items to their total recorded amount. |
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Term
| monetary-unit sampling (MUS) or probability-proportional-to-size (PPS) or dollar-unit sampling (DUS) |
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Definition
uses the dollar or another monetary unit as the sampling unit.
MUS is appropriate for testing account balances (typically assets) for overstatement when some items may be far larger than others in the population. |
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Term
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Definition
| MUS stratifies the population because the larger account balances have a greater chance of being selected. MUS is most useful if few misstatements are expected. |
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Term
| Does MUS require the use of a measure of dispersion? |
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Definition
| No, it does not require this to determine sample size or interpret the results. |
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Term
| attribute sampling & evidence |
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Definition
Attribute sampling requires the existence of evidence indicating performance of the control being tested.
It is most helpful for a large population of documentary evidence.
The performance of any task that leaves evidence of its execution is suitable for attribute sampling. |
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Term
| examples of activities subject to controls that may be tested using attribute sampling |
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Definition
Billing
Voucher processing
Payroll
Inventory pricing |
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Term
| steps for testing controls |
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Definition
1. Define the objectives of the plan.
2. Define the population.
3. Define the deviation conditions.
4. Determine the sample size.
5. Perform the sampling plan. |
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Term
| define the objectives of the plan |
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Definition
| The auditor should clearly state what is to be accomplished, for example, to determine that the deviation rate from an approval process for a transaction is at an acceptable level. |
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Term
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Definition
| The population is the focus of interest to reach conclusions about all the items in the population. |
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Term
| define the deviation conditions |
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Definition
| Careful definition of the attribute is important so that deviations (departures) from the control may be determined and the sample items properly evaluated. |
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Term
| determine the sample size |
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Definition
Four factors determine the necessary sample size:
1. Allowable risk of assessing control risk too low.
2. The tolerable deviation rate.
3. The expected population deviation rate.
4. Population size.
Tables ordinarily are used to calculate the appropriate sample size based on these factors.
1. Allowable risk of assessing control risk too low.
2. Tolerable deviation rate.
3. Expected popular deviation rate.
4. Population size. |
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Term
| allowable risk of assessing control risk too low |
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Definition
| Higher allowable risk = smaller sample size. |
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Term
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Definition
| maximum rate of deviations from the prescribed control that thee auditor is willing to accept the altering the planned assessed level of control risk |
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Term
| expected popular deviation rate |
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Definition
| estimate of the deviation rate in the current population is necessary to determine the appropriate sample size. |
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Term
| usual risk specified by auditors |
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Definition
| 5% or 10%, though the auditor can specify other levels of risk, but the tables most often presented use only these two. |
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Term
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Definition
| increase the likelihood of misstatements in the accounting records but do not always cause misstatements. |
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Term
| When is sampling inappropriate? |
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Definition
| When no deviations from controls can be tolerated. |
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Term
| Should the expected rate be more or less than the tolerable rate? |
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Definition
| Less than the tolerable rate. Otherwise, tests of controls should be omitted. |
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Term
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Definition
| The total # of sampling units in the population should be known. However, the sample size is relatively insensitive to size changes in large populations. |
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Term
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Definition
| for populations over 5,000. Use of the standard tables for sampling plans based on a smaller population size is a conservative approach b/c the sample size will be overstated. Hence, the risk of assessing control risk too low is not affected. |
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Term
| change in population compared to sample size |
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Definition
| A change in the size of the population has a very small effect on the require sample size when the population is large. |
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Term
| perform the sampling plan |
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Definition
| A random sample should be taken. Each item in the population should have an equal and nonzero change of being selected. A random number table or a computer program can be used to identify the items to be selected if a correspondence can be established between the random number and the item in the population. |
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Term
| statistical consideration for sampling plan |
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Definition
| A statistical consideration is whether to use sampling with or without replacement, which results in a conservative sample size b/c a slightly larger sample size than necessary will be indicated, However, in practice, auditor normally sample without replacement. No additional evidence is obtained by choosing the same item more than once. |
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Term
| sampling without replacement |
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Definition
| means that a population item cannot be selected again after it is selected in the sampling process. |
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Term
| evaluate and document sample results |
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Definition
| The steps include calculating the sample deviation rate and determining the achieved upper deviation limit. |
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Term
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Definition
sample deviation rate = # of deviations observed / sample size.
This rate is the best estimate of the population deviation rate; not a perfect indicator, but useful in developing a confidence level. |
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Term
| achieved upper deviation limit |
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Definition
based on the sample size and the number of deviations discovered.
The intersection of the sample size and the number of deviations indicates the upper achieved deviation level. |
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Term
| allowance for sampling risk (achieved precision) |
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Definition
| difference between achieved upper deviation limit determined from a standard table and the sample rate is the allowance for sampling risk |
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Term
| When does the sample not support the planned assessed level of control risk? |
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Definition
| When the sample deviation rate exceeds the expected population deviation rare, the achieved upper deviation limit will exceed the tolerable rate at the given risk level. |
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Term
| When the sample deviation rate does not exceed the expected population deviation rate... |
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Definition
| the achieved upper deviation limit will not exceed the tolerable rate at the given risk level. |
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Term
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Definition
| Each deviation should be analyzed to determine its nature, importance, and probable cause. |
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Term
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Definition
| provides a vehicle for forming a conclusion concerning the overall population |
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Term
| Can sampling be used a substitute for good judgment? |
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Definition
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Term
| true state of the population |
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Definition
| actual rate of deviations in the population |
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Term
| If the true deviation rate is less than the tolerable rate... |
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Definition
| the auditor should have an expectation of the effectiveness of the control tested. |
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Term
| If the true deviation rate exceeds the tolerable rate... |
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Definition
| the auditor should not have an expectation of the effectiveness of the control tested. |
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Term
| Auditor's estimate based on the sampling is... |
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Definition
| the auditor's conclusion about deviation rate. |
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Term
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Definition
| represents a correct decision to have an expectation of the effectiveness of the control tested. The population actually has a deviation rate less than the tolerable rate. |
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Term
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Definition
represents an incorrect decision not to have an expectation of the effectiveness of control tested.
The population has an acceptable deviation rate, but, because of sampling risk, the sample indicates that the pop. deviation rate is greater than the tolerable rate. So, though the control is effective, substantive testing is expanded. Thus, it relates to audit efficiency (Type I error/Alpha risk). |
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Term
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Definition
| represents an incorrect decision to have an expectation of the effectiveness of the control tested. The population has a greater than acceptable deviation rate, but the sample indicates that the deviation rate is less than the tolerable rate. The auditor expects the control to be more effective than it is, audit failure could result (Type II error/Beta risk). |
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Term
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Definition
| represents a correct decision not to have an expectation of the effectiveness of the control tested. The population has an unacceptable deviation rate, and the sample properly reflects this condition. |
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Term
| sampling for substantive testing |
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Definition
provides evidence about whether a financial statement assertion about an account balance is materially misstated.
The amount is expected to represent the true balance of the receivables, which is not known. By taking a sample and drawing a conclusion about the population, the auditor either supports or rejects the reported number. |
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Term
| steps for mean-per-unit sampling |
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Definition
1. Define the objectives of the plan.
2. Define the population and the sampling unit.
3. Determine the sample size.
4. Select the sample, execute the plan, and evaluate and document the results. |
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Term
| define the objectives of the plan |
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Definition
| The auditor intends to estimate the carrying amount of the population. |
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Term
| define the population and the sampling unit |
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Definition
| This is the balance or class of transactions and the support detail under audit. |
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Term
|
Definition
|
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Term
|
Definition
|
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Term
|
Definition
confidence coefficient or number of standard deviations related to the required confidence level (1 - risk of incorrect rejection).
Based on the risk of incorrect rejection, though the more important risk is the risk of incorrect acceptance. |
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Term
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Definition
| standard deviation of the population (an estimate based on a pilot sample or from the prior year's sample) |
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Term
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Definition
| number of items in the population |
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Term
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Definition
| allocation for sampling risk. This allowance is total. In some representations, the allowance (precision) is stated in the denominator on a per-item basis (A / N), and N would not be included in the formula. |
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Term
| allowance for sampling risk/precision or confidence interval |
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Definition
| interval around the sample statistic that is expected to include the true balance of the population at the specified confidence level. |
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Term
| When using classical variables sampling... |
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Definition
| the allowance for sampling risk is calculated based on the normal distribution. |
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Term
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Definition
maximum misstatement that may exist without causing the financial statements to be materially misstated.
Cannot exceed the auditor's preliminary judgments about materiality. |
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Term
| Which risk is more important to auditors? The risk of incorrect acceptance? Or incorrect rejection? |
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Definition
| Risk of incorrect acceptance. |
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Term
| allowance for sampling risk formula |
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Definition
| allowance for sampling risk = tolerable misstatement * ratio of desired allowance for sampling risk to tolerable misstatement |
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Term
| The ratio of desired allowance for sampling risk to tolerable misstatement is based on... |
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Definition
| allowable risks specified by the auditor. |
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Term
| select the sample, execute the plan, and evaluate and document the results |
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Definition
1. Randomly select and audit the accounts.
2. Calculate the average confirmed A/R account.
3. Calculate the sample standard deviation.
4. Evaluate the sample results. |
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Term
| best estimate of population balance formula |
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Definition
| best estimate of population balance = average A/R amount based on sample * # of items in population. |
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Term
| allowance for sampling risk (A) formula |
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Definition
| A = [(C * S * N) / (sq. root of n)] |
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Term
| monetary-unit sampling (MUS) approach to variables sampling |
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Definition
| hybrid method that uses attribute sampling methods to estimate monetary amounts. |
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Term
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Definition
| used in attribute sampling to approximate the binomial distribution; MUS is based on it. |
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Term
| What does MUS use as the sampling unit? |
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Definition
|
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Term
|
Definition
| MUS gives each monetary unit in the population an equal chance of selection. As a practical matter, however, the auditor does not examine an individual monetary unit but uses it to identify an entire transaction or balance to audit (the logical sampling unit). |
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Term
|
Definition
| MUS is appropriate for account balances that may include only a few overstated items, such as may be expected in inventory and receivables. |
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Term
| Is MUS useful for overstatements? Or understatements? Or both? |
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Definition
| Only for overstatements because a systematic selection method is applied (every nth monetary unit is selected). Accordingly, the larger the transaction or balance, the more likely it will be selected. |
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Term
| conclusions drawn from MUS |
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Definition
| MUS is used to reach a conclusion regarding the probability of overstating an account balance by a specified monetary amount. |
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Term
|
Definition
1. The largest items are selecting for testing.
2. It is ideal for testing for overstatement.
3. Small sample sizes may be considered, especially when no misstatements are expected.
4. It is relatively easy to apply, especially if no misstatements are discovered.
5. The sample size and sample evaluation can be calculated without dependence on the estimated variation (standard deviation) of the population.
6. The sample selection process may begin even before the complete population is available for testing. |
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Term
|
Definition
1. Items with zero or negative balances have no chance of selection.
2. It is useful only for detecting overstatement errors.
3. Sample sizes become relatively large if a significant amount of misstatement is expected.
4. The calculated allowance for sampling risk tends to be overstated when a significant amount of misstatement is found in the sample.
This is an inherent limitation of MUS. |
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Term
|
Definition
The steps in MUS are similar to those of other sampling methods:
1. Determine the objective of the plan.
2. Define the population and sampling unit.
3. Determine the sampling interval and sample size.
4. Select the sample.
5. Execute the sampling plan.
6. Evaluate and document the results. |
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Term
|
Definition
| recorded amount of population / sampling interval (SI) |
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Term
|
Definition
SI = TM / CF
function of the risk of incorrect acceptance and tolerable misstatement (TM). SI is determined by dividing TM by a confidence factor (CF) associated with the risk level. |
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Term
|
Definition
| discussed in the extension of the example that follows. |
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Term
| If no misstatements are discovered... |
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Definition
the auditor can form the following conclusion: that the auditor is (1 - risk of incorrect acceptance) confident that the recorded A/R balance is not overstated by more than the tolerable misstatement.
Also, b/c the sample has no misstatements, it is concluded that the population has no misstatements, but the sampling risk is needed b/c the sample likely imperfectly represents the population. |
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Term
| When has the objective of the audit test been met? |
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Definition
| When the allowance for sampling risk is less than or equal to the TM. |
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Term
| expanded sampling interval (SI) formula |
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Definition
SI = [TM - (AM * EF)] / CF
AM = anticipated misstatement
EF = appropriate for the risk of incorrect acceptance |
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Term
|
Definition
| The SI is used to select logical sampling units from the population. A monetary unit identifies a logical sampling unit. |
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Term
| cumulative balance & sampling |
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Definition
| When the cumulative balance is equal to or greater than the dollar selected, the account is selected b/c it contains the sampling unit. |
|
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Term
| If an account contains two or more logical sampling units... |
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Definition
| it is selected but given no special consideration. |
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Term
| evaluating and documenting the results |
|
Definition
The evaluation process depends on whether any misstatements are found in sample.
Project misstatements from the sample to the population.
Determine the allowance for sampling risk.
Calculate the upper misstatement limit. |
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|
Term
| allowance for sampling risk (final formula; used evaluating and documenting the results) |
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Definition
| allowance for sampling risk = basic precision (BP) + incremental allowance (IA) |
|
|
Term
| upper misstatement limit (UML) |
|
Definition
| UML = projected misstatement + allowance for sampling risk |
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Term
| If no overstatement errors are discovered... |
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Definition
the UML equals BP because...
The projected misstatement to the population is $0.
The allowance for sampling risk equals BA (IA is $0). |
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Term
|
Definition
BP = SI * CF
BP is the same as when no misstatements are found (SI * CF). |
|
|
Term
| If some overstatement errors are discovered... |
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Definition
| the evaluation process is more involved but follows that presented above. |
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Term
|
Definition
| Because each selected dollar represents a group of dollars (SI), the % of misstatement in the logical sampling unit (account selected) is the % of misstatement of the SI. This holds when the RA < SI. |
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Term
| When is tainting not calculated? |
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Definition
| When the RA of the account selected equals or exceeds the SI, the projected misstatement is the actual misstatement for the SI and no tainting is calculated. |
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Term
|
Definition
tainting % = (RA - AA) / RA
RA = recorded amount
AA = audit amount |
|
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Term
|
Definition
|
|
Term
| incremental allowance (IA) |
|
Definition
| based on projected misstatements related to logical sampling units less than SI. |
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Term
| ranking projected misstatements |
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Definition
| Projected misstatements are ranked by size (only when RA < SI). Each projected misstatement is multiplied by a factor that gives greater weights to the larger amounts. |
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