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Audit Sampling Flashcards

1
Q

What is audit sampling?

A

The application of a procedure to less than 100% of a population to draw a conclusion about the whole

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2
Q

What is attribute sampling?

A

Analyzes a sample to see how often a given attribute appears and extrapolates it to the whole population

Generally used for tests of controls – looks at several occurrences and counts how many times an occurrence deviates from the design

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3
Q

What is variable sampling?

A

Analyzes a sample to compute some particular variable for the whole, such as standard deviation

Generally used for substantive tests on transactions and account balances

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4
Q

What is dual-purpose sampling?

A

Combination of attribute sampling and variable sampling

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5
Q

What are some conditions for using dual-purpose sampling?

A

(1) The auditor should use it only if there’s a low risk that the deviation rate in the population exceeds the tolerable rate
(2) The sample size should be the greater of whatever sample sizes would have been chosen if the sampling methods were done individually

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6
Q

Is sampling always an acceptable way to reduce audit risk?

A

Nearly always – sometimes the risk is so high that all data must be examined

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7
Q

What are two components of audit risk?

A

(1) Sampling risk - risk that the conclusions drawn from the sample will falsely represent the whole population
(2) Nonsampling risk - all other possible risks (e.g. from poor planning, oversight, neglect)

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8
Q

For tests of controls, what are two different aspects of sampling risk?

A

The risk of assessing the control risk (based off the sample) as either (1) too high or (2) too low

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9
Q

For substantive tests, what are two different aspects of sampling risk?

A

(1) Risk of incorrect acceptance (beta risk) - when the sample implies that a population is not misstated when it is
(2) Risk of incorrect rejection (alpha risk) - when the sample implies that the population is misstated when it is not

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10
Q

If samples lead the auditor to conclude a higher risk than warranted, how does it hurt the audit?

A

It hurts the EFFICIENCY of the audit, since the auditor will do more work than necessary to overcome the calculated risk

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11
Q

If samples lead the auditor to conclude a lower risk than warranted, how does it hurt the audit?

A

It hurts the EFFECTIVENESS of the audit, because the auditor will not do as much testing as is needed to arrive at a stable conclusion

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12
Q

What are common procedures for collecting samples?

A 
Haphazard sampling
Random sampling
Systematic sampling
Stratified sampling
Block sampling
Probability-proportional-to-size sampling
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13
Q

What is haphazard sampling?

A

Completely unsystematic sampling, neither purposely random nor nonrandomly systematic

However, it is not simply careless – it just includes professional (unbiased) judgments

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14
Q

Can haphazard sampling be used for statistical sampling?

A

No, it is always nonstatistical

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15
Q

What is random sampling?

A

The use of random numbers (e.g. as generated by a computer or taken from a table) to accumulate a sample

Can be done with replacement (putting back an item in the population after selecting it) or without replacement
-without replacement is more common

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16
Q

What is systematic sampling?

A

Collecting a sample with a definite interval between each item selected (e.g. selecting every 7th item from a random starting point)

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17
Q

How is the interval determined for systematic sampling?

A

There is usually a uniform interval, calculated as (population size) / (sample size)

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18
Q

What is stratified sampling?

A

Sampling which first breaks apart the population into various strata (or clusters) and then treats each stratum separately

E.g. dividing accounts into (1) less than $1000, (2) between $1000 and $3000, and (3) greater than $3000, then treating them differently

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19
Q

What is the mean-per-unit (MPU) method?

A

A method which takes the mean of a sample and multiplies it by the total population to project the total value of the population

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20
Q

How does the MPU method benefit from stratified sampling?

A

By breaking up a population into homogeneous strata, the auditor can get a sample that is sure to adequately represent the range of values in the population – and thus the mean of the sample will better reflect the mean of the population

Stratified MPU is therefore more efficient

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21
Q

What is block sampling?

A

Sampling which takes a particular “block” of the population (e.g. all invoices from March, or check numbers 250-299)

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22
Q

When is it good or bad to use block sampling?

A

Bad for statistical sampling purposes

Good when trying to measure the effect of some control change, looking at the block of data around that date

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23
Q

Does sampling apply to risk assessment procedures done on internal control?

A

No

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24
Q

What is the tolerable rate of deviations for tests of controls?

A

The maximum rate of deviations in an internal control that would support the auditor’s assessed level of control risk
-if the error rate is higher, then the assessed level of control risk increases too

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25
What is allowable risk for tests of controls?
Sampling risk is the risk of assessing control risk to be too low, so allowable risk is whatever sampling risk the auditor allows Allowable risk is inversely related to the desired degree of assurance which the auditor wants from the sample -- if he wants a high degree of assurance, he should allow less sampling risk
26
What is allowable risk for substantive tests?
The risk, allowed by the auditor, of incorrect acceptance
27
What is the tolerable misstatement for substantive tests?
The maximum amount an account balance can be misstated -- above which, when combined with possible misstatements from other accounts, there would be a material misstatement for the financials as a whole
28
What is the main difference between statistical and nonstatistical sampling?
Statistical sampling allows uncertainty to be quantified (i.e. the measurement of sampling risk) Risks are included in nonstatistical sampling only as professional judgments, not strict numbers
29
Can nonstatistical sampling provide appropriate and sufficient audit evidence?
Despite that it cannot quantify sampling risk, yes
30
What is the primary reason to choose statistical or nonstatistical sampling?
Costs vs. benefits Statistical sampling takes more time to design and implement
31
What are some different methods for doing attribute sampling?
(1) Sequential sampling (2) Attribute estimation method (3) Acceptance sampling method (4) Discovery sampling method
32
What is sequential sampling?
A methodical procedure where each step depends on the previous one
33
What is the attribute estimation method?
A method where a sample is selected and error rate is extrapolated to the whole population
34
What is the acceptance sampling method?
A particular kind of attribute estimation method Involves a table which takes the population size, sample size, and number of sample errors to determine a given % confidence that the population error rate does not exceed a particular %
35
What is the discovery sampling method?
A particular kind of acceptance sampling method Determines how large a sample needs to be in order to have a % confidence that, if the population error rate is at least X%, the sample will have an error -Then, if there is no error, the auditor can conclude a maximum error rate of X%
36
When is discovery sampling typically used?
When the auditor expects a very low error rate, and when there is some special problem (e.g. possible forgery)
37
What two factors determine the tolerable rate of deviation?
The expected level of control risk and the degree of assurance desired
38
How is the tolerable rate related to the sample size?
Inversely -- a higher tolerable rate permits a sample to be smaller
39
What is the confidence level?
The level of sampling risk the auditor is willing to accept Also called the reliability level
40
How is detection risk related to the confidence/reliability level?
They must add up to 1 (e.g. DR of 20% would imply a confidence level of 80%) This is because DR is the risk of inferring that a balance is correct when it isn't, while the confidence level is the likelihood of correctly inferring that a balance is correct
41
Does sampling apply to all tests of controls?
No, there are some for which it does not apply, e.g. tests of automated application controls and tests of control for segregation of duties
42
How does an increase in population size affect the sample size?
Only slightly increases it -- the two are not directly or mathematically related
43
How does a decrease in the sample size affect the risk of assessing control risk too low?
It increases the risk -- if the sample size is smaller, there is a greater chance that errors will go unnoticed
44
If an item in a sample cannot be examined for deviation, how should it be treated?
It should be counted as a deviation An item cannot be examined usually because its documentation is missing. For items that were (properly) voided, they can be replaced by other items from the population.
45
What should the auditor do if sample results give evidence for a higher control risk level than predicted?
He can either (1) test other relevant internal controls to possibly keep the assessed level of control risk low enough, or (2) increase the assessed level of control risk and modify the planned substantive tests The goal is to keep overall detection risk down
46
What is the main characteristic of substantive tests?
The auditor primarily analyzes actual dollar amounts
47
What is the traditional method of carrying out substantive tests of details?
Variable sampling
48
What is another name for the mean-per-unit (MPU) approach in variables sampling?
Simple extension
49
Does the MPU approach require the auditor to know accounts' book values?
No, he only needs to know the sample's audited values in order to estimate the total value of the population
50
What is difference estimation?
This involves taking the difference between book value and audited value for a sample, and then multiplying the avg. difference by the whole population to determine the total difference This difference is then compared to an amount of acceptable difference
51
What is the ratio method?
This involves taking the ratio of audited value to book value for a sample size, and then multiplying that ratio times the total book value of the population to get the total audited value
52
How does the confidence level for substantive tests relate to the assessed level of control risk?
Inversely -- if control risk is assessed as low, then controls are judged as high, so the confidence level would be high This is a general confidence level, though -- the specific confidence level for specific substantive tests can vary from the general level
53
What is one formula for computing an appropriate sample size for substantive testing?
n = (c^2 x s^2 x N^2) / A^2 ``` n = sample size c = confidence coefficient s = standard deviation N = population size A = population allowance for sampling error ```
54
What is a second formula for computing an appropriate sample size for substantive testing?
n = (c^2 x s^2) / a^2 ``` n = sample size c = confidence coefficient s = standard deviation a = allowance for sampling error per item ``` This is mathematically equivalent to the first formula, since a = A / N
55
What is the confidence coefficient (c)?
The number of standard deviations which corresponds to the selected confidence level E.g. the number of standard deviations corresponding to a 90% confidence rating is 1.64
56
What is the population allowance for sampling error (A)?
The amount of tolerable misstatement in the population, minus the expected amount of misstatement
57
What is the allowance for sampling error per item (a)?
The total population allowance for sampling error (A) divided by the number of items in the population
58
What is important to know about the sample size formulas?
They often will need to be rearranged to solve for other factors besides sample size (n)
59
If A = $50,000, N = 4,000, c = 1.64 (for 90% confidence), and s = $30, the formula would yield n = 15.49, which should be rounded up to 16. What does this information mean?
If the auditor wants to have 90% confidence that a sample selected from a population of 4,000 accounts with $30 standard deviation will have an (estimated) total value within $50,000 of the actual value, then he should choose a sample of 16. In other words, for a population of 4,000 accounts with a standard deviation of $30, 90% of the possible 16-account samples would have an estimated total value within $50,000 of the actual value.
60
What is probability-proportional-to-size (PPS) sampling?
Sampling which gives a weight to different items in a population depending on their size For instance, in accounts receivable, the population might be broken down into dollars (rather than accounts), with the different dollars being randomly selected. This would give larger accounts a greater chance of being selected.
61
What is another name for probability-proportional-to-size (PPS) sampling?
Monetary unit sampling (MUS)
62
Is probability-proportional-to-size (PPS) sampling variable sampling or attribute sampling?
It is a kind of variable sampling, but it uses elements of attribute sampling, even though it is employed for substantive testing (rather than tests of control)
63
What are two unique characteristics of probability-proportional-to-size (PPS) sampling?
(1) The population is automatically stratified by dollars (or whatever unit the items are composed of) (2) Because items with larger dollar amounts have a greater chance of being selected, overstatements are more likely to be found than understatements Thus PPS is best designed for discovering overstatements
64
For what kind of accounts would PPS sampling be inappropriate?
Liability accounts, since the risk for those accounts is understatement
65
What are some disadvantages of PPS sampling?
(1) Special attention must be given to zero and negative items in the population (usually segregated and treated separately) (2) If the expected misstatement is high, then the sample size will need to be larger than otherwise needed (in order to gather more total accounts)
66
In PPS sampling, how is a confidence factor for overstatement errors usually determined?
Once the auditor has an expected number of overstatement errors and a risk of incorrect acceptance, he can use a table to get the confidence factor
67
In PPS sampling, how are items randomly selected in a population?
Through fixed interval sampling selection: once the sampling interval is determined, a random number less than that interval is the starting point, and accounts are selected for the sample from there
68
How is the sampling interval calculated for PPS sampling?
Sampling interval = (tolerable misstatement) / (reliability factor for overstatement errors)
69
What are two different ways to do a fixed-interval sampling selection?
(1) From random starting point, add first account to have new cumulative amount, and keep adding accounts. Every time the addition of an account causes the cumulative amount to surpass an interval or its multiples (e.g. if the interval is $20k, then $40k, $60k, $80k would be multiples), that account is included in the sample. (2) From random starting point, simply add the fixed interval to get a new cumulative amount (e.g. add 20k to a random start of 4,932), and the account that corresponds to the new cumulative amount (e.g. the account with the 24,392nd dollar) is included in the sample.
70
For PPS sampling, what is the distinction between top stratum and lower stratum items?
Top stratum items are accounts in a population greater than the sampling interval. They have a 100% chance of being selected because of their size. Lower stratum items are less than the interval size and therefore have <100% chance of being selected
71
How are top stratum and lower stratum items usually treated differently?
Since all top stratum items are always selected, there is no need to project their misstatements to the rest of the population. Only lower stratum misstatements are projected. This affects the calculation for projected misstatements (and the incremental allowance) in the formula for the upper limit for misstatements.
72
What is usually the appropriate estimate for a number of overstatement errors in PPS sampling?
Zero, since PPS sampling is most appropriate when no errors are expected in the first place
73
What is the risk of incorrect acceptance for PPS sampling?
The risk that an account is accepted as correct when it is actually materially overstated
74
How is the appropriate sample size calculated for PPS sampling?
Sample size = (population size) / (sampling interval)
75
How is the expected error rate calculated for PPS sampling?
Expected error rate = (expected misstatements) / (population size)
76
In PPS sampling, what is the upper limit for misstatements?
Since PPS sampling involves determining the misstatement in a sample and projecting it to the population, there will be sampling risk (risk that the sample doesn't adequately represent the population) Thus, the upper limit for misstatements is the maximum overstatement that would exist in the population given (1) the sample misstatements and (2) the specified level of sampling risk
77
In PPS sampling, what is the formula to determine the upper limit for misstatements?
Basic precision + Projected misstatements + Incremental allowance for sampling error = Upper limit for misstatements
78
What is basic precision?
The uncertainty involved in testing only a sample rather than the whole population, i.e. the sampling risk
79
In PPS sampling, how does one determine basic precision?
Basic precision = (reliability factor) x (sampling interval)
80
What is the upper limit for misstatements if no misstatements are found in the sample?
It is only the basic precision, as the other two variables would be zero If samples are found in the population, the other two variables have to be calculated, since they deal with the nature of the misstatements in the sample
81
For PPS sampling, what is the tainting percentage?
If you take the difference between a sample item's recorded value and book value, and divide it by the book value, you get the % error, which is the tainting %
82
In PPS sampling, how does one determine projected misstatements for lower stratum items?
The tainting % is obtained for all lower-stratum items Projected misstatement for lower stratum items = tainting % x sampling interval
83
In PPS sampling, how does one determine total projected misstatements (for both lower stratum and top stratum items)?
Since all top stratum items are by definition included in the sample, there is no need to project anything for them. Total projected misstatements = (top stratum misstatements) + (projected misstatement for lower stratum items)
84
In PPS sampling, what is the incremental allowance for projected misstatement?
An increase of the upper limit for misstatements depending on the statistical properties of the misstatements found in the sample This increase is beyond the projection of the tainting % to the rest of the population, since it also takes into account the confidence level
85
In PPS sampling, to determine the incremental allowance for projected misstatements, what is step 1?
For all lower stratum sample items, the projected errors are ranked from highest to lowest according to tainting %
86
In PPS sampling, to determine the incremental allowance for projected misstatements, what is step 2?
The incremental confidence factor (CF) for this error must be found Given the number of overstatement errors and a risk of incorrect acceptance, CFs can be found on a table. The INCREMENTAL CF is the difference between two CFs for a given risk %, minus 1.
87
What is an example of calculating the incremental confidence factor?
The CF for 0 overstatement errors at 15% risk is 1.90, while it is 3.38 for 1 overstatement error. Therefore the incremental CF for the first error would be 0.48 (3.38 - 1.90 - 1). The incremental CF for the second error would be 0.34, since the CF for 2 errors is 4.72. (4.72 - 3.38 - 1 = 0.34)
88
In PPS sampling, to determine the incremental allowance for projected misstatements, what is step 3?
Multiply the projected error with the highest taint % by the incremental CF for the first error, then multiply the projected error with the second-highest taint % by the incremental CF for the second error, etc. This will get you the incremental allowance for each projected error
89
In PPS sampling, to determine the incremental allowance for projected misstatements, what is step 4?
Add up the incremental allowances for each individual projected error to get the total incremental allowance for projected misstatements
90
What is a summary of the formula for the upper limit for misstatement?
(1) Basic precision = sampling risk irrespective of misstatements in sample (2) Projected misstatement = projection of lower stratum errors to rest of population (3) Incremental allowance for projected misstatement = further projection of error based on the sample misstatements for a different confidence level Add all these to get upper limit for misstatement
91
In PPS sampling, what does the auditor do once he has calculated the upper limit for misstatements?
He compares it to the previously estimated tolerable error If the upper limit < est. tolerable error, then, for that given risk of incorrect acceptance, the population is not misstated by too much
92
What must the auditor do whenever performing some sampling procedure?
Document all the details of the sampling procedure

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