| Define Attributes Sampling.
**Sampling applications occur in either one of two contexts** | Sampling for purposes of deciding whether internal controls are working as designed (tests of controls). |
| Define Variable Sampling.
**Sampling applications occur in either one of two contexts** | Sampling for purposes of deciding whether account balances (such as inventory or receivables) are fairly stated (substantive tests of details). |
| FYI: (Recall the definition of audit risk )—The probability that the auditor fails to modify the opinion on financial statements containing a material misstatement. Auditors may use the following model to evaluate the risk components explicitly | AR = RMM * AP * TD, where
AR = audit risk;
RMM = risk of material misstatement, consisting of the combined assessments of inherent risk and control risk;
AP = risk that analytical procedures performed for substantive purposes will not detect a material misstatement that occurred; and
TD = risk that tests of details will fail to detect a material misstatement that was not otherwise detected. |
| Sample Risk:
What is a Type 1 Error (False Rejection)? | Type 1 errors relate to Efficiency—
The auditor will probably achieve the appropriate conclusions, although not in the most efficient manner (perhaps taking more than one sample, maybe at the urging of the client who has faith in the effectiveness of the internal control or the fairness of the financial statement element).
***
1. Tests of controls => the risk of under-reliance on internal controls (also known as risk of assessing control risk too high).
2. Substantive testing => the risk of incorrect rejection. |
| Sample Risk:
What is a Type 2 Errors (False Acceptance)? | Type 2 errors relate to Effectiveness—
The auditor may have failed to meet the overall objective, which is to limit audit risk to an acceptably low level. (The client will have no incentive to argue about this conclusion, so the auditors will not have any reason to take a second look.)
***
1. Tests of controls => the risk of overreliance on internal controls (also known as the risk of assessing control risk too low).
2. Substantive testing => the risk of incorrect acceptance. |
| FYI:
By definition, audit risk consists of the so-called Type 2 error,, whereas sampling risk consists of both the Type 1 error and the Type 2 error. | FYI:
Statistical Sampling relates to the Sufficiency (Quantity) of the evidence—The determination of the sample size in a statistical sampling application establishes how much evidence is required. |
| Define Nonstatistical Sampling.
—Also called judgmental sampling | Refers to any other mistakes by the auditor (i.e., other than sampling risk), not a direct consequence of using a sampling approach:
1. Inappropriate auditing procedures.
2. Failure to correctly identify “errors” or amounts sampled, misinterpreting the results, etc. |
| Define Sampling Risk | Refers to the possibility that a sample is not truly representative of the population of interest. In other words, it is the chance that the auditor reaches an erroneous conclusion as a result of sampling instead of examining the entire population. |
| Define Nonsampling Risk | Refers to any 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. |
| What are the two Statistical Sampling approaches? | a. Random number—Each transaction has the same probability of being selected (the best approach).
b. Systematic—For example, selecting every 100th item |
| What are the two Judgemental (Non-Statistical Sampling) approaches?
**Not appropriate for Attributes Sampling** | a. Block—A group of contiguous items (e.g., the sales transactions for the entire month of June)
b. Haphazard—Arbitrary selection, with no conscious biases. Subconscious biases may exist without the auditor's awareness, however. |
| What are the '3' Key Factors in Attribute Sampling?
**Also applies to Variables Sampling but Population Size is explicitly consider** | 1. Type II Error - Over-Reliance <Confidence> (Indirect)
2. Expected Deviation Error <Population> (Direct)
3. Tolerable Deviation Error <Precision> (Indirect)
***can choose to use***
4. Type I Error - Under-Reliance (Indirect)
5. Population Size (Direct) |
| Define Stratification. | The auditor may reduce the overall variability within a population by classifying similar items into sub-populations (within each group, the variability may be much smaller); the resulting aggregate sample size may be smaller as a result of reducing the combined effects of variability. |
| FYI:
Difference Estimation | **This approach involves identifying the dollar differences between the sample's audit values and applicable book values.**
Sample size—As previously described. Note that we usually need at least 30 differences between audit and book values in our sample when using “difference estimation.”
1. Estimate the population's implied audit value.
Calculate the average difference between the audit value (av) and book value (bv) for items in the sample:
d = (av – bv)/n
2. Extend that average difference to the population by multiplying it by the number of items in the population:
D = d * N
3. Calculate the implied population audit value (the “point estimate”) by adding the calculated difference for the population to the population's book value:
AV = BV + D, where D can be either positive or negative |
| FYI:
Ratio Estimation | ** This approach involves identifying the ratio of the audit values and book values for the sampled items. **
Note that this approach is useful when the dollar amount of the differences between the audit and the book values is expected to be proportional to the book values.
1. Calculate the ratio for the sample, where the ratio has the sample's audit value in the numerator and the sample's book value in the denominator:
R = av/bv
2. Estimate the population's audit value (a point estimate) by multiplying the population's book value by that “ratio:”
AV = R * BV |
| FYI:
Means-Per-Unit (MPU) | ** Useful when difference or ratio estimation cannot be used—for example, for inventory when perpetual records do not exist (i.e., there is no “book” value for each individual sample item).**
Estimate the population's implied audit value.
1. Calculate the average audit value for items in the sample:
MPU = av/n
2. Multiply that average (MPU) times the number of items in the population:
AV = MPU * N |
| FYI:
Probability-Proportional-to-Size (PPS) Sampling
** PPS sampling defines the “sampling unit” to be an individual dollar associated with the financial statement element involved. (Variations of this approach are referred to as dollar-unit sampling or monetary-unit sampling.) For example, suppose accounts receivable consists of 7500 customer accounts having a total balance of $3,000,000. The population is viewed as consisting of 3,000,000 individual items (dollars) rather than 7500 accounts. However, when an individual dollar is selected as part of the sample, it attaches to the related account or logical record, which is then examined in its entirety. Accordingly, the probability that an individual account will be selected is “proportional” to that individual account's balance relative to the total for all accounts. ** | ** The sampling unit is an individual dollar (when a given dollar is selected for the sample, it attaches to the related account or item which is then examined in its entirety); note that individually material items are automatically selected.**
1. PPS is useful if there are relatively few differences between audit and book values; otherwise, the sample size can become very large and the PPS application then becomes inefficient.
2. The main advantage is efficiency—it can achieve the maximum possible stratification (which then minimizes the effects of variability on sample size).
3. The main disadvantage is that PPS does not work very well in auditing negative balances (understatements) or zero (unrecorded) balances. Applies best to audit concerns involving overstatements (e.g., accounts receivable or inventory when few misstatements are expected). |
| FYI:
PPS Sampling calculation | In PPS sampling, sample size is calculated as: "Reliability factor" × Book value/Tolerable misstatement (net) |
| PPS Sampling:
Projected Misstatements / Tainted Calculation - when to use: | (i) For accounts having a book value greater than or equal to the sample interval, the actual misstatement should be used to determine the “projected misstatement.”
(ii) For accounts having book values less than the sample interval, the auditor would have to apply the “tainting percentage” to the sample interval from which that account was selected. Suppose that the sample interval is $2,000 and that an account having a book value of $250 has an audit value of $200. The “tainting” is $50/$250 = .20; and, since the account's book value is less than the sample interval, the projected misstatement for this account would be .20 × $2,000 = $400.
(iii) When there are no misstatements in the sample, the projected misstatement is zero. |
