After you have performed your audit procedures on the set of sampled data you can use Analytics to: - project any misstatements you found to the entire account
- calculate an upper limit on misstatement amount
Even if you found no errors, you still use the evaluation feature to calculate the basic allowance for sampling risk. Note Evaluating errors requires input of some of the values previously
generated by calculating sample size. To use the evaluation feature with the results of a monetary unit sample, you must have drawn the sample using either the fixed interval or the cell selection methods. How evaluation and comparison workWhen you evaluate, Analytics uses a statistical formula to project the misstatements you found in the sample to the entire account, and calculates the Upper Error Limit (upper
misstatement limit). You compare the calculated value to the Materiality that you decided upon earlier when you calculated sample size. Based on the comparison, you decide if monetary data is fairly stated.
| Comparison | Conclusion |
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| Upper Error Limit is less than or equal to Materiality
| The amounts in the sample field as a whole are fairly stated
| | Upper Error Limit is greater than Materiality
| The amounts in the sample field as a whole are materially misstated
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StepsNote Do not include the thousands separator, or the percentage sign, when you specify values. These characters prevent the command from running, or cause errors. Select Sampling > Record/Monetary Unit Sampling > Evaluate Note The menu option is disabled if a table is not open. - On the Main tab, select Monetary.
- Enter the input values to use for evaluating misstatements:
Note The input values are explained in detail below. - On the Output tab:
- In the To panel, select one of the following:
- If you selected File as the output type, do one of the following:
- Enter a file name in the Name text box.
- Click Name and enter the file name, or select an existing file in the Save or Save File As dialog box to overwrite or append
to the file.
If Analytics prefills a file name, you can accept the prefilled name, or change it. You can also specify an absolute or relative file path, or navigate to a different folder, to save or append the file in a location other than the project location. For example: C:\Results\Output.txt or Results\Output.txt.
Note ASCII Text File or Unicode Text file (depending on which edition of
Analytics you are using) is the only option for File Type.
- Click OK.
- If the overwrite prompt appears, select the appropriate option.
The table below provides detailed information about the input values in the Evaluate dialog box. Main tab – input values
| Input values – Evaluate dialog box | Description |
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| Confidence | The same confidence level that you entered when you calculated the sample size. For more information, see Calculating sample size for a monetary unit sample.
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| Interval | The interval value that you used when you drew the sample. Note The interval value that you used might differ from the interval value initially calculated by Analytics.
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Errors (Item amount, Error) | A list of all misstatement errors that you found in the sample. Enter the book value of the amount and the misstatement amount, separated by a comma. Enter overstatements as positive amounts, and understatements as negative amounts. Tip If the list of misstatement errors is long, it may be easier to copy and paste the list from another application. ExampleIf
an amount has a book value of $1,000 and an audit value of $930, enter 1000,70. If an amount has a book value of $1,250 and an audit value of $1,450, enter 1250,-200. Enter each error on a separate line: 1000,70 1250,-200
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The figure below shows an example of input values for evaluating errors in a monetary unit sample. ResultsEvaluating the errors you found in a monetary unit sample produces the following results:
| Result value | Description |
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| Item | The list that you entered of sample amounts with misstatement error.
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| Error | The list that you entered of misstatement amounts.
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| Basic Precision | The basic allowance for sampling risk (18,850.00 in the figure below).
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Most Likely Error (projected misstatement) | The misstatement amount for each error projected to the interval containing the sample amount. Most Likely Error amounts that are not top stratum are listed in descending order. Top stratum misstatement amounts are listed between projected overstatements and projected understatements. The projection calculation is not performed on top stratum misstatement amounts.
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Upper Error Limit (upper misstatement limit) | The Most Likely Error amounts adjusted for sampling risk. The adjustment calculation is not performed on top stratum misstatement amounts, or on projected understatements. Projected understatements are listed as “0.00” so they do not affect the Upper Error Limit.
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| Totals | The Most Likely Error amount, and the Upper Error Limit amount, for the entire population or account balance.
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The figure below shows the results of evaluating errors found in a monetary unit sample.
| In the Item column | Projection calculation | Adjustment calculation |
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| First three amounts are not top stratum
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| | Fourth amount is top stratum
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| | Fifth amount is an understatement
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What the “Upper Error Limit” tells youThe total amount of Upper Error Limit, when compared to the Materiality that you decided upon when you calculated the sample size, tells you: - Whether the amount in the account balance you are examining is fairly stated
- If the amount is fairly stated, what the maximum amount of misstatement is likely to be
ExampleYou evaluate the errors you found in a monetary unit sample and Analytics returns an Upper Error Limit of $28,702.70. This amount is less than the Materiality (tolerable misstatement) of $29,000 that you specified earlier when you calculated the sample size, and specified a confidence level of 95%.
Based on this information, you can make the following statement: There is a 95% probability that the actual misstatement in the account balance does not exceed $28,702.70. If the Upper Error Limit is greater than $29,000, the account balance is probably materially misstated. You need to decide upon further appropriate steps to meet your audit objective. How the Upper Error Limit is calculated for monetary unit samplingThe Upper
Error Limit calculated by Analytics is a compound figure that adjusts for sampling risk – that is, the risk that misstatements in the sampled amounts underrepresent the true total amount of misstatement in the account balance you are examining. Show me more Upper Error Limit is the sum of the following amounts:
| Amount | Explanation |
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| Basic precision | In the absence of any misstatement errors in the sampled amounts, a basic allowance for sampling risk calculated by Analytics using a statistical formula. A basic allowance for sampling risk is required because even if you found no errors in the sampled amounts, you cannot be sure no errors exist in the population as a whole.
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| An adjusted amount for each misstatement error | The result of the following calculation: tainting percentage (misstatement amount/book value of sample amount) * interval amount * incremental allowance for sampling risk - Tainting percentage * interval amount projects the observed amount of misstatement for one sample amount to the interval containing the sample amount.
Analytics calls this projected
misstatement Most Likely Error. The sum of all projected misstatements is the Most Likely Error for the account balance. - Most Likely Error * an incremental allowance for sampling risk is calculated by Analytics using a statistical formula.
This additional adjustment is required because the Most Likely Error may still underestimate the true amount of misstatement in the account balance.
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What is tolerable error in sampling?
“Tolerable error” means the maximum error in a population that the auditor is willing to accept.
What is monetary unit sampling?
Monetary unit sampling (MUS) is a statistical sampling method that is used to determine if the account balances or monetary amounts in a population contain any misstatements.
What is tolerable error in accounting?
Tolerable error is the maximum error in the population that auditors are willing to. accept and still conclude that the audit objective has been achieved. Tolerable error is considered during the planning stage and, for substantive procedures, is related to the auditors' judgment about materiality.
How is tolerable error calculated?
According to Yamane (1967), the sample size is obtained thus:n = N /1+ N (e2)Where:n = Sample sizeN = Actual population = 12,396 e = Tolerable error = 5%N = 12,3961+ [12,396x (0.052)]= 12,3961+ (12,396 x 0.0025)= 12,3961+ 30.99= 387.5 Approximately 388 Sample size (n) = 388 SMES OwnersA simple random sampling technique ...
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