End of Chapter Questions, Exercises, and Problems for by

1. 
   Prepare a PowerPoint presentation on the facts and circumstances, investor funds, and the consolidated financial statements in the report. These sections refer to pages 7 to 35 in the report.
   
2. 
   Prepare a PowerPoint presentation on the forensic accounting analysis, and the findings and conclusions in the report. These sections are in pages 36 to 54 in the report.
   

1. 
   Can you change the strata boundaries in the data profile, or do you have to use the strata shown in Figure 4.1 in every data analysis project?
   
2. 
   Why is it inefficient to have a high proportion of low-value invoices?
   
3. 
   Can Excel 2007 be used to calculate the inputs for a histogram?
   
4. 
   Should the periodic graph always have monthly totals and also always have just 12 monthly totals?
   
5. 
   What is an Access union query?
   

6. 
   Descriptive _____ are graphical and numerical measures that are used to summarize and interpret some of the properties of a data table.
   
7. 
   The periodic graph becomes more useful after a three or four year history has been built up with the data (true/false).
   
8. 
   In Access all formatting of the output must be done in design view before the query is run (true/false).
   
9. 
   A union query is prepared in Access in QSL view (true/false).
   
10. 
    The two main Excel functions that are used for the data profile are ____ and _____ .
    

11. 
    For each stratum the data profile shows the _____________.
    
    1. 
       Count and the average and the percentage of the maximum
       
    2. 
       Count and the sum and the percentage of the totals
       
    3. 
       Count and the percentage of the total
       
    4. 
       Sum and the percentage of the total
       
12. 
    The data profile helps the investigator or auditor assess whether the file is ______ .
    
    1. 
       Complex
       
    2. 
       Open
       
    3. 
       Obsolete
       
    4. 
       Complete
       
13. 
    The data profile is also useful for finding _____ amounts in data sets that should not have _____ numbers.
    
    1. 
       Negative
       
    2. 
       Rational
       
    3. 
       Natural
       
    4. 
       Positive
       
14. 
    On the periodic graph the _____ is/are on the _____ .
    
    1. 
       Histogram, first page
       
    2. 
       Access query, data profile
       
    3. 
       Time period, x-axis
       
    4. 
       Dollars, x-axis
       
15. 
    The data profile calculations can be done more efficiently in Access using a _____ query.
    
    1. 
       Abbreviation
       
    2. 
       Communion
       
    3. 
       Reunion
       
    4. 
       Union
       

1. 
   Open the PageSoftware.xlsx file using the password Forensic. Remove the password protection. Save the file as PageSoftware.xlsx (no name change).
   
2. 
   Create a periodic graph of the monthly totals for the invoices. Use the PeriodicGraph.xlsx template.
   
3. 
   Save the PeriodicGraph.xlsx template as Case_4_16.xlsx. Delete the extra tab created for the periodic graph totals and the extra field (Month) created in the PageSoftware.xlsx file. Save the file which will now appear unchanged.
   

1. 
   Create the data profile for the data using the NigriniCycle.xlsx template. Use the default strata boundaries.
   
2. 
   What insights do you get from the data profile in (a) above?
   
3. 
   Delete all the tabs in the Excel file related to the digit graphs and save the file as Case_4_17.xlsx.
   

1. 
   What are the three guidelines for determining whether a data set should conform to Benford's Law?
   
2. 
   How large should a data set be before we would consider running Benford's Law tests?
   
3. 
   Why do we analyze positive and negative numbers separately?
   
4. 
   Why is the first-two digit test preferred to the first digit test?
   
5. 
   What are the main steps in running the first-two digits test in Access?
   

6. 
   Frank Benford was a _____ (physicist/numismatist) who published the seminal paper on the topic of digit frequencies.
   
7. 
   The expected proportion for the first digit 9 is less than the expected proportion for the second digit 9 (true/false).
   
8. 
   Benford's Law is scale invariant under multiplication. This means that if all the numbers in a Benford Set are multiplied by a nonzero constant then the new data set will also be a Benford Set (true/false).
   
9. 
   Evidence supporting rounding-up behavior by management in financial statement numbers is an excess of second digit 0s and a shortage of second digit 9s (true/false).
   
10. 
    An overall consideration for conformity to Benford's Law is that the data has more large numbers than small numbers (true/false)
    
11. 
    There are problems with graphing a large data set in Excel (true/false).
    

1. 
   Benford begins his paper by noting that the first few pages of a book of ____ ____ show more wear than the last few pages,
   

f.Differential calculus

g.Telephone numbers

h.Common logarithms

10.There are ____ possible first digits.

a.Nine

c.Ninety

11.Benford's paper was published in ____ .

a.1638

b.1738

d.1938

a.Versace

b.Fibonacci

c.Hitachi

d.Prime number

13.The formulas for the expected Benford's Law proportions use which mathematical function?

a.Square roots

b.Absolute values

c.Quadratics

d.Logarithms

14.Benford's Law gives the _____ frequencies of the digits in tabulated data.

a.Abnormal

b.Expected

c.Excessive

d.Atypical

15.___, ___, and _____ show(s) that there are practical uses of Benford's Law.

a.Auditing, forensic analytics research, legal requirements

b.Forensic analytics research, legal requirements, corporate governance

c.Tax evasion, auditing, forensic analytics research

d.Statistics, mathematics, econometrics

1. 
   Run the first-two digits test in Access.
   
2. 
   Graph the results in Excel 2007 using the NigriniCycle.xlsx template.
   
3. 
   Identify the three largest spikes on the graph.
   
4. 
   Delete columns P to AJ in the Tables tab and all the tabs except for the Tables and First-Two tabs. Your spreadsheet will therefore only have two worksheets.
   
5. 
   Save your Excel file as Case_5_19.xlsx.
   

1. 
   Import the data into Access. Excel cannot be used because the .csv file has 12,146,637 rows.
   
2. 
   Run the first-two digits test on all the positive values (i.e., >0).
   
3. 
   Graph the results in Excel 2007 using the NigriniCycle.xlsx template.
   
4. 
   Identify the three largest spikes on the graph.
   
5. 
   Did you expect shopping data to conform to Benford's Law?
   
6. 
   Save your Excel file as Case_5_20.xlsx. Save your Access file as ShopperData.accdb.
   

1. 
   Explain how changes in the number of records, N, affects the calculated Z-score?
   
2. 
   Does Excel have a function that performs the chi-square test? If so, what is the function and what is the critical value that we'd be looking for in a conformity test?
   
3. 
   Why does the cumulative density function in Figure 6.1 have the steepest slope for the lower digits (10-19) and the smallest slope for the higher digits (90-99)?
   
4. 
   Will a graph of the ordered (sorted) logs have a positive slope on every segment of the line as shown in Figure 6.5?
   
5. 
   Why does the difference between the logs in equation 6.12 need to be an integer value?
   

6. 
   The result of the Z-statistic test for the first-two digits would be 90 calculated Z-statistics, one for each digit combination (10, 11, …,90) (true/false).
   
7. 
   The critical value for the Kolmogorov-Smirnoff test does not include N, the number of records (true/false).
   
8. 
   All things being equal, a low Mean Absolute Deviation indicates a closer fit to Benford's Law (true/false).
   
9. 
   The log of a negative number is ____ (zero/undefined/negative/rare).
   
10. 
    The mantissa arc test is based on plotting the mantissas on the unit _____ (radius/number line/circle).
    

1. 
   The fractional part of the log of a number is called the _____ .
   

f.Suffix

h.Z-statistic

16.The Z-statistic is used to test whether the actual proportion for a specific first-two digit combination differs ______ from the expectation of Benford's Law.

a.Materially

b.Convincingly

c.Noticeably

d.Significantly

17.The chi-square test ________ .

a.Has to date only been used in medical research

b.Is a well-known statistical test

c.Requires specialized statistical software

d.Was invented by Hill in 1995

18.The Kolmogorov-Smirnoff test is based on the ________ .

a.Cumulative intensity junction

b.Cumulative propensity function

c.Cumulative intensity function

d.Cumulative density function

19.The formula for the Mean Absolute Deviation (MAD) _____ .

a.Uses, N, the number of records.

b.Has a square root sign in the denominator

c.Uses the absolute values of the differences between the actual and expected proportions

d.Plots the mantissas on the unit circle

1. 
   Run the first digits test in Access.
   
2. 
   Copy the actual counts from Access to cells B3:B11. Create a first digit graph that has the same format as the first-two digits graph.
   
3. 
   What is the MAD for the first digits? What is the MAD for the first-two digits? What is your conformity conclusion using the first-two digits MAD and Table 6.1?
   
4. 
   Does the data conform to Benford's Law using the chi-square test for the first digits, and a 0.05 significance level?
   
5. 
   Does the data conform to Benford's Law using the chi-square test for the first-two digits, and a 0.05 significance level?
   
6. 
   Does the data conform to Benford's Law using the Kolmogorov-Smirnoff test for the first-two digits, and a 0.05 significance level?
   
7. 
   Save the file as Case_6_16.xlsx.
   

1. 
   What is the MAD for the first-two digits? What is your conformity conclusion using the first-two digits MAD and Table 6.1?
   
2. 
   Does the data conform to Benford's Law using the chi-square test for the first-two digits, and a 0.05 significance level?
   
3. 
   Does the data conform to Benford's Law using the Kolmogorov-Smirnoff test for the first-two digits, and a 0.05 significance level?
   
4. 
   Save the file as Case_6_17.xlsx.
   

1. 
   What is a continuous distribution?
   
2. 
   Why would the mean of a uniform distribution have no effect on the differences between the ordered records?
   
3. 
   Assume that in the Page Software data set all 79 correct amounts of $50 were changed to 79 amounts of $50 million. Would the first-two digits graph be unaffected? Explain. Would the periodic graph be affected? Explain.
   
4. 
   Explain the ʃ, ||, and ln symbols in equation 7.3
   
5. 
   What is the difference between fraud prevention and fraud detection? Are the tests in this chapter more closely related to prevention or detection?
   

6. 
   When the values of a data set are placed in ascending order the result is called the ____ (align/order/position) statistics of the data.
   
7. 
   It would be difficult to run the second-order test in Access (true/false).
   
8. 
   In a data set of journal entries where the debits are shown as positive values and the credits are shown as negative values, the expected sum is ______ ($zero, equal to the number of records, equal to the range of the data).
   
9. 
   The first-two digits are grouped into the ____ (Major and minor, Prime and minor, upper and lower bounds) first-two digits.
   
10. 
    All negative numbers (including $zero) should be deleted from the data set before the second-order test is run (true/false).
    

1. 
   The second-order test is based on the ______ the elements (amounts or values) of ordered data.
   

f.Absolute values of

g.Logarithms of

h.Differences between

20.The expected result of the second-order test is a data set that is ______ .

a.Continuous

b.Normally distributed

c.Almost Benford

d.Significantly Benford

21.A data set with 1,000 records will have ____ differences between the ordered records.

a.Zero

b.999

d.1,001

a.Sums, counts

b.Counts, sums

c.Sums, mean absolute deviations

d.Mean absolute deviations, sums

23.The summation test looks for excessively ________ in the data.

a.Large gaps

b.Large numbers

c.Small mean absolute deviations

d.Small round numbers

1. 
   Copy the numeric dollar amounts from D1:D38177 in PageSoftware_Invoices.xlsx to D1:D38177 in the Data tab in the NigriniCycle.xlsx template. Close the PageSoftware_Invoices.xlsx file. Save the NigriniCycle.xlsx file as Case_7_16.xlsx. Use the Case_7_16.xlsx file for all the case requirements that follow (including Case 7-17).
   
2. 
   Delete the following tabs: DataProfile, First Digits, Second Digits, First-Two, and Last-Two. In the Data tab clear the contents of the range A2:C26. Copy the formula in E26 to the range E26:E38177. Copy the formula in F26 to the range F26:F38177. Copy the formula in G26 to the range G26:G38177. The formulas in columns E, F, and G will not actually be used for this case. Do not make any changes to columns I, J, K, or L for now.
   
3. 
   Run the second-order test on the PageSoftware data using the template. Show your completed graph and the first ten lines of the supporting table (Q1 to V12 in the Tables tab).
   
4. 
   Does the second-order test show any data anomalies? Explain. Save your file.
   

1. 
   Run the summation test on the Page Software data using the template. Show your completed graph and the first ten lines of the supporting table (X1 to AC12 in the Tables tab).
   
2. 
   Does the summation test show any data anomalies? Explain. Save your file as Case_7_17.xlsx.
   

1. 
   The result of the number duplication test is usually a report sorted by Count descending such as is shown in Figure 8.2. How else might the table be sorted and what would the goal be of a different sort?
   
2. 
   What do we mean by a psychological threshold?
   
3. 
   Do we always run the number duplication test on dollar (or currency) amounts?
   
4. 
   Why is the expected proportion for each possible last-two digit combination equal, when the first-two digits are heavily skewed towards the low digits?
   
5. 
   Do we always run the last-two digit test on dollar (or currency) amounts?
   

6. 
   A separate number duplication test is run on each of the five main strata in the data profile (true/false).
   
7. 
   For accounts payable data the number duplication test should include a comparison of the large positive numbers with the large negative numbers (true/false).
   
8. 
   The last-two digit test is not all that useful for accounts payable data (true/false).
   
9. 
   The last-two digits test is a powerful test for _______ (presented/indented/invented) numbers.
   
10. 
    There are ____ (9, 10, 90, 99, 100, 101) possible last-two digit combinations.
    

1. 
   A candidate for review on the number duplication report would include numbers linked to,
   

f.Large negative spikes on the first-order graph

g.Large positive spikes on the first-order graph

h.Large positive spikes on the periodic graph

24.The main commands in the query to run the number duplication test in Access are,

a.Group By, and Count

b.Group By, and Sum

c.Group By, and Duplicates

d.Pivot Table, and Amount

25.The details in the number duplication report usually include,

a.Blank, Amount, First-two

b.Rank, Count, First-Two

c.Date, Count, Amount, First-two

d.Rank, Count, Amount, First-Two

26._____ numbers do not have a set of last-two digits.

a.Negative

b.Even

c.Whole

27.The expected last-two digit proportion is ________ for each last-two digit combination.

a.0.01

b.0.10

d.It differs depending on whether the digits are low or high digits

1. 
   Run the number duplication test in Excel using Excel's pivot table capabilities.
   
2. 
   Prepare a report with headings and data that follow the format in Figure 8.5.
   
3. 
   Use Excel's filtering capability to limit your results to amounts greater than or equal to $10.00.
   
4. 
   Delete all the unneeded worksheets and data from your file.
   
5. 
   Save the result as Case_8_16.xlsx.
   

1. 
   Run the last-two digits test on the shopper data on the Amount field in the Training table using the cents (the two digits to the right of the decimal point) as the last-two digits. Use two queries as is set out in figures 8.19 and 8.20. Calculate the last-two digits for all the positive numbers (i.e., greater than zero).
   
2. 
   Open the Nigrinicycle.xlsx template and delete all the tabs except for Tables and Last-Two. In the Tables tab delete columns A to AC. Save the file as Case_8_17.xlsx.
   
3. 
   Paste your Access results into Column C in the Excel file. Amend the formula for the actual proportions (Column D). Click on Last-Two to see your graph. Save the file again.
   
4. 
   What anomalies do you see on the last-two digits graph?
   

1. 
   What are descriptive statistics?
   
2. 
   What is the objective of using descriptive statistics in a forensic environment?
   
3. 
   With respect to external audits, do the auditors of public companies have to follow the fraud statement SAS No. 99 issued by the AICPA?
   
4. 
   Why might external auditors be reluctant to use and deploy computer assisted audit techniques (CAATS) in their audits?
   
5. 
   Is it absolutely essential that all of the tests listed in Table 9.1 be run on each and every data set for which there is data for multiple time periods?
   

6. 
   Bolton and Hand state that we can seldom be certain by statistical analysis alone that a fraud has been perpetrated (true/false).
   
7. 
   Missing records might indicate fraud, or processing or internal control issues (true/false).
   
8. 
   The set of descriptive statistics that measures the variability or the spread of the numbers includes the mean and the median (true/false).
   
9. 
   Data that is _____ (positively/negatively) skewed consists of many small amounts and fewer large amounts.
   
10. 
    When using the My Law concept we still use the Mean Absolute Deviation (MAD) to measure conformity (true/false).