In the wake of the Enron scandal in 2002 two public accounting firms, Oscar
Anderson (OA) and Trice-Milkhouse-Loopers (TML), merged (forming OATML)
and are reviewing their methods for detecting management fraud during audits. The
two firms had each developed their own set of questions that auditors could use in
assessing management fraud.
To avoid a repeat of the problems faced by Enron’s auditors, OATML wants to
develop an automated decision tool to assist auditors in predicting whether or not their
clients are engaged in fraudulent management practices. This tool would basically ask
an auditor all the OA or TML fraud detection questions and then automatically render
a decision about whether or not the client company is engaging in fraudulent
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activities. The decision problem OATML faces is really two-fold: 1) Which of the
two sets of fraud detection questions are best at detecting fraud? and, 2) What’s the
best way to translate the answers to these questions into a prediction or classification
about management fraud?
To assist in answering these questions, the company has compiled an Excel
spreadsheet (the file Fraud.xlsm accompanying this book) that contains both the OA
and TML fraud detection questions and answers to both sets of questions based on
382 audits previously conducted by the two companies (see sheets OA and TML,
respectively). (Note: for all data 1=yes, 0=no.) For each audit, the last variable in the
spreadsheet indicates whether or not the respective companies were engaged in
fraudulent activities (i.e., 77 audits uncovered fraudulent activities, 305 did not).
You have been asked to perform the following analysis and provide a
recommendation as to what combination of fraud questions OATML should adopt.
1. For the OA fraud questions, create a correlation matrix for all the variables. Do
any of the correlations pose a concern?
2. Using the 8 questions that correlate most strongly with the dependent fraud
variable, partition the OA data with oversampling to create a training and
validation data sets with a 50% success rate in the training data. (Use the default
seed of 12345.)
3. Use each of Analytic Solver Data Mining’s classification techniques to create
classifiers for the partitioned OA dataset. Summarize the classification accuracy
of each technique on the training and validation sets. Interpret these results and
indicate which technique you would recommend OATML use.
4. For the TML fraud questions, create a correlation matrix for all the variables. Do
any of the correlations pose a concern?
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5. Using the 8 questions that correlate most strongly with the dependent fraud
variable, partition the TML data with oversampling to create training and
validation data sets with a 50% success rate in the training data. (Use the default
seed of 12345.)
6. Use each of Analytic Solver Data Mining’s classification techniques to create
classifiers for the partitioned TML dataset. Summarize the classification accuracy
of each technique on the training and validation sets. Interpret these results and
indicate which technique you would recommend OATML use.
7. Suppose OATML wants to use both fraud detection instruments and combine their
individual results to create a composite prediction. Let LR1 represent the logistic
regression probability estimate for a given company using the OA fraud detection
instrument and LR2 represent the same company’s logistic regression probability
estimate using the TML instrument. The composite score for the company might
then be defined as C = w1LR1 + (1 – w1)LR2 where 0 ≤ w1 ≤ 1. A decision rule
could then be created where we classify the company as non-fraudulent if C is less
than or equal to some cut-off value, and is otherwise considered fraudulent. Use
Solver’s evolutionary optimizer to find the optimal value of w1 and the cut-off
value that minimizes the number of classification errors for the training data.
What do you obtain for w1 and the cut-off value? Summarize the accuracy of this
technique for the training and validation data sets. How do these results compare
with the logistic regression results in questions 3 and 6?
8. What other techniques can you think for combining OA’s and TML’s fraud
detection questionnaires that might be beneficial to OATML?