Fraud and statistics

Like most power tools, statistics can be dangerous if left in the hands of the ill-trained or inebriated. Unlike rotary saws and industrial angle grinders, when you abuse statistics you don’t damage the tool but you do damage the result.

Fraud statistics

This is a general observation, but I was reminded of it recently when reading KPMG’s interesting Profile a Fraudster 2007 survey. In the survey, the authors analyse data from actual fraud investigations to better understand who commits fraud and under what circumstances. The survey presented the percentage of fraudsters between variables like gender, across age bands, across duration at the company, position within the firm and department.

While this makes interesting reading, it does very little to explain which types of people are most likely to commit fraud. Without knowing the make-up of the populations of fraudsters and honest employees, we cannot tell whether 36% of fraudsters had been with the company for between 2 and 5 years because this is when they are most likely to strike, or whether most employees, honest or dishonest have been at the company for between 2 and 5 years.

Unfortunately univariate

Employees in more senior positions are also more likely to commit fraud. This is expected since those entrusted with power are more able to commit fraud. However, given the analysis performed is univariate (considers variables one at a time) we cannot tell whether seniority in position makes a difference once the effect of the number of years at the firm has been removed.

70% of fraudsters are between the ages of 36 and 55, which probably represents about the distribution of all employees by age band. 85% of perpetrators were male – which does suggest that males are more likely to commit fraud. However, most companies will still employ more males than females. It’s unfortunate but still true that more males will be in position of power such that they can commit fraud. Maybe the representative baseline for comparison is only 60% rather than 50%, but maybe it is 70% or 75%, which tells a different story.

Selection effects and biases

Although there are more examples from this survey, I’ll finish with one last case. 91% of the cases examined in the survey involved more than 1 act of fraud or transaction. Again, this does suggest that fraudsters are likely to continue committing their crimes until discovered, and logical reasoning would also support this.

However, it is also very true that individual acts of fraud would be far more difficult to be picked up and investigated. If they were, it would be that much easier to defend it as a mistake rather than systematic fraud. The 91% figure reflects a significant selection bias, making intepretation of the real risks difficult.

The right answer

The KPMG survey makes interesting reading, and does include valuable information. However, if they had taken their data set and applied better statistical techniques, and applied them more carefully, the results could have been spectacular. In fairness, this would probably have required gathering more data about the honest employees than they had at their immediate disposal, but the results would have been worth it.

A Generalised Linear Model (GLM) could be fitted to estimate a probability of fraud for an individual employee based on their characteristics. It could also help predict points in their career where the risk increases sharply, perhaps providing a targeting opportunity for ethics training, peer review and improved controls.

The questions I’m left pondering are:

  1. Would you hire someone with a high “probability of committing fraud” based on a statistical model?
  2. Would you be allowed to discriminate on this basis?
  3. How might you manage this person differently if you had this additional information?

Published by David Kirk

The opinions expressed on this site are those of the author and other commenters and are not necessarily those of his employer or any other organisation. David Kirk runs Milliman’s actuarial consulting practice in Africa. He is an actuary and is the creator of New Business Margin on Revenue. He specialises in risk and capital management, regulatory change and insurance strategy . He also has extensive experience in embedded value reporting, insurance-related IFRS and share option valuation.

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