2. Slide 1 Basis for Pattern Detection Analytical review Isolate the “significant few” Detection of errors Quantified approach Objective 2

3. Slide 2 Understanding the Basis Quantified Approach Population vs. Groups Measuring the Difference Stat 101 – Counts, Totals, Chi Square and K-S The metrics used Objective 2

4. Slide 3 Quantified Approach Based on measureable differences Population vs. Group “Shotgun” technique Objective 2a

5. Slide 4 Detection of Fraud Characteristics Something is different than expected Objective 2a

6. Slide 5 Fraud patterns Common theme – “something is different” Groups Group pattern is different than overall population Objective 2b

7. Slide 6 Measurement Basis Transaction counts Transaction amounts Objective 2c

8. Slide 7 A few words about statistics Detailed knowledge of statistics not necessary Software packages do the “number-crunching” Statistics used only to highlight potential errors/frauds Not used for quantification Objective 2d

9. Slide 8 How is digital analysis done? Comparison of group with population as a whole Can be based on either counts or amounts Difference is measured Groups can then be ranked using a selected measure High difference = possible error/fraud Objective 2d

10. Slide 9 Histograms Attributes tallied and categorized into “bins” Counts or sums of amounts Objective 2d

11. Slide 10 Two histograms obtained Population and group Objective 2d

12. Slide 11 Compute Cumulative Amount for each Objective 2d

13. Slide 12 Are the histograms different? Two statistical measures of difference Chi Squared (counts) K-S (distribution) Both yield a difference metric Objective 2d

14. Slide 13 Chi Squared Classic test on data in a table Answers the question – are the rows/columns different Some limitations on when it can be applied Objective 2d

15. Slide 14 Chi Squared Table of Counts Degrees of Freedom Chi Squared Value P-statistic Computationally intensive Objective 2d

16. Slide 15 Kolmogorov-Smirnov Two Russian mathematicians Comparison of distributions Metric is the “d-statistic” Objective 2d

17. Slide 16 How is K-S test done? Four step process 1.For each cluster element determine percentage 2.Then calculate cumulative percentage 3.Compare the differences in cumulative percentages 4.Identify the largest difference Objective 2d

18. Slide 17 Classification by metrics Stratification Day of week Happens on holiday Round numbers Variability Benford’s Law Trend lines Relationships (market basket) Gaps Duplicates Objective 2e

19. Slide 18 Kolmogorov-Smirnov Objective 2d - KS

20. Slide 19 Auditor’s “Top 10” Metrics 1.Outliers / Variability 2.Stratification 3.Day of Week 4.Round Numbers 5.Made Up Numbers 6.Market basket 7.Trends 8.Gaps 9.Duplicates 10.Dates Objective e

21. Slide 20 Understanding the Basis Quantified Approach Population vs. Groups Measuring the Difference Stat 101 – Counts, Totals, Chi Square and K-S The metrics used Objective 2

22. Slide 21 Objective 2 - Summarized 1.Understand why and how 2.Understand statistical basis for quantifying differences 3.Identify ten general tools and techniques 4.Understand examples done using Excel 5.How pattern detection fits in Next are the metrics …