Basis for Pattern Detection

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

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

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

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

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

6. Objective 2c Measurement Basis • Transaction counts • Transaction amounts

7. Objective 2d 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

8. Objective 2d 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

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

10. Objective 2d Two histograms obtained • Population and group

11. Objective 2d Compute Cumulative Amount for each

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

13. Objective 2d 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

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

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

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

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

18. Objective 2d - KS Kolmogorov-Smirnov

19. Objective e Auditor’s “Top 10” Metrics • Outliers / Variability • Stratification • Day of Week • Round Numbers • Made Up Numbers • Market basket • Trends • Gaps • Duplicates • Dates

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

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