Consider a person who is accused of cheating on a lottery. A prosecutor may point out that there was only a 1 in 10,000,000 chance of the person winning, so they must have cheated. This may neglect the fact that 20,000,000 tickets were sold and someone had to win.
False Positives
As another example, consider a crime that is investigated by scanning a database of 10,000,000 people. A match is found to a suspect and at trial the prosecutor may state there was only a 2% false positive rate. They fail to mention that this is extremely significant whereby a total of 200,000 false positives would be generated by scanning all 10,000,000 entries.Number of False Positives = Population Size × False Positive Rate
Number of False Positives = 10,000,000 × 0.02
Number of False Positives = 200,000 false positives
Number of False Positives = 10,000,000 × 0.02
Number of False Positives = 200,000 false positives
Significance
The Prosecutor's Fallacy is not specific to law. It has implications for scientific analysis, business analysis, problem solving and decision making.| Overview: Prosecutors Fallacy | ||
Type | Statistical Fallacy | |
Definition | An invalid interpretation of a valid statistic. | |
Common Cause | Using a specific probability while ignoring a more general probability.Neglecting the importance of margin of error and sample size.Pointing out that the sequence of events that make someone innocent have a low probability without considering that the sequence of events that make someone guilty are equally improbable. | |
Related Concepts | Base Rate FallacyStatistical FallaciesCognitive Biases | |
