In 1895, An Italian Criminologist Named Cesare Lombroso Prop

1in 1895 An Italian Criminologist Named Cesare Lombroso Proposed Tha

In 1895, an Italian criminologist named Cesare Lombroso proposed that blood pressure could be used as a measure of truthfulness, as he believed that one’s blood pressure increased when not telling the truth. In the 1930s, William Marston added measurements of respiration and perspiration as measures of truthfulness and called his machine the polygraph, or lie-detector. Today, the federal court system will not consider polygraph tests as evidence, but close to half of the state courts permit polygraph test results under certain conditions. In addition, use of the polygraph in screening job applicants has increased since the 1980s. But how well does it work?

A research study conducted by Michael Phillips, Allen Brett, and John Beary tested the polygraph's accuracy by recruiting 1000 participants—500 actual truth-tellers and 500 liars. The study assumed a 50% probability of lying and 50% of telling the truth. The results showed the polygraph made errors: it incorrectly classified 185 truth-tellers as liars and 120 liars as truth-tellers.

The study's findings are summarized in the following table:

Paper For Above instruction

Understanding the effectiveness of polygraph tests is essential in forensic and employment contexts. The given data provide the foundation for analyzing the statistical independence between the polygraph decisions and actual truthfulness, assessing error-induced implications, and discussing the potential for Type I and Type II errors.

Analysis of Statistical Independence

To evaluate whether the polygraph decisions are statistically independent of reality, we examine the conditional probabilities. Two events A and B are independent if and only if P(A|B) = P(A) and P(B|A) = P(B). Here, event A could be "polygraph indicates truth" and B "the individual is actually a truth-teller."

Calculating P(polygraph indicates truth | individual is truth-teller) gives:

P(Truth-indicated | Truth) = 435 / 620 ≈ 0.7016

Similarly, P(polygraph indicates lie | individual is liar) = 120 / 380 ≈ 0.3158

To test independence, we check if the joint probability equals the product of marginal probabilities. For the truth-teller group:

P(Truth-teller and Truth-indicated) = 435 / 1000 = 0.435

The marginal probability of the polygraph indicating truth is:

P(Truth-indicated) = (435 + 185) / 1000 = 0.62

The marginal probability of being a truth-teller is 0.50.

Multiplying P(Truth-teller) and P(Truth-indicated): 0.5 * 0.62 = 0.31

Since 0.435 ≠ 0.31, the events are not independent. The polygraph decision and actual truthfulness are statistically dependent.

Implications for Employment Decisions

When the company relies on polygraph results to decide employment, understanding the probabilities of errors is crucial. Given the data, the probability of a false positive (denying a truthful applicant) is:

P(Denied employment | Truthful applicant) = P(polygraph indicates lie | truth) = 120 / 620 ≈ 0.1935 or 19.35%

This represents the probability that a truthful candidate will be wrongly classified as a liar, leading to a wrongful denial of employment.

Total Error Analysis and Classification of Errors

In statistical hypothesis testing, a Type I error occurs when a true null hypothesis is rejected (false positive), and a Type II error occurs when a false null hypothesis is not rejected (false negative).

For the scenario where an individual is truly truthful but classified as a liar, the error is a Type I error. Conversely, if a liar is classified as truthful, it constitutes a Type II error.

Probability of Dishonest Applicant Evading Detection

Considering an individual who is genuinely dishonest (i.e., a liar), the probability that the polygraph incorrectly classifies them as truthful is:

P(polygraph indicates truth | liar) = 260 / 380 ≈ 0.6842 or 68.42%

This implies a high likelihood that a malicious individual could evade detection, thereby increasing the risk to the employer.

In this case, the error corresponds to a Type II error, where the false null hypothesis (the individual is truthful) is not rejected, despite the individual being a liar.

Conclusion

The statistical analysis of the polygraph data reveals dependence between the test decisions and actual truthfulness, emphasizing the test's limitations. The probabilities indicate significant chances of misclassification, which translate into wrongful employment denials and continued dishonesty in the workplace. Recognizing the occurrence of Type I and Type II errors informs policy decisions regarding the use of polygraph tests in legal and employment contexts. While polygraphs provide useful information, they should complement, not replace, holistic evaluative processes given their imperfect accuracy.

References

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