# Are the polygraph decisions and reality statistically independent events? Present applicable conditional probability calculations and state your answer.

1)    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.

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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?  Around this time, three physicians—Michael Phillips, Allen Brett and John Beary conducted a polygraph research study in which they subjected the polygraph to the same standard of testing given to medical diagnostic tests.  They recruited a sample of 1000 people—500 of whom told lies while connected to a polygraph, and the other 500 told the truth while connected to a polygraph.  So in reality, the probability of lying was .50 or 50%, and the probability of telling the truth was also 50%.

The polygraph, however, did make errors.  It decided that 185 of the actual truth-tellers were liars, and also decided that 120 of the actual liars were truth-tellers.

The results of the study were published in June 1986 issue of Discover in an article entitled, “Lie detectors can make a liar out of you.”  The actual results of the study are displayed in the table below:

|        reality

decision | truth-tel       liar |     Total

|  (not B)         (B) |

————-+———————-+———-

truth-teller |       315        120 |       435

(not A)    |     31.50      12.00 |     43.50

————-+———————-+———-

Liar |       185        380 |       565

(A)|     18.50      38.00 |     56.50

————-+———————-+———-

Total |       500        500 |     1,000

|     50.00      50.00 |    100.00

FYI – In the application of a polygraph test, an individual is assumed to be a truth-teller (H0) until proven a liar (Ha).

1.    Question1)Are the polygraph decisions and reality statistically independent events? Present applicable conditional probability calculations and state your answer.

1.    Question2)Consider a situation in which you are competing for a position in a company. Your application package, references and interview performance are stellar and the company is almost ready to make you an offer.  But the company is convinced that a polygraph test will reveal something about you that it believes none of the other information has—your honesty.  Thus, the company will decide to make you an offer on the basis of whether the polygraph identifies you as a truth-teller or a liar.

Question3)What is the probability of being denied employment because the polygraph judged you a liar when, in fact, you are a truth-teller?  Would the polygraph commit a Type I or Type II error in this case?  Explain.

1.    Question 4)Consider an alternative situation where in reality, you are a dishonest applicant (hypothetically, of course).  What is the probability that you will successfully evade the truth during the polygraph test, secure an offer from the company and become its most dishonest employee ever because the polygraph judged you a truth-teller when, in fact, you are a liar?  Would the polygraph commit a Type I or Type II error in this case?  Explain.