Suppose that under a certain condition the probability that a woman would be ref

ID: 3174580 • Letter: S

Question

Suppose that under a certain condition the probability that a woman would be referred for additional testing is 0.874 and for men it is 0.912

1)Suppose that a press release about the study stated that the odds of referral for

additional testing for women are 70% of the odds for men. Explain how they obtained

70% (more accurately 67%)..

2) Suppose that a news story that described the study stated that "Doctors were only

70% as likely to order additional testing for women as for men". What is wrong with this

interpretation? Set up but do not complete the computation of the value for the correct

interpretation of this result.

Odds for women being refered for additional testing is 0.874 to (1-0874) = 0.874 to 0.126

Lets express this odds as a decimal...0.874/0.126 = 6.94

Similarly,odds for men being referred for additional testing is 0.912 to (1-0.912) = 10.36

Odds for women/odds for men = 6.94/10.36 = 0.67 = 70%

2) This interpretation is wrong because, 70% of probability of men being reffered for additional testing = 0.7x0.912 = 0.64

This is not the probability of women being referred for additional testing. The problem here arises due to misusage of probability instead of odds.

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