The false positive and false negative rates for the medical test are given as:
- 6.67% and
- 4.00% respectively.
<h3>What is a false positive?</h3>
A false positive is an outcome in which the model forecasts the positive class inaccurately. A real positive result is one in which the model accurately predicts the positive class.
To determine the false positives and false negatives of the tests, we use the principle of probability.
Probability (p) = Number of Favorable outcomes/Total number of Exhaustive outcomes
Recall that 240 of the 250 patients were accurately recognized. Also, 50 healthy people were diagnosed to have the ailment. Hence, the test's false positive (FP) and false negative (FN) rates can be estimated as follows:
Hence P (False Positive) = 50 / 750 = o.0667 or 6.67%
P (False Negative) = 10/750 = 0.0400 or 4.00%.
Therefore, the required rates are 6.67% and 4.00% accordingly.
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Full Question:
Testing the test Are false positives too common in some medical tests? Researchers conducted an experiment involving 250 patients with a medical condition and 750 other patients who did not have the medical condition. The medical technicians who were reading the test results were unaware that they were subjects in an experiment.
Question: Technicians correctly identified 240 of the 250 patients with the condition. They also identified 50 of the healthy patients as having the condition. What were the false positive and false negative rates for the test? (See table below)
Medical patients Other Conditions Total
Correctly identified 240 700 940
Incorrectly identified 10 50 60
Total 250 750 1000
= 605,100 