P_{(A)} = .005 | the probability that the disease will be present in any particular person |
P_{(~A)} = 1—.005 = .995 | the probability that the disease will not be present in any particular person |
P_{(B|A)} = .99 | the probability that the test will yield a positive result [B] if the disease is present [A] |
P_{(~B|A)} = 1—.99 = .01 | the probability that the test will yield a negative result [~B] if the disease is present [A] |
P_{(B|~A)} = .05 | the probability that the test will yield a positive result [B] if the disease is not present [~A] |
P_{(~B|~A)} = 1—.05 = .95 | the probability that the test will yield a negative result [~B] if the disease is not present [~A] |
P_{(B)} = [P_{(B|A)} x P_{(A)}] + [P_{(B|~A)} x P_{(~A)}]
= [.99 x .005]+[.05 x .995] = .0547 | the probability of a positive test result [B], irrespective of whether the disease is present [A] or not present [~A] |
P_{(~B)} = [P_{(~B|A)} x P_{(A)}] + [P_{(~B|~A)} x P_{(~A)}]
= [.01 x .005]+[.95 x .995] = .9453 | the probability of a negative test result [~B], irrespective of whether the disease is present [A] or not present [~A] |
which in turn allows for the calculation of the four remaining conditional probabilities
P_{(A|B)} = [P_{(B|A)} x P_{(A)}] / P_{(B)}
= [.99 x .005] / .0547 = .0905 | the probability that the disease is present [A] if the test result is positive [B] (i.e., the probability that a positive test result will be a true positive) |
P_{(~A|B)} = [P_{(B|~A)} x P_{(~A)}] / P_{(B)}
= [.05 x .995] / .0547 = .9095 | the probability that the disease is not present [~A] if the test result is positive [B] (i.e., the probability that a positive test result will be a false positive) |
P_{(~A|~B)} = [P_{(~B|~A)} x P_{(~A)}] / P_{(~B)}
= [.95 x .995] / .9453 = .99995 | the probability that the disease is absent [~A] if the test result is negative [~B] (i.e., the probability that a negative test result will be a true negative) |
P_{(A|~B)} = [P_{(~B|A)} x P_{(A)}] / P_{(~B)}
= [.01 x .005] / .9453 = .00005 | the probability that the disease is present [A] if the test result is negative [~B] (i.e., the probability that a negative test result will be a false negative) |
P_{(A)} or P_{(~A)} P_{(B|~A)} or P_{(~B|~A)} P_{(B|A)} or P_{(~B|A)} | After the three probability values (one from each pair) have been entered, click the cursor anywhere in the gray field of the table to complete the intermediate calculations, then click the "Calculate" button. ~~Note that no probability value can be less than 0.0 or greater than 1.0. |
~A | A | ||
B | |||
~B | |||
Home | Click this link only if you did not arrive here via the VassarStats main page. |