Backward Probability Template
Although this page is adaptable to a variety of backward probability situations, its exemplary case is the one in which one is seeking to make sense of the result of a medical test. Suppose, for example, that a certain disease is randomly found in one-half of one percent (.005) of the particular population in question. A certain clinical blood test is 99 percent (.99) effective in detecting the presence of this disease; that is, it will yield an accurate positive result in 99 percent of the cases where the disease is actually present. But it also yields false positive results in 5 percent (.05) of the cases where the disease is not present. Question: In any particular instance, what is the probability that the test result accurately or innacurately indicates the presence or absence of the disease?T
To perform a calculation of this sort, enter one value for each of the following complementary pairs of probabilities (the other item in each pair will be calculated automatically), then click the «Calculate» button. Probability values may be entered as either common fractions or decimal fractions (e.g., 1/200 or .005).

To illustrate the details of data entry, click here to enter the values given in the above example.

 Probability that the disease is present/absent in any particular instance: Present Absent If the disease is present, the probability that the test will be accurately positive or falsely negative: Positive Negative If the disease is absent, the probability that the test will be accurately negative or falsely positive: Negative Positive

 For any particular test result: probability that it will be positive: probability that it will be negative: For any particular positive test result: probability that it is a true positive: probability that it is a false positive: For any particular negative test result: probability that it is a true negative: probability that it is a false negative: [All results are rounded to 6 decimal places.]

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