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False-Positive Rate & Population Shares

Separate a classifier’s false-positive rate from false-positive and true-negative shares of the whole population.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With 10% prevalence and 95% specificity, false positives are 4.5% of the population and true negatives are 85.5%. The false-positive rate among actual negatives is 5%.

FPR = 1 − specificity; false-positive share = FPR × (1 − prevalence)

Worked example

Enter these known values and leave the other values blank.

Actual-positive population share
10 %
Specificity among actual negatives
95 %
False positives as a share of everyone
4.5 %
True negatives as a share of everyone
85.5 %
False-positive rate among actual negatives
5 %

Assumptions and limitations

  • All entries are percentages from 0% to 100%, with prevalence strictly below 100% so an actual-negative group exists.
  • Specificity is the true-negative rate within actual negatives. The false-positive and true-negative population shares sum to one minus prevalence.
  • These inputs do not establish the probability that a positive classification is false. That calculation also needs sensitivity or the true-positive population share.

Common questions

Why are 4.5% and 5% both correct in the example?

They use different denominators: 4.5% of everyone, or 5% of the 90% who are actual negatives.

Can this tell me whether a particular positive result is correct?

No. It calculates aggregate rates from the supplied model, without sensitivity, individual information or uncertainty intervals.

References

Bookify limits the false-positive population share to at most 100%.

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