The false positive paradox calculator works out positive predictive value (ppv) from base rate or prevalence, sensitivity and specificity. Enter what you have and the relationship is applied straight away, so you get the answer without working through the algebra yourself.
What Is the False Positive Paradox Calculator?
The false positive paradox calculator turns a set of measurements into positive predictive value (ppv), with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the False Positive Paradox Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with base rate or prevalence set to 10, sensitivity set to 5, specificity set to 2, the calculator returns positive predictive value (ppv) of 0.84746. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out positive predictive value (ppv)?
Enter base rate or prevalence, sensitivity and specificity. The calculator then works through the relationship and reports positive predictive value (ppv).
What does the false positive paradox actually calculate?
It takes base rate or prevalence, sensitivity and specificity and converts them into positive predictive value (ppv) using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter base rate or prevalence?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.