F-Score test for statistical tests

F-Score is a measure of a test’s accuracy in statistics.
Since accuracy has atleast two parts, precision and recall/repeatability it is actually the harmonic mean of both of them.

i.e: \frac{1}{F} = \frac{(\frac{1}{precision} + \frac{1}{recall})}/(\frac{1}/{2})

or simplifying
F = 2*\frac{(precision*recall)}{(precision + recall)}

Note that in this case precision and recall are both probabilities computed the traditional way.
i.e: precision = \frac{correct values}{total result values returned}
and recall = \frac{correct values}{no.of results} that must have been returned.

Also note that the above definition if for a single dimension case. That is F1
and for Fx there’s a different formula like:
$latex Fx = \frac{(1+x^2)*(precision*recall)}{((x^2)(precision)+recall)}

It is often used in information search, retrieval and similar fields.

Relevant posts: Measure theory and stack ranking  and types of mean..

UPDATE: An alternative score/measure is Mathews Correlation Coefficient.  If you reduce the above equation to confusion matrix cells(that’s TP, FP, FN, TN), you’ll find that there’s a common pattern in the numerator of multiplying differences, but there’s a square root in the MCC formulation above. Without going through the steps and looking for actual equations, I’d guess that MCC is the quadratic mean of precision and recall while F-Score is the harmonic mean. 


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