The F beta formula according to the wikipedia is The weighted harmonic mean of precision and recall. I can not understand why in the left part of equation there is beta and in the right one is beta^2:To my mind if I claim that Precision is 5 times important than Recall:F beta = (1+beta)/(beta/P+1/R)=(1+beta)PR/(beta*R+P), where beta=0.2.Is this right? 
Explanation of the F beta formula
classification;statistics
That's a great question, because on its face it seems like the weight should be $\beta$ alone, and, it should be in front of recall. The answer is in the text from which that reference is taken, on page 133: http://www.dcs.gla.ac.uk/Keith/pdf/Chapter7.pdfThe definition is designed to make the metric indifferent to a change in precision or recall when $P/R = \beta$. That is, $F_\beta$ increases by the same amount when either precision or recall increases, at the point where precision is already $\beta$ times bigger than recall.The definition does indeed weight recall more highly as you can verify. Honestly on re-reading the text above, I was confused, because I don't see how it makes sense to think of equilibrium as the point where precision is much bigger, if recall matters more.I plugged in the formula to Wolfram Alpha, and:Hm. These are only equal if $R/P = \beta$! I think the paper may have misstated this then, or else I've really missed something. It's a formula whose value changes at the same rate with respect to precision or recall, when recall is already $\beta$ times larger, and in that sense it corresponds to treating recall as $\beta$ time more important.