• If precision and recall is equally important, then use $\beta$ = 1 which becomes F1 Score
• If False positive has more importance, then use $\beta$ = $[0,1]$
  • as that will make FN weight less on denominator and so FN weight more overall
  • So if FN is big -> $\beta \ast FN$ will be small -> the $F_{\beta }$ will be big
  • But if FP is big -> the $F_{\beta }$ will be small
• If False Negative has more importance, the use $\beta$ > 1
  • As that will make FN weight more on denominator and so FN weight less overall
  • So if FN is big -> $\beta \ast FN$ will be bigger -> the $F_{\beta }$ will be small
  • But it FP is big -> the weight is smaller than $\beta \ast FN$, so has less weight on $F_{\beta }$

References