I have a series of experiments for different objects from the experiments let me put it in an abstract way there is a condition A for a specific object O the success rate/percentage is p(A) generally speaking, for most of values of A (A=a1, A=a2, A=a3.....blabla) p(A) is 100% but for some of A, p(A) is 0 and for some of A p(A) is between 0 and 1
so there are 2 variables: object and condition for each object, the success rate may for different conditions now I want to compare different object in terms of success rate how to define a metric for the comparison? thanks!
For each object $O$ you have a vector of numbers between $0$ and $1$, namely success rates for A=a1, A=a2, etc.
The problem becomes: how to define a metric on the set of vectors $x=(x_1,\dots,x_n)$ with all entries between $0$ and $1$? There is no canonical answer. The two simplest metrics are $$d_1(x,y)=|x_1-y_1|+\dots +|x_n-y_n|$$ and $$d_\infty (x,y)=\max(|x_1-y_1|, \dots , |x_n-y_n|)$$