Let us assume that we have two algorithms, $A$ and $B$. Based on 3 different values of a parameter, $P$, $A$ takes $a_1, a_2, a_3$ seconds and $B$ takes $b_1, b_2, b_3$ seconds. What would be a proper way to measure which algorithm is more sensitive to $P$?
To address a diverse community, I will give an analogy: let us assume that depending on whether it rains heavily (value 2), mildly (1) or none(0) at all, one crop growing procedure $A$ takes $a_1, a_2, a_3$ time and another one, $B$, takes $b_1, b_2, b_3$ time. What would be a suitable statistical methodology to determine which procedure is more dependent on ("sensitive to") raining? We can also assume that:
We are growing same crops with $A$ and $B$ on the same kind of field.
$a_i$, $b_i$ can vary over different execution and the execution times for $A$ and $B$ are reported in terms of averages and standard deviation. $a_i$, $b_i$-s' can be averages (for each $i$-th value of $P$) or just a single execution time (for the $i$th value of $P$).
I am interested in measuring the "sensitivity" of the algorithm when the variance in the execution time of an algorithm is reported in either relative ("execution time of A increased by 5%") or absolute scale ("execution time of A increased by 5 sec") or both.
The exact problem I am working with is to compare the execution time of two distributed graph algorithms and decide which algorithm is more sensitive to underlying runtime parameters.