Comparing a %increase with a %decrease I'm struggling to compare the %increase/decrease in the average homicide rate of a select group of cities to the state homicide rate.
For example, if the state saw a 4% decrease (-4) in the homicide rate over a two-year period but the average homicide rate in my group of comparison cities increased by 2%(+2), how much bigger was the increase in my group of comparison cities compared to the state? Is it possible to make a statement along these lines: "The average homicide rate of the comparison group increased X times more than the state rate over the same period."
It can't be this |-4|/2 = 2 because it's definitely more than double.
Appreciate any help!

Imagine that the state initially had a homicide rate of $100$. A $4$ percent decrease would be $96$. If we instead pretend that the state behaved like the group of comparison cities, then a $2$ percent increase would be $102$. Overall, the ratio between the two scenarios is $\frac{102}{96} = 1.0625$, which is a $6.25$ percent increase.
