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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!

Brittany Nieto
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  • Unfortunately you cannot do this with the percentages alone, because the different cities and the state as a whole have different actual numbers of murders and population. You would need to know the percentages and both this and the previous years' [actual number of murders or population]. – Nij Mar 18 '22 at 21:12
  • I may have been unclear. I’m comparing the change in the homicide RATE. So differing #s of homicides & population sizes shouldn’t be a factor.

    I looked at the homicide rate per 100k [(# of homicides/population)*100k]for 2018- 2019 and calculated the percentage increase or decrease between these years. I did the same thing for the cities except combined & averaged their homicide rates.

    Now I’m just trying to talk about my results: A state that saw a decrease in the homicide rate, while the average homicide rate in this cluster of cities increased.

    Hope that makes sense!

     – Brittany Nieto Mar 19 '22 at 18:40

1 Answers1

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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.

Adriano
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