how to analyze components of a whole to compare 'before' and 'after' performance

mrdlau

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Mar 28, 2019
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Suppose I have a scenario where I want to compare the performance of 2 different time periods, but I want to break down exactly what caused the difference in performance.
For example: I have performance of 3 telemarketers (t1, t2, and t3):
t1 called 50 customers and sold 20. his success is 20/50, or 40%
t2 called 75 and sold 10. his success is 10/75 or 13.3%
t3 called 200 and sold 95. his success is 95/200 or 47.5%.
the total success all 3 combined is 38%.

the following year, I have the following performance:
t1 called 60 customers and sold 10. his success is 10/60, or 16%
t2 called 105 and sold 95. his success is 95/105 or 90%
t3 called 25 and sold 1. his success is 1/25 or 4%.
the total success is 55%.

the difference between the two totals is 55%-3%8 = 17%.
what I want to show is that of the 17% difference, t1 contributed to x%, t2 contributed to y% and t3 contributed to z%. x+y +z should equal 17%.

I've tried a couple things but cant get the numbers to tie out. I know an issue is that the denominators aren't the same, so I dont know how to calculate this one out.

I've tried doing some sorted of weighted difference, tried taking each impact separately, but still can't get the numbers to balance. can someone let me know their thoughts and let me know if this is possible.

thanks!
 
I suppose you would add the probabilities for each individual member and do some manipulations. Can anyone correct me?
 
I don't think there's any meaningful way to define what you are asking for. Each person did not contribute a specific portion of the change; it just can't be broken up in that way, to get three numbers that add up to 17%.

To be specific, the 17% comes from this calculation:

[MATH]\frac{10+95+1}{60+105+25} - \frac{20+10+95}{50+75+200} = 0.173[/MATH]​

That can't be rewritten as a sum of three quantities that are functions of each person's statistics. Each contributed part of both numerators and both denominators, and how much the overall percentage changed involves all the numbers, intricately interacting.
 
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