# Next year weighted goal

this is my first question here.

I have to calculate next year´s goal by department on justice claims. In 2014, we had 8910 claims. Some departments drop their totals comparing with 2013 and others didn't.

I want a total reduction of 5%, but this % should not be equal for every department: those ones that rose their totals must have a more aggressive goal, while those that have drop their totals can have a less aggressive.

Any ideas?

I have the totals per department and the variation 2014/2013:

DEPT. / TOTAL 2014 PER DEPT. / DIFFERENCE (2014-2013) PER DEPT.
A     /  554                 / +122
B     / 2412                 / -641
C     / 4303                 / +736
D     / 1214                 / +240
E     /  389                 / -340
F     /   38                 / -11


The sum of 2014 is 8910. So, 5% less cases in 2015 gives us -445 cases. How to distribute them among the departments in a way that C and D get the more aggressive goals while B and E get the less ones? I guess that I should use some type of weighting, but just can´t figure out how to do it.

A look at the data (since I have forgot the original table in my job, I´m posting a very approximate replication):

DEPT A  1   2   3   4   5   6   7   8   9   10  11  12  Yr. Tot Variation
2011    234 435 267 125 176 185 123 238 294 279 123 435 2914    -
2012    272 473 305 163 214 223 161 276 332 317 161 476 3373    459
2013    214 415 247 105 156 165 103 218 274 259 103 422 2681    -692
2014    778 499 877 451 604 631 445 790 958 913 445 111 7502    4821

DEPT B  1   2   3   4   5   6   7   8   9   10  11  12  Yr. Tot Variation
2011    234 345 678 987 234 645 234 456 265 135 543 476 5232    -
2012    224 335 668 977 224 635 224 446 255 125 533 466 5112    -120
2013    204 315 648 957 204 615 204 426 235 105 513 446 4872    -240
2014    169 280 613 922 169 580 169 391 200 70  478 411 4452    -420

DEPT C  1   2   3   4   5   6   7   8   9   10  11  12  Yr. Tot Variation
2011    678 789 768 776 567 890 987 546 345 546 765 877 8534     -
2012    693 804 783 791 582 905 954 561 360 561 780 892 8666    132
2013    738 849 828 836 627 950 986 606 405 606 825 937 9193    527
2014    750 861 840 848 639 962 975 618 417 618 837 949 9314    121


So just to remember:

Total Number of 2014 cases: 23504 We want to reduce overall number of cases by 5%: minus 1175 cases in 2015 Finishing 2015 with: 22329 cases

But since DEPT B is lowering its cases year after year, we think that it´s not fair to assign a -5% goal for next year. We want to transfer a little amount of it goals for the other two departments leaving it with a goal like -3,5%, while rising DEPT A and DEPT C goals (let´s say 5,75 for both).

With this goals distribution we have na overall mean of -5% reduction (as needed) but I have not a statistical reason to apply it.

So based on this historic rising and lowering numbers and from 2014 totals (to get the 5% reduction absolute amount), is there any technique or workaround that could be made to stabilish 2015 goals as needed?

• There really isn't enough information here to help you--there are infinitely many ways to do this. Is there anything you can say to help us understand (quantitatively, not just qualitatively) how the "aggressiveness" is supposed to be related to the 2014 totals and the 2013-2014 changes? What are you attempting to achieve by means of this differential goal setting? Do the different departments have different capabilities of responding to your targets? Do you at least have more historical data to help assess variability in claims over time?
– whuber
Jan 23, 2015 at 18:55
• Hi, Whuber. Thank you very much for your response. This overall goal of 5% was a demand from the "boss". Agressiveness is this: if a dept has rise its total number (A,C,D) their goal should be, let´s say, 8% drop in total number of cases. Those depts wich droped their totals (B,E,F) can have a less agressive goal, let´s say, 2%. The mean final goal is 5% and then we have different goals for the different depts, but I can´t figure how to determine the exact % goals for each department and distribute the values among the depts. I have historical data for 2011-2014. Do you need it? How to post? Jan 23, 2015 at 19:09
• There is a good reason you can't figure it out: there isn't enough information. A danger is that you might wind up setting goals on the basis of random variation that is beyond the control of any department, which would be unfair and counterproductive. The historical data could help (a little) to assess the amount of random variation. Posting the small amounts of data you have is simple: make a text table, paste it into your question, select it, and format it with the "Code Sample" tool, as @gung has done in his recent edit.
– whuber
Jan 23, 2015 at 19:58
• @Leonardo did you just edit the post with another account? If so please let the moderators merge them. The edit is quite substantial and I'm not sure if someone else high-jacks the questions.
– Momo
Jan 24, 2015 at 13:34