Question

Topic: Research/Metrics

Weighting Problem

Posted by Anonymous on 12/3/2009 at 11:46 AM ET 250 Points
Hi, Can anyone shed me the light how to calculate the weights for this problem?

Eg. there are two variables Var1 and Var2 and three rows A, B, C

Var1 Var2 Weights
A 1 4 wa
B 1 4 wb
C 5 0 wc

The sum of each row is 5. Now I want to weight the three rows so that the sum of Var1 is 30% of the total (15=5*3), And the sum of Var2 is 70% of the total？

The actual data has more rows and more columns than the example, could anyone tell me the formula for this?

Thanks very much!!!!!
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RESPONSES

  • Posted by Dawson on 12/3/2009 at 12:32 PM Accepted
    If I understand the problem correctly, you want Var1 to be 30% of the overall score (VarA + VarB). If so, you should calculate and index of VarA then an index of VarB them multiply these indicies by 0.3 & 0.7 respectively.

    Make sense?
  • Posted by koen.h.pauwels on 12/3/2009 at 2:43 PM Accepted
    If that is the case, I agree with Dawson. But can you please give us more details on what you exactly want and why?
  • Posted by mgoodman on 12/3/2009 at 5:23 PM Accepted
    I suspect I'm not understanding this fully. To do what you are suggesting, you would take the sum of Var1 (in this case, 7) and scale it to 30% of 15, or 4.5. That means multiplying the sum of Var1 by .643 (4.5 / 7.0).

    Then you would multiply the sum of Var2 (8 in your example) by 1.3125 so that it would be 70% of 15 (or 10.5).

    The problem with this is that it isn't really "weighting" in the normal sense of the term. If you want to really weight Var1 at 30% and Var2 at 70%, you would need to multiply EACH OBSERVATION by .3 or .7, and then sum those numbers in order to get a weighted total. When you then divide by n (number of rows) you'll have your weighted average.

    This doesn't look like a normal kind of problem, so I suspect you have a good understanding of why you want to weight this way.
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