Weighting a Percent of Change

Thread view:

Enable EMail Alerts

Start New Thread

Thread rating:

Jessica - 08 Feb 2008 17:34 GMT

Hi Everyone,

I need to weight my percent of change by province. E.g.

    2004    2005    2005 Distribution    % Change    Weight
AB    182    268    6%    47%    2.8%
MB    1,285    1,295    29%    1%    0.2%
SK    784    887    20%    13%    2.6%
TOTAL    4255    4455        4.7%    5.7%

I see that MB has 29% of the market share, but only a % change of 1% in
volume.
AB has a small market share 6%, but is pulling the % change way up. But why
doesn't my weight formulas add up to total % change 4.7<>5.7?
My weight formula is 2005 Distribution times % Change.

Reply to this Message

joeu2004 - 08 Feb 2008 17:56 GMT

> I need to weight my percent of change by province. E.g.
> 2004 2005 2005 Distribution % Change Weight
[quoted text clipped - 5 lines]
> [....] why doesn't my weight formulas add up to total % change
> 4.7<>5.7?

Mostly because AB+MB+SK does not equal TOTAL. Either you have a
computation in those columns, or there are categories contributing to
TOTAL that you have not included in the table above.

Oh, I think I see your problem: your TOTAL includes the year title,
2004 and 2005 respectively. The correct totals are 2251 and 2450. So
you total change is about 10.9%.

Of course, changing the totals affects the "distribution" (proportion)
and weighted averages. But using the numbers above, it appears that
your "distribution" and "weight" formulas are correct.

So if you fix the TOTAL formula, I think everything will work out --
especially if you fix the format so that it consistently shows tenths
of a percent.

HTH.

Reply to this Message

Jessica - 08 Feb 2008 18:09 GMT

Ok, i fixed the totals.

    2004    2005    2005 Distribution    % Change    Weight
AB    182    268    11%    47%    5.2%
MB    1,285    1,295    53%    1%    0.4%
SK    784    887    36%    13%    4.8%
TOTAL    2251    2450        8.8%    10.3%

8.8% still does not equl the sum of the weighted percentages 10.3%
Is should equal my total % change right?

> > I need to weight my percent of change by province. E.g.
> > 2004 2005 2005 Distribution % Change Weight
[quoted text clipped - 23 lines]
>
> HTH.

Reply to this Message

joeu2004 - 08 Feb 2008 20:34 GMT

> Ok, i fixed the totals.
>
[quoted text clipped - 6 lines]
> 8.8% still does not equl the sum of the weighted percentages 10.3%
> Is should equal my total % change right?

First, sorry for saying the total change was 10.9%. Silly misreading
of the calculator.

And sorry for not recognizing your other mistake initially: you want
to look at the proportion ("distribution") of the 2004 numbers, not
the 2005 numbers. For example, for AB, instead of 268/2450, compute
182/2251.

As for the reason why.... The way my wife explains it might make the
best sense: since the base for the %Change is the 2004 numbers, the
base for the proportion should be the 2004 numbers.

If that works for you, great. Stop here.

I need to look at it mathematically, but I arrive at the same
conclusion. For the total %Change, we compute (b1+b2+b3)/(a1+a2+a3) -
1, where the "b's" are 2005 and the "a's" are 2004. For the
individual %Change, we compute b1/a1, for example. So in order for
the sum of the weighted averages to equal the total %Change, we need
to have a1+a2+a3 in the denominator. Therefore, we multiply b1/a1 - 1
by a1/(a1+a2+a3). The "a1's" cancel, giving us b1/(a1+a2+a3) - a1/
(a1+a2+a3). When we sum that "b1 term" with the b2 and b3 terms, we
do indeed get (b1+b2+b3)/(a1+a2+a3) - 1.

Whew! That should be clear as mud ;-). Now go back and read my
wife's explanation :-).

HTH.

Reply to this Message