3228.0 - Demographic Estimates and Projections: Concepts, Sources and Methods, 1999  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 30/08/1999   
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Contents >> Appendix 7. The Plus-Minus Proportionate Adjustment technique

A7.1. The Plus-Minus Proportionate Adjustment technique is a procedure for prorating a distribution with positive and negative frequencies. The procedure minimises the adjustments to the original distribution. It requires the use of two factors, one for the positive frequencies and one for the negative frequencies. The formulae are as follows:

    Adjustment Factor for positive items

    Adjustment Factor for negative items :

    where:
    =the sum of absolute frequencies
    n=the algebraic sum of frequencies
    N= the assigned total that the distribution must sum to.
A7.2. Having calculated the adjustment factors for positive and negative items, the adjusted values of these items are obtained by multiplying the positive items by the positive factor and the negative items by the negative factor.

A7.3. The technique is illustrated in the following table where the algebraic sum of the frequencies is adjusted from 10 to 15.

A7.1: Pro-rata Adjustment of Plus/Minus Frequency Distribution

i

ni
Adjustment
factor*
Adjusted
ni
1
30
1.045
31
2
-50
0.955
-47
3
30
1.045
31
Total
10
15
        Where
             n = 10
             N = 15
          N - n  = 5
         = 110

        and (*)
        Positive Adjustment factor =

        Negative Adjustment Factor =






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