where the population weight is denoted [A.sup.i]/[[summation].sub.i][A.sup.i] Whereas MAPE gives each observation equal weighting in the calculation of average error, MPAD weights the APE for each observation by its population size.
It was applied here to MAPE, MedAPE and MPAD in the form:
MPAD displays the smallest numbers because many LGAs in Queensland have very small populations.
MAPE and MPAD are the chosen measures for this question because MedAPE is less stable with small sample sizes (Rayer 2007).
For example, the MPAD of the official 2003 round of projections after five years was 2.15% whilst for the linear extrapolation it was 3.84%.
A more complex picture emerges if MAPE is presented by population size category, and if MPAD, which weights error by population size, is also calculated.
For areas with the smallest populations, the Queensland projections are less inaccurate than the Texas and North Dakota projections according to both MAPE and MPAD, but as population size increases the differences in error are less marked.
In addition, the value of different perspectives on error, as measured by MAPE and MPAD for example, was demonstrated in this section.
Projection horizon MAPE LGAs State (years) MAPE MedAPE MPAD MAPE 2001 & 2003 projection rounds 5 6.3 4.3 2.9 2.2 1996 & 1998 projection rounds 5 7.1 5.4 4.5 1.4 10 8.S 7.0 7.5 2.0 1989, 1992 & 1994 projection rounds 5 6.5 4.4 3.7 D.7 10 10.9 7.9 8.2 2.4 15 14.fi 11.3 12.2 1.9 Source: the Authors Table 3.