Taking into account garden numbers helps
When calculating a national average, the results must be adjusted to reflect the proportion of gardens from each region.
In an ideal situation, a survey return would be received each year from every garden in every region. Failing this, the number of survey returns from each region should be proportional to the number of gardens in that region. If the number of survey returns from each region was proportional to the number of gardens, then the mean number of birds per garden could be calculated as before and the mean birds per garden would be representative. Any changes in the mean count could more reliably be attributed to actual changes in population size.
This is unlikely to occur in practice – for whatever reason, some regions will be under or over-represented in the survey. Fortunately, we can correct for this by taking a weighted average of the count data with the weights equal to the proportion of the population from each region. To do this, averages are calculated for each region, and then multiplied by the proportion of the population that live in each region, and these values summed. For example, Canterbury contains approximately 12.6% of the population, whereas Northland contains only 3% of the population. Therefore the regional averages from Canterbury are multiplied by 0.126, and the regional averages from Northland are multiplied 0.03, etc
This weighted average removes the bias that can arise when regions are under or over represented in the survey returns, and more importantly when the percentage of survey returns from a region changes over time.
When we apply this weighting, we can see the trend in tūī per garden is much less pronounced.
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