Sampling Errors
LEVEL ESTIMATES
Introduction
The estimates in this publication are based on a sample drawn from units in the surveyed population. Because the entire population is not surveyed, the published estimates are subject to sampling error. The most common way of quantifying such sampling error is to calculate the standard error for the published estimate or statistic.
Example of use
To illustrate, let us say that the published level estimate for total capital expenditure is $10,500m and the calculated standard error in this case is $173m. The standard error is then used to interpret the level estimate of $10,500m. For instance, the standard error of $173m indicates that:
- There are approximately two chances in three that the real value falls within the range $10,327m to $10,673m ($10,500m ± $173m)
- There are approximately 19 chances in 20 that the real value falls within the ranges $10,154m and $10,846m ($10,500m ± $346m)
The real value in this case is the result we would obtain if we could enumerate the total population.
The following table shows the standard errors for quarterly level estimates. These standard errors are based on a smoothed average of capital expenditure estimates.
|
| Buildings and structures | Equipment, plant and machinery | Total | |
| $m | $m | $m | |
| |
Mining | 11 | 16 | 36 | |
Manufacturing | 16 | 51 | 62 | |
Construction | 7 | 35 | 40 | |
Wholesale trade | 5 | 57 | 65 | |
Retail trade | 7 | 22 | 34 | |
Transport and storage | 10 | 40 | 45 | |
Finance and insurance | 3 | 29 | 31 | |
Property and business services | 52 | 62 | 84 | |
Other services | 69 | 36 | 89 | |
Total | 90 | 124 | 173 | |
New South Wales | 17 | 77 | 92 | |
Victoria | 73 | 71 | 108 | |
Queensland | 10 | 35 | 44 | |
South Australia | 2 | 13 | 27 | |
Western Australia | 5 | 25 | 32 | |
Tasmania | 1 | 8 | 8 | |
Northern Territory | na | na | 2 | |
Australian Capital Territory | na | na | 6 | |
Australia | 90 | 124 | 173 | |
| |
na not available |
| | | | |
Movement Estimates
Example of use
The following example illustrates how to use the standard error to interpret a movement estimate. Let us say that one quarter the published level estimate for total capital expenditure is $10,500m, and the next quarter the published level estimate is $11,100m. In this example the calculated standard error for the movement estimate is $221m. The standard error is then used to interpret the published movement estimate of +$600m.
For instance, the standard error of $221m indicates that:
- There are approximately two chances in three that the real movement over the two quarter period falls within the range $379m to $821m ($600m ±$221m)
- There are approximately nineteen chances in twenty that the real movement falls within the range $158m to $1,042m ($600m ± $442m)
The following table shows the standard errors for national quarterly movement estimates. These standard errors are based on a smoothed average of capital expenditure estimates.
| Equipment, plant and machinery | Total | |
| $m | $m | |
| |
Mining | 23 | 49 | |
Manufacturing | 64 | 78 | |
Construction | 48 | 55 | |
Wholesale trade | 51 | 66 | |
Retail trade | 25 | 45 | |
Transport and storage | 49 | 53 | |
Finance insurance | 40 | 32 | |
Property and business services | 84 | 114 | |
Other services | 46 | 119 | |
Total | 153 | 221 | |
New South Wales | 99 | 103 | |
Victoria | 114 | 117 | |
Queensland | 75 | 100 | |
South Australia | 84 | 84 | |
Western Australia | 87 | 91 | |
Tasmania | 21 | 21 | |
Northern Territory | na | 33 | |
Australian Capital Territory | na | 67 | |
Australia | 153 | 221 | |
| |
na not available |