5625.0 - Private New Capital Expenditure and Expected Expenditure, Australia, Dec 2009
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APPENDIX 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

The following example illustrates how to use the standard error to interpret a level estimate.

Let us say that the published level estimate for total capital expenditure is \$30,007m and the calculated standard error in this case is \$719m. The standard error is then used to interpret the level estimate of \$30,007m.

For instance, the standard error of \$719m indicates that:

• There are approximately two chances in three that the real value falls within the range \$29,288m to \$30,726m (\$30,007m ± \$719m)
• There are approximately 19 chances in 20 that the real value falls within the ranges \$28,569m to \$31,445m (\$30,007m ± \$1,438m)

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 December Quarter 2009 estimates.

 Buildings and Structures Equipment, Plant and Machinery Total \$m \$m \$m Mining 45 69 89 Manufacturing 46 189 195 Electricity, Gas, Water and Waste Services 7 25 26 Construction 32 187 191 Wholesale Trade 47 116 128 Retail Trade 8 114 115 Transport, Postal and Warehousing 35 193 199 Information Media and Telecommunications 13 45 46 Financial and Insurance Services 24 68 75 Rental, Hiring and Real Estate Services 211 493 571 Professional, Scientific and Technical Services 48 108 132 Other Selected Services 141 141 208 Total 249 614 719 New South Wales 108 283 308 Victoria 65 524 533 Queensland 104 142 167 South Australia 43 79 92 Western Australia 203 168 276 Tasmania - 34 34 Northern Territory 2 24 24 Australian Capital Territory 1 58 58 Australia 249 614 719 - nil or rounded to zero (including null cells)

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 \$24,651m and the next quarter the published level estimate is \$30,007m. In this example the calculated standard error for the movement estimate is \$682m. The standard error is then used to interpret the published movement estimate of \$5,356m.

For instance, the standard error of \$682m indicates that:
• There are approximately two chances in three that the real movement over the two quarter period falls within the range \$4,674m to \$6,038m (\$5,356m ±\$682m)
• There are approximately nineteen chances in twenty that the real movement falls within the range \$3,992m to \$6,720m (\$5,356m ± \$1,364m).

The following table shows the standard errors for December Quarter 2009 estimates.

 Buildings and Structures Equipment, Plant and Machinery Total \$m \$m \$m Mining 44 60 83 Manufacturing 34 222 231 Electricity, Gas, Water and Waste Services 15 30 34 Construction 32 242 233 Wholesale Trade 50 85 104 Retail Trade 15 114 118 Transport, Postal and Warehousing 36 303 306 Information Media and Telecommunications 10 18 24 Financial and Insurance Services 19 71 78 Rental, Hiring and Real Estate Services 223 288 353 Professional, Scientific and Technical Services 17 123 124 Other Selected Services 113 183 227 Total 244 642 682 New South Wales 60 440 454 Victoria 88 332 361 Queensland 107 207 217 South Australia 50 105 121 Western Australia 204 304 389 Tasmania 1 34 34 Northern Territory 2 27 26 Australian Capital Territory 1 36 36 Australia 244 642 682