TECHNICAL NOTE DATA QUALITY
INTRODUCTION
1 Since the estimates in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of dwellings was included. There are about 2 chances in 3 (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs. Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.
2 Due to space limitations, it is impractical to print the SE of each estimate in the publication. Instead, a table of SEs is provided to enable readers to determine the SE for an estimate from the size of that estimate (see table T1). The SE table is derived from a mathematical model, referred to as the "SE model", which is created using the data collected in this survey. It should be noted that the SE model only gives an approximate value for the SE for any particular estimate, since there is some minor variation between SEs for different estimates of the same size.
CALCULATION OF STANDARD ERROR
3 An example of the calculation and the use of SEs in relation to estimates of households is as follows. Table 5.3 shows that the estimated number of households in Victoria that have a dishwasher was 910,300. Since this estimate is between 500,000 and 1,000,000, table T1 shows that the SE for Victoria will lie between 15,150 and 18,300 and can be approximated by interpolation using the following general formula:
4 Therefore, there are about 2 chances in 3 that the value that would have been produced if all persons had been included in the survey will fall within the range 892,600 to 928,000 and about 19 chances in 20 that the value will fall within the range 874,900 to 945,700. This example is illustrated in the diagram below.
5 In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases. Very small estimates are thus subject to such high RSEs so that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of less than 25% are considered reliable for most purposes. Estimates with RSEs of 25% and greater are preceded by an asterisk (e.g. *1.8) to indicate they are subject to high SEs and should be used with caution.
PROPORTIONS AND PERCENTAGES
6 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y.
7 For example, in table 5.3, the estimate for the total number of dwellings in Victoria is 1,916,400. The estimated number of dwellings in Victoria which have a dishwasher was 910,300, so the proportion of dwellings in Victoria which have dishwashers is 910,300/1,916,400 or 47.5%. The SE of the total number of dwellings in Victoria may be calculated by interpolation as 21,141 or 21,100 rounded to the nearest 100. To convert this to a RSE we express the SE as a percentage of the estimate, or 21,100/1,916,400 = 1.1%. The SE for the number of dwellings in Victoria that have a dishwasher was calculated above as 17,700, which converted to a RSE is 17,700/ 910,300 = 1.9%. Applying the above formula, the RSE of the proportion is giving a SE for the proportion (47.5%) of 0.7 percentage points (=47.5x .015).
8 Therefore, there are about 2 chances in 3 that the proportion of dwellings in Victoria that have a dishwasher is between 46.8% and 48.2% and 19 chances in 20 that the proportion is within the range 45.1% to 48.9%.
DIFFERENCES
9 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:
10 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
NON-SAMPLING ERROR
11 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfect reporting by respondents, errors made in collection such as in recording and coding data, and errors made in processing the data. Inaccuracies of this kind are referred to as non-sampling error, and they may occur in any enumeration, whether it be a full count or a sample. It is not possible to quantify non-sampling error, but every effort is made to reduce it to a minimum. This is done by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.
T1 Standard errors for household level estimates |
| |
| NSW | Vic. | Qld. | SA | WA | Tas. | NT | ACT | Aust. | |
size of estimates | no. | no. | no. | no. | no. | no. | no. | no. | no. | |
| |
100 | 130 | 110 | 80 | 80 | 100 | 80 | 50 | 70 | 130 | |
200 | 230 | 190 | 150 | 160 | 180 | 150 | 120 | 140 | 220 | |
300 | 320 | 270 | 220 | 220 | 260 | 200 | 190 | 200 | 290 | |
500 | 460 | 400 | 340 | 330 | 390 | 300 | 330 | 290 | 410 | |
700 | 590 | 510 | 450 | 430 | 500 | 380 | 450 | 380 | 520 | |
1,000 | 750 | 660 | 610 | 560 | 640 | 470 | 600 | 480 | 660 | |
1,500 | 980 | 880 | 830 | 750 | 850 | 610 | 820 | 620 | 860 | |
2,000 | 1 190 | 1 070 | 1 030 | 900 | 1 030 | 720 | 990 | 740 | 1 030 | |
2,500 | 1 350 | 1 250 | 1 200 | 1 050 | 1 200 | 800 | 1 150 | 850 | 1 200 | |
3,000 | 1 550 | 1 400 | 1 400 | 1 150 | 1 300 | 900 | 1 250 | 950 | 1 350 | |
3,500 | 1 700 | 1 550 | 1 550 | 1 300 | 1 450 | 950 | 1 350 | 1 000 | 1 450 | |
4,000 | 1 850 | 1 650 | 1 650 | 1 400 | 1 550 | 1 050 | 1 450 | 1 050 | 1 600 | |
5,000 | 2 100 | 1 900 | 1 950 | 1 600 | 1 800 | 1 150 | 1 600 | 1 200 | 1 800 | |
7,000 | 2 550 | 2 350 | 2 400 | 1 900 | 2 150 | 1 300 | 1 800 | 1 400 | 2 200 | |
10,000 | 3 150 | 2 850 | 2 950 | 2 300 | 2 550 | 1 550 | 1 950 | 1 600 | 2 750 | |
15,000 | 3 900 | 3 550 | 3 750 | 2 800 | 3 100 | 1 750 | 2 100 | 1 850 | 3 450 | |
20,000 | 4 550 | 4 150 | 4 350 | 3 150 | 3 550 | 1 950 | 2 100 | 2 000 | 4 000 | |
30,000 | 5 600 | 5 050 | 5 350 | 3 750 | 4 200 | 2 150 | 2 100 | 2 250 | 5 000 | |
40,000 | 6 450 | 5 800 | 6 150 | 4 150 | 4 700 | 2 300 | 2 050 | 2 400 | 5 800 | |
50,000 | 7 150 | 6 450 | 6 750 | 4 500 | 5 100 | 2 450 | 1 950 | 2 500 | 6 550 | |
100,000 | 9 800 | 8 650 | 8 950 | 5 600 | 6 350 | 2 700 | 1 600 | 2 700 | 9 250 | |
150,000 | 11 650 | 10 100 | 10 350 | 6 200 | 7 050 | 2 850 | 1 350 | 2 800 | 11 200 | |
200,000 | 13 100 | 11 250 | 11 350 | 6 650 | 7 550 | 2 900 | 1 150 | 2 800 | 12 800 | |
300,000 | 15 300 | 12 900 | 12 800 | 7 200 | 8 200 | 2 900 | - | 2 750 | 15 400 | |
500,000 | 18 400 | 15 150 | 14 550 | 7 750 | 8 900 | 2 850 | - | - | 19 250 | |
1,000,000 | 23 100 | 18 300 | 16 600 | 8 250 | 9 600 | - | - | - | 25 600 | |
2,000,000 | 28 300 | 21 400 | 18 200 | 8 400 | 9 850 | - | - | - | 33 400 | |
5,000,000 | 35 500 | 25 050 | 19 150 | - | - | - | - | - | 46 250 | |
10,000,000 | - | - | - | - | - | - | - | - | 57 900 | |
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- nil or rounded to zero (including null cells) |
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