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TECHNICAL NOTE DATA QUALITY


INTRODUCTION

1 The estimation process for this survey ensures that estimates of persons and households calibrate exactly to independently produced population totals at broad levels. The known population totals, commonly referred to as 'benchmarks', are produced according to the scope of the survey. The same is true for estimates of persons and households produced in this survey. However, in these cases the person and household benchmarks are actually estimates themselves and not strictly known population totals.

2 Since this survey was last conducted, the process for producing person and household benchmarks has been refined. Whilst this process is still under review, it represents a significant improvement to the previous method and person and household benchmarks produced using the new method are considered sufficient quality for use in household survey estimation. In addition, measures of the variability in person and household benchmarks have been incorporated into household estimates for the first time. These changes may result in unexpected movements in total households (at some broad levels) due to revised benchmark methodology.

3 A paper entitled A Revised Method for Estimating the Number of Households in Australia (cat. no. 3107.055.007), describing these issues in detail is currently being developed and is due for release in early 2007.

RELIABILITY OF ESTIMATES

4 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.

5 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.

6 This publication contains estimates for persons and households. Table T1 gives SEs for estimates of households, while SEs for estimates of persons are presented in T2. Tables containing estimates of households are found in Chapters 2 and 3, while Chapter 4 contains estimates of persons.

CALCULATION OF STANDARD ERROR

7 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 4.1 shows that the estimated number of persons aged 18 years and over in New South Wales who do not travel to work or study was 211,800. Since this estimate is between 200,000 and 300,000, table T2 shows that the SE for New South Wales will lie between 19,150 and 22,600 and can be approximated by interpolation using the following general formula:

8 Therefore, there are about 2 chances in 3 that the value that would have been produced if all persons in New South Wales had been included in the survey will fall within the range 192,200 to 231,400 and about 19 chances in 20 that the value will fall within the range 172,600 to 251,000. This example is illustrated in the diagram below.

11 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. *2.1) to indicate they are subject to high SEs and should be used with caution.

PROPORTIONS AND PERCENTAGES

12 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.

13 For example, in table 4.1, the estimate for the total number of persons aged 18 years and over in New South Wales is 3,193,000. The estimated number of persons aged 18 years and over who do not travel to work or study was 211,800, so the proportion of persons aged 18 years and over in New South Wales who does not travel to work or study is 211,800/3,193,000 or 6.6%. The SE of the total number of persons aged 18 years and over in New South Wales may be calculated by interpolation as 46,815 or 46,800 rounded to the nearest 100. To convert this to a RSE we express the SE as a percentage of the estimate, or 46,800/3,193,000 = 1.5%. The SE for the number of persons aged 18 years and over in New South Wales who do not travel to work or study was calculated above as 19,600, which converted to a RSE is 19,600/ 211,800 = 9.3%. Applying the above formula, the RSE of the proportion is giving an SE for the proportion (6.6%) of 0.6 percentage point (i.e. 6.6 x .092).

14 Therefore, there are about 2 chances in 3 that the proportion of persons aged 18 years and over in New South Wales who do not travel to work or study is between 6.0% and 7.2% and 19 chances in 20 that the proportion is within the range 5.4% to 7.8%.

DIFFERENCES

15 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:

16 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.

NON-SAMPLING ERROR

17 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 estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.
100	100	80	130	70	90	80	130	100	110
200	180	140	220	130	160	150	200	160	180
300	240	200	290	180	220	200	260	210	240
500	370	310	420	280	330	290	360	290	340
700	470	410	530	360	410	370	440	350	430
1,000	610	550	670	480	530	470	540	440	540
1,500	820	740	870	640	690	610	670	550	710
2,000	1 000	920	1 040	780	830	720	790	640	860
2,500	1 150	1 100	1 200	900	950	800	900	700	1 000
3,000	1 300	1 200	1 350	1 050	1 050	900	950	800	1 100
3,500	1 450	1 350	1 450	1 150	1 150	1 000	1 050	850	1 200
4,000	1 600	1 500	1 600	1 250	1 250	1 050	1 100	900	1 350
5,000	1 850	1 700	1 800	1 400	1 450	1 200	1 250	1 000	1 500
7,000	2 300	2 150	2 200	1 750	1 750	1 400	1 450	1 200	1 850
10,000	2 800	2 650	2 650	2 100	2 100	1 650	1 700	1 400	2 300
15,000	3 600	3 350	3 300	2 600	2 600	1 950	2 050	1 650	2 900
20,000	4 200	3 950	3 850	3 000	3 000	2 150	2 300	1 850	3 450
30,000	5 250	4 900	4 700	3 600	3 650	2 450	2 700	2 100	4 300
40,000	6 100	5 700	5 400	4 100	4 100	2 700	3 000	2 350	5 050
50,000	6 850	6 350	6 000	4 500	4 550	2 900	3 250	2 500	5 650
100,000	9 550	8 700	8 150	5 800	6 000	3 450	4 100	3 050	8 100
150,000	11 450	10 250	9 700	6 550	6 950	3 700	4 650	3 350	9 900
200,000	12 950	11 450	10 900	7 100	7 650	3 900	5 050	3 600	11 400
300,000	15 300	13 250	12 700	7 900	8 700	4 100	-	3 900	13 800
500,000	18 600	15 650	15 300	8 800	10 100	4 300	-	-	17 450
1,000,000	23 700	19 000	19 300	9 800	12 000	-	-	-	23 600
2,000,000	29 300	22 200	23 750	10 450	13 850	-	-	-	31 400
5,000,000	37 250	25 900	30 150	-	-	-	-	-	44 550
10,000,000	-	-	-	-	-	-	-	-	56 950
- nil or rounded to zero (including null cells)

T2 Standard errors for person level estimates
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Aust.
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.
100	140	130	170	90	100	70	60	90	180
200	250	240	290	180	190	150	140	170	300
300	360	340	400	260	280	220	220	240	400
500	530	510	590	400	420	340	370	370	570
700	690	660	750	530	550	450	500	480	720
1,000	900	860	960	700	720	590	680	620	910
1,500	1 210	1 160	1 250	930	970	790	930	810	1 190
2,000	1 480	1 420	1 510	1 140	1 190	960	1 140	970	1 430
2,500	1 750	1 650	1 750	1 350	1 400	1 100	1 300	1 100	1 650
3,000	1 950	1 850	1 950	1 500	1 550	1 250	1 450	1 250	1 850
3,500	2 150	2 050	2 150	1 650	1 700	1 350	1 600	1 350	2 050
4,000	2 350	2 250	2 300	1 800	1 900	1 450	1 750	1 450	2 200
5,000	2 750	2 600	2 650	2 050	2 150	1 650	1 950	1 600	2 550
7,000	3 400	3 200	3 200	2 500	2 650	2 000	2 300	1 900	3 100
10,000	4 200	4 000	3 900	3 000	3 200	2 350	2 650	2 200	3 800
15,000	5 350	5 000	4 850	3 700	4 000	2 750	3 000	2 550	4 800
20,000	6 250	5 850	5 600	4 200	4 600	3 100	3 250	2 800	5 600
30,000	7 800	7 250	6 800	5 000	5 600	3 500	3 500	3 150	7 000
40,000	9 100	8 400	7 800	5 600	6 350	3 800	3 650	3 400	8 150
50,000	10 150	9 350	8 600	6 100	6 950	4 000	3 700	3 550	9 150
100,000	14 150	12 800	11 550	7 650	9 050	4 550	3 700	3 950	12 950
150,000	16 950	15 150	13 500	8 550	10 350	4 750	3 550	4 100	15 750
200,000	19 150	16 950	15 000	9 150	11 300	4 850	3 350	4 150	18 050
300,000	22 600	19 650	17 250	9 900	12 650	4 850	-	4 150	21 700
500,000	27 350	23 350	20 300	10 700	14 250	4 750	-	-	27 100
1,000,000	34 600	28 650	24 650	11 450	16 100	-	-	-	36 050
2,000,000	42 500	34 000	29 100	11 650	17 500	-	-	-	47 150
5,000,000	53 350	40 600	34 600	-	-	-	-	-	65 300
10,000,000	-	-	-	-	-	-	-	-	81 800
- nil or rounded to zero (including null cells)