TECHNICAL NOTE DATA QUALITY


INTRODUCTION

1 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 two chances in three (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 data from a number of past Labour Force Surveys. 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 ERRORS

3 An example of the calculation and the use of SEs in relation to estimates of people is as follows. Table 2 shows that the estimated number of persons in Australia who were other business operators was 1,013,500. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows the SE for Australia will be between 13,600 and 19.750 and can be approximated by interpolation using the following general formula:



4 There are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall in the range 999,800 to 1,013,500, and about 19 chances in 20 that the value will fall within the range 986,100 to 1,040,900. 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 that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% but less than or equal to 50% are preceded by an asterisk (e.g. *3.4) to indicate that they are subject to high SEs and should be used with caution. Estimates with RSEs of greater than 50%, preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less.


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 Considering the example above, of the 1,013,500 persons who were other business operators, 404,000 or 39.9% were female. The SE of 404,000, may be calculated by interpolation as 8,700. To convert this to an RSE we express the SE as a percentage of the estimate, or 8,700/404,000 = 2.2%. The SE for 1,013,500 was calculated previously as 13,700, which converted to an RSE is 13,700/1,013,500 = 1.4%. Applying the above formulae, the RSE of the proportion is:



8 The SE for the proportion of females who were other business operators, is 0.6 percentage points, calculated as (39.9/100)x1.7. There are about two chances in three that the proportion of female business operators is between 39.2% and 40.6% and 19 chances in 20 that the proportion is within the range 38.5% to 41.3%.

9 All other estimates produced from population estimates smaller than the values in T2 have RSEs larger than 25% and should be used with caution. T2 also indicates the size of the population estimates that would produce all other estimates with RSEs greater than 50% are considered too unreliable for general use.


DIFFERENCES

10 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 appropriate SE of the difference between two estimates (x-y) may be calculated by the following formulae:



11 While this formulae 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.


STANDARD ERRORS

T1 Standard Errors of Estimates
									AUST.
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT
Size of estimate	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	360	250	250	190	240	110	50	120	130	130.0
200	480	320	360	260	320	150	80	200	220	110.0
300	570	380	440	310	380	190	100	250	310	103.3
500	700	470	560	380	460	230	120	320	440	88.0
700	810	530	650	430	530	270	140	360	560	80.0
1000	930	610	760	490	610	310	170	400	700	70.0
1500	1 100	710	900	580	710	350	200	430	900	60.0
2000	1 230	800	1 010	640	790	390	220	460	1 070	53.5
2500	1 350	850	1 100	700	850	400	250	500	1 200	48.0
3000	1 450	950	1 200	750	900	450	250	500	1 350	45.0
3500	1 550	1 000	1 250	800	1 000	450	250	550	1 450	41.4
4000	1 600	1 050	1 300	850	1 050	500	250	550	1 550	38.8
5000	1 750	1 150	1 400	900	1 100	500	300	600	1 700	34.0
7000	2 000	1 300	1 600	1 000	1 250	600	350	700	2 000	28.6
10000	2 300	1 450	1 800	1 150	1 450	700	450	800	2 300	23.0
15000	2 650	1 700	2 000	1 300	1 650	850	650	1 000	2 700	18.0
20000	2 950	1 900	2 200	1 450	1 850	950	800	1 150	3 000	15.0
30000	3 400	2 200	2 500	1 700	2 100	1 250	1 150	1 500	3 350	11.2
40000	3 800	2 400	2 800	1 950	2 350	1 450	1 450	1 750	3 650	9.1
50000	4 100	2 600	3 050	2 200	2 550	1 650	1 700	2 000	3 950	7.9
100000	5 200	3 450	4 200	3 300	3 750	2 400	2 950	2 650	4 950	5.0
150000	6 100	4 150	5 150	4 250	4 950	2 850	4 050	3 000	5 800	3.9
200000	7 050	4 850	6 000	4 950	5 950	3 150	5 100	3 150	6 500	3.3
300000	8 850	6 250	7 650	6 100	7 500	3 650	6 950	3 300	7 700	2.6
500000	12 400	8 650	10 300	7 650	9 550	4 200	. .	3 300	9 650	1.9
1000000	18 400	13 150	14 700	9 750	12 150	4 800	. .	. .	13 600	1.4
2000000	24 800	19 450	19 800	11 600	14 100	. .	. .	. .	19 750	1.0
5000000	31 600	31 100	26 700	13 050	14 700	. .	. .	. .	32 950	0.7
10000000	33 850	42 900	31 200	. .	. .	. .	. .	. .	44 000	0.4
15000000	. .	. .	. .	. .	. .	. .	. .	. .	49 600	0.3
. . not applicable

T2 POPULATION LEVELS AT WHICH ESTIMATES HAVE RSES OF 25% AND 50%
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Aust.
	no.	no.	no.	no.	no.	no.	no.	no.	no.
Relative Standard Error (RSE) of 25%	8 600	4 200	6 100	3 000	4 200	1 400	500	1 800	8 800
Relative Standard Error (RSE) of 50%	2 800	1 400	2 000	1 000	1 400	400	100	700	2 300