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 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 ERROR

3 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 5 shows the estimated number of part-time employees in main job was 3,046,100. Since the estimate is between 2,000,000 and 5,000,000, table T1 shows that the SE for Australia will lie between 17,050 and 28,450 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 within the range 3,025,100 to 3,067,100 and about 19 chances in 20 that the value will fall within the range 3,004,100 to 3,088,100. 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 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 less than 25%. Table T2 presents the levels at which estimates have RSEs of 25% and 50%.


MEANS AND MEDIANS

6 The RSEs of estimates of mean and median weekly earnings (see paragraph 20 of the Explanatory Notes) are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median (see table T1) and then multiplying the resulting number by the following factors for Australian estimates:

• mean weekly earnings: 0.9
• median weekly earnings: 1.0

7 The following is an example of the calculation of SEs where the use of a factor is required. Table 5 shows an estimate of 3,046,100 part-time employees in main job and table 4 shows mean weekly earnings for the same group as $485. The SE of 3,046,100 was calculated previously as 21,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 21,000/3,046,100 = 0.7%.

8 The RSE of the estimate of mean weekly earnings is calculated by multiplying this number, 0.7%, by the appropriate factor shown in paragraph 6 (in this case 0.9): 0.7 x 0.9 = 0.63%. The approximate SE of this estimate of mean weekly earnings of part-time employees in main job is therefore 0.63% of $485, that is $3 (to the nearest dollar). Therefore, there are two chances in three that the mean weekly earnings for female part-time employees that would have been obtained if all dwellings had been included in the survey would have been within the range $482 to $488, and about 19 chances in 20 that it would have been within the range $479 to $491.

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


ALL OTHER ESTIMATES

10 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 with RSEs greater than 50% which are considered too unreliable for general use.


PROPORTIONS AND PERCENTAGES

11 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.



12 Considering the example from the previous page, of the 3,046,100 part-time employees in their main job, 835,800 or 27.4% were males. The SE and RSE of 3,046,100 were calculated previously as 21,000 and 0.7% respectively. The SE for 835,800 calculated by interpolation is 10,600 which converted to a RSE is 10,600/835,800 = 1.3%. Applying the above formula, the RSE of the proportion is:



13 The SE for the proportion, 27.4%, of male part-time employees, is 0.3 percentage points, calculated as (27.4/100)x1.1. There are about two chances in three that the proportion of male part-time employees, was between 27.1% and 27.7%, and 19 chances in 20 that the proportion is within the range 26.8% to 27.4%.


DIFFERENCES

14 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:



15 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.


STANDARD ERRORS

T1 Standard errors of estimates
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	AUST. SE	RSE
Size of estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	290	290	220	180	220	110	80	100	110	110.0
200	400	380	320	240	290	160	120	170	190	95.0
300	470	440	390	280	340	190	150	210	260	86.7
500	580	540	500	340	420	240	190	270	380	76.0
700	660	620	580	390	480	270	230	300	480	68.6
1000	760	710	680	450	550	310	260	330	610	61.0
1500	900	830	810	530	640	360	310	360	780	52.0
2000	1 010	930	910	590	710	390	340	390	920	46.0
2500	1 100	1 000	1 000	650	800	400	350	400	1 050	42.0
3000	1 200	1 100	1 050	700	850	450	400	450	1 150	38.3
3500	1 250	1 150	1 100	700	900	450	400	450	1 250	35.7
4000	1 300	1 200	1 200	750	900	500	450	450	1 350	33.8
5000	1 450	1 300	1 250	800	1 000	500	450	500	1 500	30.0
7000	1 650	1 500	1 450	900	1 150	600	550	600	1 700	24.3
10000	1 850	1 700	1 600	1 050	1 300	700	700	700	2 000	20.0
15000	2 150	1 950	1 800	1 200	1 500	850	1 000	850	2 350	15.7
20000	2 400	2 200	1 950	1 350	1 650	1 000	1 250	1 000	2 550	12.8
30000	2 800	2 550	2 250	1 550	1 900	1 250	1 750	1 250	2 900	9.7
40000	3 100	2 800	2 500	1 800	2 100	1 500	2 250	1 500	3 150	7.9
50000	3 350	3 050	2 750	2 000	2 300	1 700	2 650	1 650	3 400	6.8
100000	4 250	4 000	3 750	3 000	3 400	2 400	4 650	2 250	4 300	4.3
150000	5 000	4 850	4 600	3 850	4 450	2 850	6 350	2 500	5 000	3.3
200000	5 750	5 650	5 400	4 550	5 350	3 200	7 950	2 650	5 600	2.8
300000	7 250	7 250	6 850	5 550	6 750	3 700	10 850	2 800	6 650	2.2
500000	10 150	10 050	9 250	7 000	8 600	4 250	. .	2 800	8 350	1.7
1000000	15 100	15 250	13 200	8 900	10 950	4 850	. .	. .	11 750	1.2
2000000	20 350	22 550	17 700	10 600	12 700	. .	. .	. .	17 050	0.9
5000000	25 900	36 100	23 900	11 900	13 250	. .	. .	. .	28 450	0.6
10000000	27 750	49 750	27 950	. .	. .	. .	. .	. .	37 950	0.4
. . 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.
25% RSE
Mean weekly earnings	5 600	5 000	4 000	1 900	3 000	1 100	500	1 300	5 900
Median weekly earnings	6 300	5 500	5 100	2 500	3 800	1 400	700	1 500	7 200
Relative standard error of all other estimates	6 300	5 400	5 100	2 600	3 500	1 400	1 100	1 400	6 800
50% RSE
Mean weekly earnings	1 800	1 600	1 300	600	1 000	300	100	500	1 400
Median weekly earnings	2 000	1 800	1 700	800	1 200	400	200	600	1 800
Relative standard error of all other estimates	2 000	1 800	1 700	800	1 200	500	300	600	1 600