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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 female part-time employees in main job was 1,762,000. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows that the SE for Australia will lie between 11,550 and 15,250 and can be approximated by interpolation using the following general formula:

4 Therefore, 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 1,747,600 to 1,776,400 and about 19 chances in 20 that the value will fall within the range 1,733,200 to 1,790,800. This example is illustrated in the diagram below.

MEANS AND MEDIANS

6 The RSEs of estimates of mean and median weekly earnings (see paragraphs 18 and 19 of the Explanatory Notes) are obtained by first finding the RSE of the estimate of the total number of persons contributing to the estimate (see table T1) and then multiplying the resulting number by the following factors:

mean weekly earnings: 0.8
median weekly earnings: 1.0

8 The RSE of the estimate of mean weekly earnings is calculated by multiplying this number (0.8%) by the appropriate factor shown in paragraph 6 (in this case 0.8): 0.8 x 0.8 =0.6%. The approximate SE of this estimate of mean weekly earnings of female part-time employees in main job is therefore 0.6% of $355, that is about $2.10. 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 $352.90 to $357.10, and about 19 chances in 20 that it would have been within the range $350.80 to $359.20.

PROPORTIONS AND PERCENTAGES

9 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.

10 Considering the example from the previous page, the 1,762,000 females who were part-time employees in their main job represent 46.3% of the 3,802,200 female employees. The SE and RSE of 1,762,000 were calculated previously as 14,400 and 0.8% respectively. The SE for 3,802,200 calculated by interpolation is 20,100, which converted to a RSE is 20,100/3,802,200 =0.5%. Applying the above formula, the RSE of the proportion is:

11 Therefore, the SE for the proportion (46.3%) is 0.3 percentage points (=(46.3/100)x 0.6). Therefore, there are about two chances in three that the proportion of female part-time employees was between 46.0% and 46.6%, and 19 chances in 20 that the proportion is within the range 45.7% to 46.9%.

DIFFERENCES

12 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:

13 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
									AUST.
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	SE	RSE
Size of estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	90	100	180	160	160	110	110	130	80	80.0
200	160	170	260	220	220	140	140	160	140	70.0
300	220	230	310	260	260	170	170	180	190	63.3
500	330	320	390	320	340	210	210	220	270	54.0
700	420	400	460	370	390	240	240	240	350	50.0
1,000	530	500	540	420	460	280	280	270	440	44.0
1,500	690	630	650	500	550	330	330	310	580	38.7
2,000	820	750	740	570	620	370	370	350	700	35.0
2,500	950	850	800	600	700	400	400	400	800	32.0
3,000	1,050	950	900	650	750	450	450	400	900	30.0
3,500	1,150	1,000	950	700	800	450	450	450	1,000	28.6
4,000	1,250	1,100	1,000	750	850	500	500	450	1,050	26.3
5,000	1,400	1,200	1,100	850	900	550	500	500	1,200	24.0
7,000	1,650	1,400	1,300	950	1,050	600	600	550	1,450	20.7
10,000	1,950	1,700	1,500	1,100	1,200	700	700	650	1,750	17.5
15,000	2,350	2,000	1,800	1,300	1,450	800	800	750	2,150	14.3
20,000	2,700	2,250	2,050	1,450	1,600	900	850	850	2,450	12.3
30,000	3,150	2,650	2,450	1,700	1,850	1,050	1,000	1,000	2,950	9.8
40,000	3,500	2,900	2,750	1,900	2,100	1,200	1,150	1,100	3,350	8.4
50,000	3,800	3,150	3,000	2,100	2,250	1,300	1,200	1,250	3,700	7.4
100,000	4,750	4,000	4,000	2,750	2,900	1,700	1,550	1,650	4,850	4.9
150,000	5,350	4,600	4,750	3,250	3,350	1,950	1,800	2,000	5,600	3.7
200,000	5,900	5,150	5,300	3,650	3,750	2,150	2,000	2,300	6,250	3.1
300,000	6,900	6,100	6,250	4,300	4,300	2,500	. .	2,750	7,250	2.4
500,000	8,550	7,700	7,650	5,250	5,050	3,050	. .	. .	8,800	1.8
1,000,000	11,950	10,800	10,050	6,850	6,350	. .	. .	. .	11,550	1.2
2,000,000	17,600	15,650	13,100	9,000	7,800	. .	. .	. .	15,250	0.8
5,000,000	31,550	26,900	18,450	. .	. .	. .	. .	. .	23,400	0.5
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	40,950	0.4
. . not applicable

T2 LEVELS AT WHICH ESTIMATES HAVE RSE'S OF 25% AND 50%(a)
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Aust.
	no.	no.	no.	no.	no.	no.	no.	no.	no.
25% RSE
Mean weekly earnings	5,500	4,200	3,800	2,200	2,600	1,100	1,100	1,000	4,000
Median weekly earnings	6,800	5,200	4,600	2,600	3,200	1,300	1,300	1,200	5,100
All other estimates	6,200	4,700	4,100	2,500	2,900	1,200	1,200	1,100	4,600
50% RSE
Mean weekly earnings	1,000	900	1,100	700	800	300	300	400	600
Median weekly earnings	1,300	1,100	1,300	800	900	400	400	400	800
All other estimates	1,200	1,000	1,200	800	900	400	400	400	700
(a) Refers to the number of persons contributing to the estimate.