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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 underemployed part-time workers was 340,700. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 6,350 and 8,100 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 334,000 to 347,400 and about 19 chances in 20 that the value will fall within the range 327,300 to 354,100. This example is illustrated in the following diagram.

MEANS AND MEDIANS

6 The RSEs of estimates of mean duration of insufficient work, median duration of insufficient work and mean preferred number of extra hours 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:

• mean duration of insufficient work: 1.6
• median duration of insufficient work: 2.5
• mean preferred number of extra hours: 0.7

8 The RSE of the estimate of median duration of insufficient work is calculated by multiplying this number (2.8%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.8 x 2.5 = 7.0%. The SE of this estimate of median duration of insufficient work is therefore 7.0% of 21, i.e. about 1 (rounded to the nearest whole week). Therefore, there are two chances in three that the median duration of insufficient work for males that would have been obtained if all dwellings had been included in the survey would have been within the range 20-22 weeks, and about 19 chances in 20 that it would have been within the range 19-23 weeks.

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 paragraph 3, of the 340,700 female underemployed part-time workers, 121,400 or 35.6% had insufficient work for 52 weeks or more. The SE of 121,400 may be calculated by interpolation as 4,300. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,300/121,400 = 3.5%. The SE for 340,700 was calculated previously as 6,700, which converted to an RSE is 6,700/340,700 = 2.0%. Applying the above formula, the RSE of the proportion is:

11 Therefore, the SE for the proportion of females who have a current period of insufficient work of 52 weeks or more is 1.0 percentage points (=(35.6/100)x2.9). Therefore, there are about two chances in three that the proportion of females who have a current period of insufficient work of 52 weeks or more was between 34.6% and 36.6% and 19 chances in 20 that the proportion is within the range 33.6% to 37.6%.

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
	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	290	250	250	150	160	100	100	140	100	100.0
200	380	330	330	210	220	140	150	180	180	90.0
300	440	390	390	250	260	180	200	200	240	80.0
500	540	470	470	300	330	220	260	230	350	70.0
700	620	540	540	350	380	260	310	260	430	61.4
1000	710	620	610	400	440	300	360	280	540	54.0
1500	830	730	710	470	520	340	430	320	690	46.0
2000	920	810	790	530	590	370	470	340	820	41.0
2500	1 000	900	850	550	650	400	500	350	900	36.0
3000	1 100	950	900	600	700	400	550	400	1 000	33.3
3500	1 150	1 000	950	650	750	450	550	400	1 100	31.4
4000	1 200	1 050	1 000	700	750	450	600	400	1 200	30.0
5000	1 300	1 150	1 100	750	850	500	650	450	1 300	26.0
7000	1 500	1 300	1 250	850	950	550	800	500	1 550	22.1
10000	1 700	1 500	1 400	950	1 100	650	1 000	600	1 800	18.0
15000	2 000	1 750	1 600	1 100	1 250	800	1 300	750	2 100	14.0
20000	2 200	1 950	1 800	1 200	1 400	950	1 650	850	2 300	11.5
30000	2 600	2 300	2 050	1 450	1 600	1 250	2 250	1 100	2 650	8.8
40000	2 850	2 550	2 250	1 700	1 750	1 500	2 800	1 350	2 900	7.3
50000	3 100	2 800	2 450	1 900	1 950	1 750	3 350	1 500	3 100	6.2
100000	4 050	3 600	3 400	2 900	3 050	2 600	6 000	2 050	4 000	4.0
150000	4 800	4 350	4 250	3 700	4 100	3 200	8 500	2 350	4 700	3.1
200000	5 550	5 200	5 100	4 400	4 950	3 650	11 000	2 450	5 300	2.7
300000	7 100	6 800	6 800	5 450	6 250	4 300	15 900	2 550	6 350	2.1
500000	9 950	9 300	9 550	6 900	7 950	5 150	. .	2 550	8 100	1.6
1000000	14 950	13 700	13 500	9 000	10 050	6 250	. .	. .	11 600	1.2
2000000	21 350	19 350	16 550	11 000	11 400	. .	. .	. .	17 150	0.9
5000000	31 500	28 550	17 350	13 000	11 500	. .	. .	. .	29 250	0.6
10000000	39 750	36 450	15 250	. .	. .	. .	. .	. .	39 200	0.4
15000000	. .	. .	. .	. .	. .	. .	. .	. .	44 050	0.3
. . not applicable

t2 levels at which estimates have relative standard errors of 25% and 50%(a)
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Australia
	no.	no.	no.	no.	no.	no.	no.	no.	no.
RSE of 25%
Mean duration of current period of insufficient work	11 700	10 400	9 200	4 300	6 000	2 400	3 500	2 000	12 900
Median duration of current period of insufficient work	28 800	24 600	23 600	13 300	14 200	6 200	. .	7 500	24 900
Mean preferred number of extra hours	3 300	3 200	2 500	1 500	1 800	900	1 400	700	3 000
All other estimates	5 400	4 400	4 100	2 200	2 600	1 300	1 800	1 200	5 500
RSE of 50%
Mean duration of current period of insufficient work	3 800	3 400	3 100	1 400	2 000	800	1 200	800	3 700
Median duration of current period of insufficient work	9 500	8 000	8 300	4 600	4 800	2 300	12 400	2 700	8 200
Mean preferred number of extra hours	1 100	1 000	800	500	600	300	400	300	500
All other estimates	1 800	1 400	1 400	700	800	400	500	400	1 200
. . not applicable
(a) Refers to the number of people contributing to the estimate.