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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 300,300. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 5,950 and 7,500 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 294,300 to 306,300 and about 19 chances in 20 that the value will fall within the range 288,300 to 312,300. 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 (2.7%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.7 x 2.5 = 6.8%. The SE of this estimate of median duration of insufficient work is therefore 6.8% of 25, i.e. about 2 (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 23-27 weeks, and about 19 chances in 20 that it would have been within the range 21-29 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 300,300 female underemployed part-time workers, 104,200 or 34.7% had insufficient work for 52 weeks and over. The SE of 104,200 may be calculated by interpolation as 3,900. To convert this to an RSE we express the SE as a percentage of the estimate, or 3,900/104,200 = 3.7%. The SE for 300,300 was calculated previously as 6,000, which converted to an RSE is 6,000/300,300 = 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 1.1 percentage points (=(34.7/100)x3.1). 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 33.6% and 35.8% and 19 chances in 20 that the proportion is within the range 32.5% to 36.9%.

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
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Australia
Size of estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	270	260	190	160	180	100	110	90	100	100.0
200	360	340	280	210	240	150	160	140	170	85.0
300	430	400	340	250	280	180	210	180	240	80.0
500	530	490	440	310	340	220	270	230	340	68.0
700	610	550	510	350	390	250	310	260	430	61.4
1,000	700	640	590	400	450	290	360	290	550	55.0
1,500	830	740	700	470	520	340	420	310	700	46.7
2,000	930	830	790	530	580	370	470	330	830	41.5
2,500	1 000	900	850	550	650	400	500	350	950	38.0
3,000	1 100	950	900	600	700	400	550	350	1 050	35.0
3,500	1 150	1 050	1 000	650	700	450	550	400	1 100	31.4
4,000	1 200	1 100	1 050	700	750	450	600	400	1 200	30.0
5,000	1 300	1 150	1 100	750	800	500	650	450	1 350	27.0
7,000	1 500	1 350	1 250	850	950	550	800	500	1 550	22.1
10,000	1 700	1 500	1 400	950	1 050	650	1 000	600	1 800	18.0
15,000	2 000	1 750	1 550	1 100	1 200	800	1 350	700	2 100	14.0
20,000	2 200	1 950	1 700	1 200	1 350	900	1 750	850	2 300	11.5
30,000	2 550	2 250	1 950	1 400	1 550	1 150	2 400	1 050	2 600	8.7
40,000	2 850	2 500	2 200	1 600	1 700	1 400	3 050	1 250	2 850	7.1
50,000	3 100	2 750	2 400	1 800	1 900	1 600	3 650	1 450	3 050	6.1
100,000	3 950	3 550	3 250	2 700	2 750	2 250	6 350	1 900	3 850	3.9
150,000	4 600	4 350	4 000	3 450	3 650	2 700	. .	2 150	4 500	3.0
200,000	5 300	5 050	4 700	4 050	4 400	3 000	. .	2 300	5 050	2.5
300,000	6 700	6 500	5 950	5 000	5 500	3 450	. .	. .	5 950	2.0
500,000	9 350	9 000	8 050	6 250	7 000	. .	. .	. .	7 500	1.5
1,000,000	13 900	13 700	11 500	8 000	8 950	. .	. .	. .	10 550	1.1
2,000,000	18 750	20 250	15 450	. .	10 350	. .	. .	. .	15 300	0.8
5,000,000	23 900	32 400	20 850	. .	. .	. .	. .	. .	25 550	0.5
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	34 100	0.3
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	38 500	0.3
. . not applicable