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 3,154,800. Since the estimate is between 2,000,000 and 5,000,000, table T1 shows that the SE for Australia will lie between 19,750 and 32,950 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 3,130,000 to 3,179,600 and about 19 chances in 20 that the value will fall within the range 3,105,200 to 3,204,400. 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 19 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 3,154,800 part-time employees in main job and table 4 shows mean weekly earnings for the same group as $527. The SE of 3,154,800 was calculated previously as 24,800. To convert this to an RSE we express the SE as a percentage of the estimate, or 24,800/3,154,800 = 0.8%.

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 0.9): 0.8 x 0.9 = 0.72%. The approximate SE of this estimate of mean weekly earnings of part-time employees in main job is therefore 0.72% of $527, that is $4 (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 $523 to $531, and about 19 chances in 20 that it would have been within the range $519 to $535.

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 3,154,800 part-time employees in their main job, 887,100 or 28.1% were males. The SE and RSE of 3,154,800 were calculated previously as 24,800 and 0.8% respectively. The SE for 887,100 calculated by interpolation is 12,700 which converted to a RSE is 12,700/887,100 = 1.4%. Applying the above formula, the RSE of the proportion is:

13 The SE for the proportion, 28.1%, of male part-time employees, is 0.3 percentage points, calculated as (28.1/100)x1.1. There are about two chances in three that the proportion of male part-time employees, was between 27.8% and 28.4%, and 19 chances in 20 that the proportion is within the range 27.5% to 28.7%.


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
										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	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	130	320	440	88.0
	700	810	530	650	430	530	270	150	360	560	80.0
	1,000	930	610	760	490	610	310	170	400	700	70.0
	1,500	1 100	710	900	580	710	350	200	430	900	60.0
	2,000	1 230	800	1 010	640	790	390	220	460	1 070	53.5
	2,500	1 350	850	1 100	700	850	400	250	500	1 200	48.0
	3,000	1 450	950	1 200	750	900	450	250	500	1 350	45.0
	3,500	1 550	1 000	1 250	800	1 000	450	250	550	1 450	41.4
	4,000	1 600	1 050	1 300	850	1 050	500	300	550	1 550	38.8
	5,000	1 750	1 150	1 400	900	1 100	500	300	600	1 700	34.0
	7,000	2 000	1 300	1 600	1 000	1 250	600	350	700	2 000	28.6
	10,000	2 300	1 450	1 800	1 150	1 450	700	450	800	2 300	23.0
	15,000	2 650	1 700	2 000	1 300	1 650	850	650	1 000	2 700	18.0
	20,000	2 950	1 900	2 200	1 450	1 850	950	800	1 150	3 000	15.0
	30,000	3 400	2 200	2 500	1 700	2 100	1 250	1 150	1 500	3 350	11.2
	40,000	3 800	2 400	2 800	1 950	2 350	1 450	1 450	1 750	3 650	9.1
	50,000	4 100	2 600	3 050	2 200	2 550	1 650	1 750	2 000	3 950	7.9
	100,000	5 200	3 450	4 200	3 300	3 750	2 400	3 000	2 650	4 950	5.0
	150,000	6 100	4 150	5 150	4 250	4 950	2 850	4 100	3 000	5 800	3.9
	200,000	7 050	4 850	6 000	4 950	5 950	3 150	5 150	3 150	6 500	3.3
	300,000	8 850	6 250	7 650	6 100	7 500	3 650	7 050	3 300	7 700	2.6
	500,000	12 400	8 650	10 300	7 650	9 550	4 200	. .	3 300	9 650	1.9
	1,000,000	18 400	13 150	14 700	9 750	12 150	4 800	. .	. .	13 600	1.4
	2,000,000	24 800	19 450	19 800	11 600	14 100	. .	. .	. .	19 750	1.0
	5,000,000	31 600	31 100	26 700	13 050	14 700	. .	. .	. .	32 950	0.7
	10,000,000	33 850	42 900	31 200	. .	. .	. .	. .	. .	44 000	0.4
	15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	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.
25% RSE
Mean weekly earnings	7 750	3 940	4 710	2 250	3 560	1 060	170	1 570	7 710
Median weekly earnings	8 710	4 340	6 020	2 840	4 450	1 330	280	1 820	9 300
Relative standard error of all other estimates	8 600	4 240	6 070	2 970	4 170	1 380	500	1 800	8 760
50% RSE
Mean weekly earnings	2 520	1 280	1 550	730	1 170	330	20	620	1 950
Median weekly earnings	2 840	1 420	2 020	930	1 470	430	40	740	2 490
Relative standard error of all other estimates	2 800	1 390	2 040	980	1 370	450	110	730	2 310