TECHNICAL NOTE DATA QUALITY


INTRODUCTION

1 Since the estimates published 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 (or occupants) 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.

2 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.

RSE% = (SE/estimate ) x 100

3 RSEs for 2008 Labour Mobility Survey estimates are published for the first time in 'direct' form. Previously a statistical model was produced that relates the size of estimates to their corresponding RSEs, and this information was displayed via a 'standard errors of estimates' table. RSEs for Labour Mobility Survey estimates will be calculated for each separate estimate and published individually. The Jackknife method of variance estimation is used for this process, which involves the calculation of 30 'replicate' estimates based on 30 different sub-samples of the original sample. The variability of estimates obtained from these sub samples is used to estimate the sample variability surrounding the main estimate.

4 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication. However, RSEs for all these estimates are released in spreadsheet format as an attachment to this publication, Labour Mobility, Australia (cat. no. 6209.0) on the ABS website. As a guide, the population estimates and RSEs for selected data from Table 10 is presented at table T1 in this Technical Note.

5 In the tables in this publication, only estimates (numbers and percentages) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *13.5) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g. **2.1) to indicate that they are considered too unreliable for general use.


CALCULATION OF STANDARD ERROR

6 The RSEs have been derived using the Jackknife method. SEs can be calculated from the estimates and their corresponding RSEs.

7 An example of the calculation of the SE from an RSE follows. Table T1 shows that there were an estimated 220,400 people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months. The RSE for this estimate is 5.5%. The SE is:

SE of estimate
= (RSE / 100) x estimate
= 0.055 x 220,400
= 12,100 (rounded to the nearest 100)

8 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 208,300 to 232,500 and about 19 chances in 20 that the value will fall within the range 196,200 to 244,600. This example is illustrated in the following diagram.

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 table T1, of the 611,600 people who ceased a job involuntarily during the year ending February 2008, 317,500 or 51.9% gave their main reason as 'Job was temporary or seasonal'. The RSE for 317,500 is 4.1% and the RSE for 611,600 is 2.6%. Applying the above formula, the RSE for the proportion of people who gave their main reason as 'Job was temporary or seasonal' is:



11 Therefore, the SE for the proportion of people who gave their main reason as 'Job was temporary or seasonal' is 1.6 percentage points (=(51.9/100)x3.17). Therefore, there are about two chances in three that the proportion of persons who gave their main reason for involuntarily ceasing their last job as 'Job was temporary or seasonal' is between 49.1% and 54.7% and 19 chances in 20 that the proportion is within the range 46.3% to 57.5%.


SUM OR DIFFERENCES BETWEEN ESTIMATES

12 Published estimates may also be used to calculate the sum of, or difference between, two survey estimates (of numbers or percentages). Such estimates are also subject to sampling error.

13 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:



14 The sampling error of the sum of two estimates is calculated in a similar way. An approximate SE of the sum of two estimates (x+y) may be calculated by the following formula:



15 An example follows. From paragraph 7 the estimated number of people who gave their main reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months is 220,400 and the SE is 12,100. From table T1, the estimate of people who reported their main reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was '1 year and under 2 years' is 44,900 and the SE is 4,700. The estimate of people who reported their main reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 2 years is:

220,400 + 44,900 = 265,300

16 The SE of the estimate of people whose duration of last job was less than 2 years and gave their main reason for ceasing last job as 'Job was temporary or seasonal' is:



17 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 252,300 to 278,300 and about 19 chances in 20 that the value will fall within the range 239,300 to 291,300.

18 While these formula will only be exact for sums of, or differences between, separate and uncorrelated characteristics or sub-populations, it is expected to provide a good approximation for all sums or differences likely to be of interest in this publication.


SELECTED ESTIMATES AND RELATIVE STANDARD ERRORS

T1 persons who ceased a job involuntarily during the year ending february 2008, Reason for ceasing last job
				REASON FOR CEASING LAST JOB
Duration of last job				Retrenched, employer went out of business	Job was temporary or seasonal	Own ill health or injury	Total
Person counts
	Under 12 months		'000	89.3	220.4	32.2	341.8
		Under 3 months	'000	34.4	132.5	13.1	180.1
		3 months and under 6 months	'000	20.6	43.4	*6.9	70.8
		6 months and under 12 months	'000	34.3	44.5	12.1	90.9
	1 year and under 2 years		'000	32.9	44.9	13.8	91.6
	2 years and under 3 years		'000	20.3	18.2	8.7	47.2
	3 years and under 5 years		'000	22.9	11.3	10.0	44.2
	5 years and under 10 years		'000	16.9	14.0	9.5	40.4
	10 years and under 20 years		'000	13.8	*5.2	10.2	29.3
	20 years and over		'000	6.5	*3.5	*7.1	17.0
	Total		'000	202.6	317.5	91.4	611.6
Relative standard errors of person counts
	Under 12 months		RSE%	6.7	5.5	15.3	3.8
		Under 3 months	RSE%	11.9	6.2	20.7	4.9
		3 months and under 6 months	RSE%	15.5	8.6	30.5	6.3
		6 months and under months	RSE%	9.6	11.7	21.2	7.0
	1 year and under 2 years		RSE%	11.7	10.4	17.3	6.9
	2 years and under 3 years		RSE%	12.6	15.0	19.1	8.6
	3 years and under 5 years		RSE%	14.5	20.1	17.2	9.7
	5 years and under 10 years		RSE%	15.1	16.2	21.7	8.8
	10 years and under 20 years		RSE%	18.7	27.3	19.7	10.7
	20 years and over		RSE%	21.1	41.4	25.9	18.8
	Total		RSE%	4.7	4.1	6.9	2.6
* estimate has a relative standard error of 25% to 50% and should be used with caution