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TECHNICAL NOTE DATA QUALITY

INTRODUCTION

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.

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

RSEs for Retirement and Retirement Intentions estimates have been calculated using the Jackknife method of variance estimation. This process 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.

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 available free-of-charge on the ABS web site <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Retirement and Retirement Intentions, Australia (cat. no. 6238.0). As a guide, the population estimates and RSEs for selected data from tables 1 and 3 are presented at table T1 and table T2 in this Technical Note.

In the tables in this publication, only estimates (numbers, percentages, means and medians) 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 AND RELATIVE STANDARD ERROR

RSEs are routinely presented as the measure of sampling error in this publication and related products. SEs can be calculated using the estimates (counts or means) and the corresponding RSEs.

An example of the calculation of the SE from an RSE follows. Table T1 shows that the estimated number of females aged 55–59 who retired from the labour force aged less than 55 years is 119,900, and the RSE for this estimate is 8.3%. The SE is:

SE of estimate
= (RSE / 100) x estimate
= 0.083 x 119,900
= 10,000 (rounded to the nearest 100)

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 109,900 to 129,900 and about 19 chances in 20 that the value will fall within the range 99,900 to 139,900. This example is illustrated in the following diagram.



Proportions and percentages

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 RSEs of proportions not provided in the spreadsheets is given below. This formula is only valid when x is a subset of y.



Considering table T1, of the 1,850,800 females who were retired from labour force, 1,013,100 or 54.7% were aged less than 55 years at retirement. The RSE of 1,013,100 is 3.2% and the RSE for 1,850,800 is 1.5% (as shown in the corresponding RSE table for T1). Applying the above formula, the RSE for the proportion of females who retired aged less than 55 years is:



Therefore, the SE for the proportion of females who retired from the labour force aged less than 55 years is 1.5 percentage points (= (54.7/100) x 2.8). Therefore, there are about two chances in three that the proportion of females who retired from the labour force aged less than 55 years is between 53.2% and 56.2%, and 19 chances in 20 that the proportion is within the range 51.7% to 57.7%.

Sums or Differences between estimates

Published estimates may also be used to calculate the sum of, or difference between, two survey estimates (of numbers, means or percentages) where these are not provided in the spreadsheets. Such estimates are also 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:



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:



An example follows. From paragraph 7 the estimated number of females aged 55–59 who retired from the labour force aged less than 55 years is 119,900 and the SE is 10,000. From table T1, the estimate of females aged 60–64 who retired from the labour force aged less than 55 years is 148,000, the RSE is 9.4% and the SE is 13,900 (rounded to nearest 100). The estimate of females aged 55–64 who retired from the labour force aged less than 55 years is:

119,900 + 148,000 = 267,900

The SE of the estimate of females aged 55–64 who retired from the labour force aged less than 55 years is:



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 250,800 to 285,000 and about 19 chances in 20 that the value will fall within the range 233,700 to 302,100.

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

SELECTED ESTIMATES AND RSES

AGE AT RETIREMENT FROM THE LABOUR FORCE (YEARS)
		Less than 55	55-59	60-64	65-69	70 and over	Total
ESTIMATES ('000)
Males
	Age group (years)
	45-49	25.0	-	-	-	-	25.0
	50-54	59.9	-	-	-	-	59.9
	55-59	50.7	24.0	-	-	-	74.8
	60-64	48.9	75.2	45.0	-	-	169.1
	65-69	67.4	58.3	118.2	59.7	-	303.6
	70 and over	109.0	176.3	228.1	191.1	115.7	820.3
	Total	361.0	333.8	391.3	250.9	115.7	1 452.7
Females
	Age group (years)
	45-49	54.5	-	-	-	-	54.5
	50-54	88.1	-	-	-	-	88.1
	55-59	119.9	31.8	-	-	-	151.7
	60-64	148.0	79.9	52.7	-	-	280.6
	65-69	153.3	79.6	95.9	38.2	-	367.0
	70 and over	449.4	151.4	173.5	88.5	46.3	909.0
	Total	1 013.1	342.7	322.1	126.6	46.3	1 850.8
Persons
	Age group (years)
	45-49	79.5	-	-	-	-	79.5
	50-54	148.0	-	-	-	-	148.0
	55-59	170.6	55.9	-	-	-	226.5
	60-64	196.9	155.1	97.6	-	-	449.7
	65-69	220.7	137.8	214.1	97.9	-	670.5
	70 and over	558.4	327.7	401.6	279.6	162.0	1 729.4
	Total	1 374.1	676.5	713.4	377.5	162.0	3 303.5
RSES OF ESTIMATES (%)
Males
	Age group (years)
	45-49	22.9	-	-	-	-	22.9
	50-54	14.8	-	-	-	-	14.8
	55-59	17.1	22.4	-	-	-	12.4
	60-64	12.7	14.8	20.1	-	-	9.5
	65-69	15.3	17.6	9.1	10.4	-	4.0
	70 and over	12.4	8.6	8.6	8.2	13.0	2.1
	Total	6.2	7.6	5.9	7.5	13.0	2.5
Females
	Age group (years)
	45-49	21.1	-	-	-	-	21.1
	50-54	12.1	-	-	-	-	12.1
	55-59	8.3	24.2	-	-	-	7.5
	60-64	9.4	12.0	16.4	-	-	5.3
	65-69	6.0	11.1	11.8	13.8	-	2.8
	70 and over	5.0	9.8	6.6	15.8	15.5	1.6
	Total	3.2	5.9	6.8	11.5	15.5	1.5
Persons
	Age group (years)
	45-49	14.2	-	-	-	-	14.2
	50-54	10.3	-	-	-	-	10.3
	55-59	8.2	17.7	-	-	-	6.8
	60-64	7.9	9.9	12.8	-	-	4.7
	65-69	5.6	10.9	7.2	6.9	-	2.3
	70 and over	4.6	6.0	6.0	7.4	9.4	1.3
	Total	2.9	5.1	4.0	6.0	9.4	1.3

T2 PERSONS AGED 45 YEARS AND OVER, Retirement and retirement intentions – By sex
					Males	Females	Persons
ESTIMATES ('000)
In the labour force					2 608.7	2 137.7	4 746.4
	Employed				2 521.6	2 055.8	4 577.3
		Full-time workers (a)			2 081.1	1 095.0	3 176.1
			Intends to continue with full-time work:		671.0	325.2	996.2
				Intends to retire from the labour force	615.9	309.1	925.0
				Did not know whether intends to retire from the labour force	55.1	*16.1	71.2
			Intends to retire from full-time work and work part time:		755.6	420.3	1 176.0
				Intends to retire from the labour force	659.0	351.2	1 010.2
				Never intends or did not know whether intends to retire from the labour force	96.6	69.1	165.7
			Did not know whether intends to take up part-time work:		474.1	271.2	745.4
				Intends to retire from the labour force	383.6	225.3	609.0
				Never intends or did not know whether intends to retire from the labour force	90.5	45.9	136.4
			Never intends to retire from full-time work		180.3	78.2	258.5
		Part-time workers (a) (b)			440.5	960.8	1 401.3
			Intends to retire from the labour force		295.8	786.7	1 082.5
			Did not know whether will retire		53.2	81.2	134.4
			Never intends to retire		91.5	92.8	184.4
	Unemployed (c)				87.2	81.9	169.1
Not in the Labour Force					1 661.0	2 391.8	4 052.7
	Retired from the labour force				1 452.7	1 850.8	3 303.5
	Not retired from the labour force				152.5	254.5	407.0
	Had never worked				55.7	286.5	342.2
Total					4 269.7	4 529.4	8 799.1

RSES OF ESTIMATES (%)
In the labour force					1.3	1.6	0.9
	Employed				1.4	1.7	1.0
		Full-time workers (a)			1.5	2.8	1.3
			Intends to continue with full-time work:		5.0	5.9	3.7
				Intends to retire from the labour force	5.6	6.5	4.0
				Did not know whether intends to retire from the labour force	18.2	32.9	17.8
			Intends to retire from full-time work and work part time:		4.1	4.7	3.4
				Intends to retire from the labour force	4.8	5.1	3.8
				Never intends or did not know whether intends to retire from the labour force	14.9	17.7	10.2
			Did not know whether intends to take up part-time work:		5.4	7.3	4.6
				Intends to retire from the labour force	6.2	8.1	4.6
				Never intends or did not know whether intends to retire from the labour force	16.5	18.0	13.1
			Never intends to retire from full-time work		8.5	10.5	6.0
		Part-time workers (a) (b)			5.1	3.1	2.6
			Intends to retire from the labour force		5.4	4.0	3.2
			Did not know whether will retire		15.8	12.1	7.9
			Never intends to retire		12.0	12.1	9.5
	Unemployed (c)				13.8	10.2	8.6
Not in the Labour Force					2.1	1.4	1.1
	Retired from the labour force				2.5	1.5	1.3
	Not retired from the labour force				11.4	7.7	7.8
	Had never worked				14.8	7.9	6.9
Total					–	–	–