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TECHNICAL NOTE RELIABILITY OF ESTIMATES


RELIABILITY OF ESTIMATES

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, tables of SEs and RSEs for estimates of numbers of persons and estimates of numbers of training courses and qualifications appear at the end of these Technical Notes. Each SE table is derived from a mathematical model, referred to as the "SE model", which is created using the data collected in this survey. 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 among SEs for different estimates of the same size. SEs and RSEs for estimates of earnings, income and mean, median and total training hours have not been included in this publication, but are available on request.

Calculation of standard errors

3 An example of the calculation and use of SEs in relation to estimates of numbers of persons is as follows. Table 15 shows that the estimated number of persons aged 25 to 34 who have completed one non-school qualification is 1,160,600. Since this estimate is between 1,000,000 and 2,000,000 in the SE table for person estimates, the SE will be between 15,600 and 20,600, and can be approximated by interpolation as 16,400 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 16,400 persons of the survey estimate, i.e. in the range 1,144,200 to 1,177,000, and about 19 chances in 20 that the value will fall within 32,800 persons of the survey estimate, i.e. in the range 1,127,800 to 1,193,400. This example is illustrated in the diagram below.

6 The SE can be calculated from the RSE and the estimate using the following formula:

PROPORTIONS AND PERCENTAGES

7 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:

8 Consider the example above of the number of people who have completed one non-school qualification aged 25 to 34 (1,160,600). Of these, 596,100 or 51.4% were estimated to be male. The SE of 1,160,600 is approximately 16,400 so the RSE is 1.4%. The RSE for 596,100 is 2.1%. Applying the formula above, the RSE of the proportion is 1.5%, giving a SE for the proportion (51.4%) of 0.8 percentage points. Therefore there are about two chances in three that the proportion of persons aged 25 to 34 who have completed one non-school qualification who were male is between 50.6% and 52.2%, and 19 chances in 20 that the proportion is within the range 49.8% and 53.0%.

Differences

9 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:

10 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub-populations, it is expected to provide a good approximation for all differences likely to be of interest in this publication. Actual RSEs are available on request.

Standard Errors

STANDARD ERRORS OF PERSON 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	150	140	130	110	120	90	110	70	150	150.0
200	230	220	210	170	190	150	170	130	220	110.0
300	300	280	270	220	240	200	210	170	280	93.3
500	420	390	370	300	320	270	280	240	380	76.0
700	510	480	450	360	390	320	340	300	460	65.7
1,000	630	590	550	440	470	390	410	370	560	56.0
1,500	800	750	690	550	590	480	490	450	700	46.7
2,000	940	880	810	630	680	550	560	520	810	40.5
2,500	1 050	1 000	900	700	750	600	600	600	900	36.0
3,000	1 200	1 100	1 000	800	850	650	650	600	1 000	33.3
3,500	1 300	1 200	1 100	850	900	700	700	650	1 100	31.4
4,000	1 350	1 250	1 150	900	950	750	750	700	1 200	30.0
5,000	1 550	1 400	1 300	1 000	1 100	800	800	750	1 300	26.0
7,000	1 850	1 700	1 550	1 150	1 250	900	900	850	1 600	22.9
10,000	2 150	2 000	1 800	1 350	1 500	1 000	1 050	950	1 900	19.0
15,000	2 650	2 450	2 200	1 600	1 800	1 150	1 150	1 000	2 300	15.3
20,000	3 000	2 750	2 500	1 800	2 000	1 250	1 250	1 100	2 650	13.3
30,000	3 600	3 300	2 950	2 150	2 400	1 350	1 400	1 150	3 250	10.8
40,000	4 050	3 750	3 350	2 400	2 700	1 450	1 500	1 200	3 750	9.4
50,000	4 450	4 100	3 650	2 600	2 950	1 500	1 600	1 200	4 150	8.3
100,000	5 850	5 350	4 750	3 300	3 850	1 650	1 800	1 200	5 750	5.8
150,000	6 800	6 200	5 500	3 800	4 500	1 700	1 900	1 200	6 900	4.6
200,000	7 550	6 850	6 100	4 150	4 950	1 750	2 000	1 150	7 850	3.9
300,000	8 650	7 850	7 000	4 650	5 700	1 750	. .	1 050	9 400	3.1
500,000	10 150	9 250	8 200	5 350	6 750	1 750	. .	. .	11 700	2.3
1,000,000	12 400	11 250	10 000	6 400	8 350	. .	. .	. .	15 600	1.6
2,000,000	14 800	13 400	12 000	7 400	10 100	. .	. .	. .	20 600	1.0
5,000,000	18 100	16 350	14 750	. .	. .	. .	. .	. .	29 350	0.6
10,000,000	20 600	. .	. .	. .	. .	. .	. .	. .	37 900	0.4
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	43 850	0.3
20,000,000	. .	. .	. .	. .	. .	. .	. .	. .	48 500	0.2
. . not applicable

ESTIMATES WITH RELATIVE STANDARD ERRORS OF 25% AND 50%
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Aust.
Size of estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.
Estimates with RSEs of 25%	7 600	6 500	5 400	3 200	3 700	2 400	2 400	2 200	5 600
Estimates with RSEs of 50%	1 700	1 500	1 200	800	900	600	700	500	1 300

STANDARD ERRORS OF WORK-RELATED TRAINING COURSES & QUALIFICATION ESTIMATES
									AUST.
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	SE	RSE
Size of estimate (training & qualifications)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	210	230	180	160	210	140	140	120	270	270.0
200	330	350	280	250	310	210	230	180	390	195.0
300	420	440	360	310	390	260	300	240	480	160.0
500	570	580	500	430	510	340	410	330	620	124.0
700	700	700	610	520	610	410	510	410	730	104.3
1,000	860	850	750	640	740	500	620	500	880	88.0
1,500	1 100	1 070	960	800	910	620	780	640	1 080	72.0
2,000	1 300	1 250	1 130	940	1 060	730	920	750	1 250	62.5
2,500	1 450	1 400	1 300	1 050	1 200	800	1 050	850	1 400	56.0
3,000	1 650	1 550	1 450	1 200	1 300	900	1 150	950	1 550	51.7
3,500	1 800	1 700	1 550	1 300	1 400	1 000	1 200	1 000	1 650	47.1
4,000	1 950	1 800	1 700	1 400	1 500	1 050	1 300	1 100	1 800	45.0
5,000	2 200	2 050	1 900	1 550	1 700	1 200	1 450	1 250	2 000	40.0
7,000	2 650	2 450	2 300	1 850	2 050	1 450	1 700	1 450	2 350	33.6
10,000	3 200	2 950	2 800	2 250	2 450	1 750	2 000	1 750	2 850	28.5
15,000	4 000	3 700	3 450	2 750	3 000	2 150	2 350	2 150	3 500	23.3
20,000	4 700	4 300	4 000	3 200	3 450	2 500	2 650	2 450	4 050	20.3
30,000	5 850	5 300	4 950	3 950	4 200	3 100	3 050	2 950	5 000	16.7
40,000	6 800	6 150	5 750	4 550	4 850	3 600	3 400	3 400	5 750	14.4
50,000	7 650	6 900	6 400	5 050	5 400	4 050	3 650	3 700	6 450	12.9
100,000	11 000	9 850	9 050	7 050	7 550	5 850	4 500	4 950	9 200	9.2
150,000	13 550	12 050	11 000	8 500	9 150	7 250	5 000	5 800	11 350	7.6
200,000	15 650	13 950	12 550	9 650	10 500	8 400	5 400	6 500	13 150	6.6
300,000	19 200	17 050	15 150	11 600	12 700	10 400	. .	7 500	16 200	5.4
500,000	24 700	22 000	19 100	14 500	16 100	13 550	. .	. .	21 000	4.2
1,000,000	34 550	30 850	25 850	19 450	22 150	. .	. .	. .	30 000	3.0
2,000,000	48 000	43 050	34 600	25 800	30 250	. .	. .	. .	42 800	2.1
5,000,000	73 200	66 450	50 000	. .	. .	. .	. .	. .	68 450	1.4
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	97 750	1.0
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	120 350	0.8
. . not applicable

ESTIMATES WITH RELATIVE STANDARD ERRORS OF 25% AND 50%
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Aust.
Size of estimate (training & qualifications)	no.	no.	no.	no.	no.	no.	no.	no.	no.
Estimates with RSEs of 25%	17 500	14 500	12 600	8 000	9 400	4 500	6 600	4 900	13 000
Estimates with RSEs of 50%	3 700	3 300	2 700	1 800	2 300	1 000	1 700	1 000	3 200