8146.0 - Household Use of Information Technology, Australia, 2004-05

ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 15/12/2005

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TECHNICAL NOTE

RELIABILITY OF THE ESTIMATES

1 As the estimates in this publication are based on information obtained from a sample of households and persons, they are subject to sampling variability. That is, they may differ from the figures that would have been produced if all households and persons in Australia 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 households and persons was included. There are about 2 chances in 3 that a sample estimate will differ by less than one SE from the figure that would have been obtained if all households and persons had been included in the survey and about 19 chances in 20 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.

3 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 annotated to indicate they are subject to higher SEs and should be used with caution. Estimates with RSEs of 10% to less than 25% are preceded by a (^), and estimates with RSEs of 25% to 50% are preceded by an asterisk (*) to indicate that they should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (**) to indicate that they are considered too unreliable for general use.

4 To assist readers of this publication to ascertain the approximate levels of reliability of estimates throughout this publication, tables of SEs and RSEs for certain estimates of population counts for the data appear at the end of this Technical Note. These values do not give a precise measure of the SEs or RSEs for a particular estimate but will provide an indication of their magnitude.

USING STANDARD ERRORS FOR POPULATION ESTIMATES

5 An example of the use of SEs in relation to estimates is as follows.

6 From table 3.4, it is estimated that 7,793,000 households accessed the Internet from home in 2004-05. Since this estimate is between 5,000,000 and 10,000,000, the SE for Australia will lie between 41,850 and 52,200 and can be approximated by interpolation to be 48,000. This estimate has a SE of around 48,000. This means there are about two chances in three that the value that would have been obtained from a complete census is within the range 7,745,000 to 7,841,000 households and about 19 chances in 20 that the true value is in the range 7,697,000 to 7,889,000 households.

7 Particular care should be taken when comparing figures over time. It is not correct to assume that an apparent difference between figures is actually significant. Such an estimate is subject to sampling error. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:

8 The estimated increase in the number of adults who purchased or ordered goods or services over the Internet in 2004-05 was 2,500,000 people (from 2,204,000 persons in 2002 to 4,704,000 in 2004-05). The SE on this movement has been calculated to be around 69,000. There are 2 chances in 3 that the true value is within the range 2,431,000 to 2,569,000 persons and 19 chances in 20 that the true value is in the range 2,362,000 to 2,638,000 persons.

TABLES OF STANDARD ERRORS AND RELATIVE STANDARD ERRORS

STANDARD ERRORS OF PERSON ESTIMATES-2004-05

		STANDARD ERROR								AUSTRALIA
		NSW	VIC	Qld	SA	WA	Tas.	NT	ACT	Standard error	Relative standard error
		no.	no.	no.	no.	no.	no.	no.	no.	no.	%

Size of estimate
	100	200	510	200	240	270	190	160	220	180	180
	200	340	710	330	360	400	290	250	330	290	145
	300	450	860	450	460	500	360	320	410	390	130
	500	650	1 090	640	620	670	480	440	540	560	112
	700	820	1 280	810	750	800	580	540	650	700	100
	1,000	1 050	1 510	1 020	910	970	690	670	780	890	89
	1,500	1 370	1 810	1 320	1 130	1 200	860	840	950	1 160	77
	2,000	1 640	2 070	1 580	1 310	1 390	990	990	1 080	1 390	70
	2,500	1 900	2 300	1 800	1 500	1 550	1 100	1 100	1 200	1 600	64
	3,000	2 100	2 500	2 000	1 600	1 700	1 200	1 250	1 300	1 800	60
	3,500	2 350	2 650	2 200	1 750	1 850	1 300	1 350	1 400	2 000	57
	4,000	2 550	2 850	2 400	1 900	1 950	1 400	1 450	1 500	2 150	54
	5,000	2 900	3 150	2 700	2 100	2 200	1 550	1 600	1 650	2 450	49
	7,000	3 550	3 650	3 300	2 450	2 550	1 800	1 950	1 900	3 000	43
	10,000	4 350	4 300	3 950	2 950	3 050	2 150	2 300	2 150	3 700	37
	15,000	5 400	5 150	4 900	3 550	3 650	2 550	2 800	2 550	4 650	31
	20,000	6 350	5 850	5 650	4 050	4 150	2 900	3 250	2 850	5 450	27
	30,000	7 850	7 000	6 850	4 850	5 000	3 450	3 900	3 250	6 750	23
	40,000	9 100	7 950	7 850	5 500	5 650	3 850	4 450	3 600	7 850	20
	50,000	10 150	8 800	8 650	6 000	6 200	4 250	4 900	3 900	8 800	18
	100,000	14 150	11 900	11 600	8 000	8 300	5 550	6 600	4 800	12 450	13
	150,000	17 050	14 200	13 600	9 400	9 750	6 500	7 800	5 400	15 100	10
	200,000	19 350	16 100	15 150	10 500	10 900	7 200	8 750	5 850	17 250	9
	300,000	23 000	19 200	17 450	12 200	12 750	8 350	-	6 500	20 700	7
	500,000	28 300	23 950	20 650	14 650	15 400	9 950	-	-	25 800	5
	1,000,000	36 800	32 200	25 350	18 500	19 700	-	-	-	34 200	3
	2,000,000	46 900	43 150	30 350	23 000	24 850	-	-	-	44 600	2
	5,000,000	62 500	63 400	36 950	-	-	-	-	-	61 500	1
	10,000,000	-	-	-	-	-	-	-	-	76 800	1
	15,000,000	-	-	-	-	-	-	-	-	86 700	1
	20,000,000	-	-	-	-	-	-	-	-	94 100	1

- nil or rounded to zero (including null cells)

Person estimates with relative standard errors of 25% to 50%-2004-05

		NSW no.	Vic no.	Qld no.	SA no.	WA no.	Tas. no.	NT no.	ACT no.	Aust. no.

Size of estimate
	Estimate with RSEs of 25%	32 919	26 576	25 385	13 496	14 381	7 434	8 555	7 918	23 927
	Estimate with RSEs of 30%	22 480	19 135	17 796	9 575	10 254	5 283	5 898	5 801	16 001
	Estimate with RSEs of 35%	16 107	14 483	13 035	7 124	7 669	3 938	4 272	4 433	11 259
	Estimate with RSEs of 40%	11 960	11 372	9 865	5 489	5 943	3 040	3 209	3 496	8 228
	Estimate with RSEs of 45%	9 129	9 183	7 656	4 346	4 732	2 412	2 481	2 824	6 192
	Estimate with RSEs of 50%	7 124	7 582	6 062	3 517	3 852	1 956	1 961	2 326	4 770

STANDARD ERRORS OF HOUSEHOLD ESTIMATES-2004-05

		STANDARD ERROR								Australia
		NSW no.	Vic no.	Qld no.	SA no.	WA no.	Tas. no.	NT no.	ACT no.	Standard error no.	Relative standard error %

Size of estimate
	100	130	340	130	160	180	130	110	140	120	120
	200	220	470	220	360	260	190	170	220	200	100
	300	300	570	300	460	330	240	210	270	270	90
	500	430	720	420	620	440	320	290	360	380	76
	700	540	840	530	750	530	380	360	430	480	69
	1,000	690	990	670	910	640	460	440	510	600	60
	1,500	900	1 200	870	1 130	790	560	560	620	790	53
	2,000	1 090	1 370	1 050	1 310	920	650	650	720	950	48
	2,500	1 250	1 500	1 200	1 500	1 050	750	750	800	1 100	44
	3,000	1 400	1 650	1 350	1 600	1 100	800	800	850	1 200	40
	3,500	1 550	1 750	1 450	1 750	1 200	850	900	900	1 350	39
	4,000	1 650	1 850	1 600	1 900	1 300	900	950	1 000	1 450	36
	5,000	1 900	2 050	1 800	2 100	1 450	1 000	1 050	1 100	1 650	33
	7,000	2 350	2 400	2 150	2 450	1 700	1 200	1 300	1 250	2 050	29
	10,000	2 850	2 850	2 600	2 950	2 000	1 400	1 550	1 450	2 500	25
	15,000	3 600	3 400	3 250	3 550	2 400	1 700	1 850	1 700	3 150	21
	20,000	4 200	3 850	3 750	4 050	2 750	1 900	2 150	1 850	3 700	19
	30,000	5 200	4 650	4 550	4 850	3 300	2 250	2 600	2 150	4 600	15
	40,000	6 000	5 250	5 150	5 500	3 750	2 550	2 950	2 400	5 350	13
	50,000	6 700	5 800	5 700	6 000	4 100	2 800	3 250	2 550	6 000	12
	100,000	9 350	7 850	7 650	8 000	5 450	3 650	4 350	3 200	8 450	9
	150,000	11 250	9 400	8 950	9 400	6 450	4 300	5 150	3 550	10 250	7
	200,000	12 800	10 650	10 000	10 500	7 200	4 750	5 800	3 850	11 700	6
	300,000	15 200	12 700	11 550	12 200	8 400	5 500	-	4 300	14 050	5
	500,000	18 700	15 800	13 650	14 650	10 150	6 550	-	-	17 550	4
	1,000,000	24 300	21 250	16 750	18 500	13 000	-	-	-	23 250	2
	2,000,000	30 950	28 500	20 050	23 000	16 400	-	-	-	30 350	2
	5,000,000	41 250	41 850	24 400	-	-	-	-	-	41 850	1
	10,000,000	-	-	-	-	-	-	-	-	52 200	1

- nil or rounded to zero (including null cells)

Household estimates with relative standard errors of 25% to 50%-2004-05

		NSW no.	Vic no.	Qld no.	SA no.	WA no.	Tas. no.	NT no.	ACT no.	Aust no.

Size of estimate
	Estimate with RSEs of 25%	13 519	12 552	11 065	6 108	6 597	3 380	3 609	3 854	10 041
	Estimate with RSEs of 30%	8 918	9 017	7 490	4 260	4 641	2 365	2 426	2 773	6 499
	Estimate with RSEs of 35%	6 185	6 812	5 306	3 120	3 430	1 737	1 717	2 085	4 434
	Estimate with RSEs of 40%	4 451	5 339	3 888	2 371	2 629	1 324	1 262	1 619	3 147
	Estimate with RSEs of 45%	3 296	4 305	2 924	1 853	2 073	1 038	956	1 290	2 302
	Estimate with RSEs of 50%	2 497	3 550	2 244	1 481	1 672	832	741	1 048	1 725