Australian Bureau of Statistics
Celebrating the International Year of Statistics 2013

TECHNICAL NOTE DATA QUALITY


RELIABILITY OF THE ESTIMATES

1 Since the estimates in this publication are based on information obtained from a sample of persons, they are subject to sampling variability. That is, they may differ from those that would have been produced had all persons 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 persons was included. There are about 2 chances in 3 that the sample estimate will differ by less than one SE from the number that would have been obtained if all persons had been surveyed, 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 RSEs for these estimates are available to download free-of-charge as Excel spreadsheets from Attendance at Selected Cultural Venues and Events, Australia, 2009-10 (cat. no. 4114.0).

4 In the tables in this publication, only estimates (numbers or 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.*3.4) to indicate they are subject to high SEs relative to their estimate 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 ERRORS

5 Standard errors can be calculated using the estimates (counts or percentages) and the corresponding RSEs. For example, Table 3 shows the estimated number of Females 15-17 years old who attended popular music concerts to be 187,600. The corresponding RSE table available on the ABS website shows the RSE for this estimate is 11.7%. The SE is calculated by:



6 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 165,700 and 209,500 and about 19 chances in 20 that the value will fall within the range 143,800 to 231,400. This example is illustrated in the diagram below.

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. The formula to approximate the RSE of a percentage is given below. The formula is only valid when x is a subset of y:



8 As an example, using estimates from Table 3, of the 405,700 females age 15-17 years, 187,600, or 46.2% attended popular music concerts in the 12 months prior to being surveyed. The RSE for 187,600 is 11.7% and the RSE for 405,700 is 5.7% (see Table 3 Relative Standard Errors in the RSE Tables section on the ABS website). Applying the above formula, the RSE for the percentage of females age 15-17 years who attended popular music concerts in the 12 months prior to being surveyed is:



9 Therefore, the SE for the percentage of females age 15-17 years who attended popular music concerts in the 12 months prior to being surveyed, is 4.7 percentage points (=10.22/100 x 46.2%). Hence, there are about two chances in three that the percentage of females age 15-17 years who attended popular music concerts in the 12 months prior to being surveyed is between 41.5% and 50.9%, and 19 chances in 20 that the percentage is between 36.8% and 55.6%.


DIFFERENCES

10 Published estimates may also be used to calculate the difference between two survey estimates (of counts 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:




SIGNIFICANCE TESTING

11 A statistical significance test for any of the comparisons between estimates can be performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula shown prior to this paragraph. This standard error is then used to calculate the following test statistic:



12 If the absolute value of this test statistic is greater than 1.96, there is evidence of a statistically significant difference (with a 95% level of confidence) in the two estimates with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations with respect to that characteristic.

13 The selected tables in this publication that show the results of significance testing are annotated to indicate where the estimates which have been compared are significantly different from each other with respect to the test statistic. In all other tables which do not show the results of significance testing, users should take account of RSEs when comparing estimates for different populations.

14 The imprecision due to sampling variability, labelled sampling error, should not be confused with non-sampling error. Non-sampling error may occur in any collection, whether it is based on a sample or a full count such as a census. Sources of non-sampling error include non-response, errors in reporting by respondents or recording answers by interviewers and errors in coding and processing data. Every effort was made to reduce the non-sampling error by careful design and testing of the questionnaire, training and supervision of interviewers, extensive editing and quality control procedures at all stages of data processing and follow up of initial non-respondents.


RELATIVE STANDARD ERRORS

15 Limited space does not allow the SEs and/or RSEs of all the estimates to be shown in this publication. Only RSEs for Table 1 are included below. However, RSEs for all tables are available free-of-charge on the ABS website <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication.

Attendance rate at cultural events and venues, By states and territories - 2009-10
		NSW	Vic.	Qld.	SA	WA	Tas.	NT(a)	ACT	Aust.
ATENDANCE RATE (%)
Art galleries		25.7	26.2	25.7	25.6	22.7	26.8	30.2	45.9	25.9
Museums		23.2	25.6	25.5	28.2	23.9	36.0	44.6	46.2	25.5
Zoological parks and aquariums		35.2	38.5	32.7	40.9	41.6	30.6	53.1	43.6	36.8
Botanic gardens		31.5	40.0	36.0	36.6	31.4	35.2	43.1	39.6	35.2
Libraries		32.4	33.4	35.5	35.4	31.1	34.5	35.8	38.4	33.5
Archives		3.1	4.4	2.2	3.0	3.4	3.8	*4.6	15.9	3.5
Performing arts
	Classical music concerts	9.4	9.9	6.3	8.3	9.4	9.3	7.9	13.8	8.9
	Popular music concerts	29.3	31.1	27.9	30.7	36.3	25.3	31.5	35.9	30.3
	Theatre performances	16.4	17.4	13.9	16.3	15.9	21.1	16.1	22.9	16.3
	Dance performances	10.9	9.3	9.0	10.4	11.1	8.8	14.5	13.5	10.1
	Musicals and operas	16.7	20.5	13.4	13.5	12.1	17.3	12.4	19.3	16.3
	Other performing arts	15.6	18.0	16.0	18.4	17.4	15.5	22.7	19.6	16.8
	Total attending at least one performing arts event	51.4	54.5	49.6	52.5	53.7	48.9	54.3	63.9	52.3
Cinemas		64.4	69.2	68.9	65.7	67.6	59.3	68.6	76.1	67.0
Total attending at least one venue or event		83.2	87.2	87.0	87.6	86.2	83.9	91.4	93.0	85.8
ATTENDANCE RATE RSE (%)
Art galleries		3.3	3.6	4.0	6.4	4.8	6.7	8.2	5.4	1.6
Museums		3.7	3.2	4.7	5.3	4.2	4.8	5.3	6.2	1.9
Zoological parks and aquariums		3.1	2.8	3.4	3.5	2.6	4.6	3.9	6.6	1.5
Botanic gardens		3.3	2.3	3.7	5.5	3.9	5.6	6.3	5.6	1.3
Libraries		2.5	3.7	2.9	3.8	3.3	6.8	6.7	6.8	1.5
Archives		10.4	8.3	13.9	12.4	13.0	15.5	29.9	11.1	4.5
Performing arts
	Classical music concerts	7.1	5.5	8.8	10.0	8.5	11.4	16.6	12.3	2.8
	Popular music concerts	3.5	3.4	3.2	4.2	3.0	5.2	6.3	5.9	1.7
	Theatre performances	5.3	4.9	5.6	6.2	7.4	8.2	11.0	8.5	2.5
	Dance performances	5.2	6.3	9.5	6.9	8.1	9.1	13.8	14.4	2.7
	Musicals and operas	4.2	4.6	5.2	8.7	5.2	7.0	14.3	9.3	2.4
	Other performing arts	4.9	5.1	4.4	6.3	4.5	8.9	12.5	9.9	2.4
	Total attending at least one performing arts event	2.2	2.0	1.8	3.3	2.4	3.6	5.0	3.8	1.1
Cinemas		1.4	1.1	1.4	2.1	1.9	3.1	3.3	2.6	0.7
Total attending at least one venue or event		0.9	0.9	0.7	1.0	1.1	1.7	1.5	1.5	0.4
* estimate has a relative standard error of 25% to 50% and should be used with caution
(a) Refers to mainly urban areas. See paragraph 7 of Explanatory Notes.