Australian Bureau of Statistics
Celebrating the International Year of Statistics 2013

TECHNICAL NOTE


ESTIMATION PROCEDURES

1 Estimates from the survey were derived using a complex estimation procedure which ensures that survey estimates conform to independent population estimates by state, part of state, age and sex.


RELIABILITY OF THE ESTIMATES

2 Two types of error are possible in an estimate based on a sample survey: sampling error and non-sampling error. The sampling error is a measure of the variability that occurs by chance because a sample, rather than the entire population, is surveyed. 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 the figures 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). There are about two chances in three that a sample estimate will differ by less than one SE from the figure that would have been obtained if all dwellings had been included, and about 19 chances in 20 that the difference will be less than two SEs.

3 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. The RSE is a useful measure in that it provides an immediate indication of the percentage errors likely to have occurred due to sampling, and thus avoids the need to refer also to the size of the estimate.



4 Space does not allow for the separate presentation of the SEs and/or RSEs of all the estimates in this publication. However, RSEs for all estimates are available free-of-charge on the ABS website <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, National Survey of Mental Health and Wellbeing: Summary of Results (cat. no. 4326.0). As a guide, the population and RSE estimates for Table 2 are presented on the following page.

12-MONTH MENTAL DISORDERS(a), Relative Standard Error Estimates
			Males		Females		Persons
			'000	RSE %	'000	RSE %	'000	RSE %
Any 12-month mental disorder
	Anxiety disorders
		Panic Disorder	180.5	15.6	229.8	10.9	410.3	9.3
		Agoraphobia	170.5	17.4	279.9	9.6	450.4	8.3
		Social Phobia	298.9	13.4	461.0	7.0	759.9	6.2
		Generalised Anxiety Disorder	155.2	18.1	280.9	11.6	436.1	10.5
		Obsessive-Compulsive Disorder	130.6	17.6	175.0	11.0	305.6	10.3
		Post-Traumatic Stress Disorder	366.3	10.6	665.7	6.3	1 031.9	5.0
		Any Anxiety disorder(b)	860.7	6.7	1 442.3	3.8	2 303.0	3.3
	Affective disorders
		Depressive Episode(c)	245.0	13.7	407.4	8.2	652.4	7.2
		Dysthymia	79.7	21.4	124.0	15.9	203.8	12.0
		Bipolar Affective Disorder	145.3	17.3	140.3	13.2	285.6	10.8
		Any Affective disorder(b)	420.1	9.8	575.8	7.1	995.9	5.5
	Substance Use disorders
		Alcohol Harmful Use	300.8	10.5	169.3	15.6	470.1	8.2
		Alcohol Dependence	174.9	15.7	55.3	18.5	230.2	12.2
		Drug Use disorders(d)	165.7	13.5	65.7	16.8	231.4	10.0
		Any Substance Use disorder(b)	556.4	8.8	263.5	10.7	819.8	6.5
	Any 12-month mental disorder(a)(b)		1 400.1	5.5	1 797.7	2.9	3 197.8	2.7
	No 12-month mental disorder(e)		6 549.7	1.2	6 267.8	0.8	12 817.5	0.7
	Total persons aged 16-85 years		7 949.8	-	8 065.5	-	16 015.3	-
- nil or rounded to zero (including null cells)
(a) Persons who met criteria for diagnosis of a lifetime mental disorder (with hierarchy) and had symptoms in the 12 months prior to interview. See paragraphs 30-31 of Explanatory Notes.
(b) A person may have had more than one 12-month mental disorder. The components when added may therefore not add to the total shown.
(c) Includes Severe Depressive Episode, Moderate Depressive Episode, and Mild Depressive Episode.
(d) Includes Harmful Use and Dependence.
(e) Persons who did not meet criteria for diagnosis of a lifetime mental disorder and those who met criteria for diagnosis of a lifetime mental disorder (with hierarchy) but did not have symptoms in the 12 months prior to interview. See paragraphs 30-31 of Explanatory Notes.

5 The smaller the estimate the higher is the RSE. Very small estimates are subject to such high SEs (relative to the size of the estimate) as to detract seriously from their value for most reasonable uses. In the tables in this publication, only estimates with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs, between 25% and less than 50% have been included and are preceded by an asterisk (eg *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs of 50% or more are preceded with a double asterisk (eg **0.6). Such estimates are considered unreliable for most purposes.

6 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by interviewers and respondents and errors made in coding and processing of data. Inaccuracies of this kind are referred to as the non-sampling error, and they may occur in any enumeration, whether it be in a full count or only a sample. In practice, the potential for non-sampling error adds to the uncertainty of the estimates caused by sampling variability. However, it is not possible to quantify the non-sampling error.


STANDARD ERRORS OF 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. For proportions where the denominator is an estimate of the number of persons in a group and the numerator is the number of persons in a sub-group of the denominator group, the formula to approximate the RSE is given by:



8 From the above formula, the RSE of the estimated proportion or percentage will be lower than the RSE of the estimate of the numerator. Thus an approximation for SEs of proportions or percentages may be derived by neglecting the RSE of the denominator, ie by obtaining the RSE of the number of persons corresponding to the numerator of the proportion or percentage and then applying this figure to the estimated proportion or percentage.


COMPARISON OF ESTIMATES

9 Published estimates may also be used to calculate the difference between two survey estimates. 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 the above formula will be exact only for differences between separate and uncorrelated (unrelated) characteristics of sub-populations, it is expected that it will provide a reasonable approximation for all differences likely to be of interest in this publication.


SIGNIFICANCE TESTING

11 For comparing estimates between surveys or between populations within a survey it is useful to determine whether apparent differences are 'real' differences between the corresponding population characteristics or simply the product of differences between the survey samples. One way to examine this is to determine whether the difference between the estimates is statistically significant. This is done by calculating the standard error of the difference between two estimates (x and y) and using that to calculate the test statistic using the formula below:



12 If the value of the statistic is greater than 1.96 then we may say there is good evidence of a statistically significant difference between the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations.

13 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error, and they occur in any enumeration, whether it be a full count or sample. Every effort is made to reduce non-sampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.