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TECHNICAL NOTE 4 IDENTIFYING CENSUS LATE RETURNS


LATE CENSUS FORMS

1 For some people who have not returned a Census form, contact from the ABS following selection in the PES acts as a reminder to return a completed Census form. These late returns, if not identified, would have resulted in the PES sample having a higher proportion of Census response than in the overall population. To protect against this, and maintain the statistical independence of the PES from the Census, all Census forms received after the start of 2011 PES field work were deemed 'late' and treated differently in PES estimation.

2 For the purpose of PES estimation, the dwellings from which 'late' Census forms were received were treated as though they had not been contacted in the Census and classified to the Census 'non-contact sector'.


CENSUS NON-CONTACT SECTOR

3 As detailed in Components of net undercount, the non-contact sector also contains dwellings which were non-responding in the Census. During Census processing, a 'hot-deck' imputation method (see Glossary) imputed people into these dwellings, together with imputed values for Age, Sex, Marital status and Place of usual residence. These values were, in many cases, based on information provided by the Census collector about the dwelling and its residents. Values for all other variables (e.g. Indigenous status, Country of birth) were set to 'not-stated' or 'not applicable', depending on the imputed value for age.

4 Inevitably, the imputed values differ from the true but unknown values, at both the dwelling and aggregate level. Imputed records made up the majority of the 2011 Census non-contact sector records, with late returns (as defined above) making up only a small component of this sector. Given that late returns prompted by PES would otherwise have been classed as non-response in the Census, the PES sample is representative of the whole non-contact sector, even though it cannot split late returns from non-responses in a manner comparable to the Census.


ESTIMATING THE NUMBER OF PEOPLE IN CENSUS LATE RETURN AND IMPUTED DWELLINGS

5 As was began in 2006, the 2011 PES processed the data returned from Linking and Matching, assigning a weight to each record, including those that corresponded to the Census non-contact sector. Hence the PES provides an estimate of the total number of people who should have been counted in the Census non-contact sector (i.e. late return and non-response dwellings).

6 PES estimates of the population in the non-contact sector have relatively high sampling errors because of the small sample size (there were relatively few Census non-contact dwellings selected by chance in the PES sample); and also because Census person counts for this sector were not available to use as a weighting 'benchmark'. This lack of Census person counts also means that, while the dwelling weights used for the non-contact sector were estimated from the sector itself, the adjustments applied to provide final person weights depend strongly on information observed in the contact sector. This is a potential source of non-sampling error, as is any bias arising from peculiarities of the non-respondents in this sector. Both these sources of non-sampling error are expected to be small, compared to the sampling error of the population estimate for the non-contact sector.

7 Using PES estimates for the non-contact sector population leads to a rise in the standard error of the overall population estimates, representing the uncertainty associated with estimating the contribution of the non-contact sector. On the other hand, the alternative, as was done prior to 2006, where this sector is not measured by PES but is treated as accurately represented by the Census figures, can have a bias associated with Census imputation for non-response.

8 The standard error of the PES estimate of the population in the non-contact sector has been used to compare the accuracy of the PES estimate with that of the unadjusted Census count for this sector. Analysis showed that the overall population estimates are considerably more accurate if the PES estimates are used for this sector rather than using the Census counts (which in this sector were mostly imputed). As a result, estimates of net undercount for the 2011 Census incorporate the PES estimate of the number of people who should have been counted in the non-contact sector.


THE IMPORTANCE OF CORRECTING FOR CENSUS IMPUTATION ERROR

9 The majority of Census non-contact sector records are imputed records, with the remainder made up of late returns. The Census count of late returns is considered an accurate measure, given the special procedures in place for identifying 2011 late returns. By subtracting the Census count of late returns from the PES estimate of people who should have been counted in the non-contact sector, a PES estimate (and corresponding standard error) of the number of people who should have been imputed in the Census can be calculated. The Census imputation error is the difference between this PES estimate and the actual Census count of imputed people.

10 It is important to understand the level of accuracy associated with Census imputation in order to properly understand the impact it has had on PES estimates of net undercount. Consider the equation below.

11 The PES estimate of the number of people who should have been counted in the Census (A) less those who were counted in the Census, including imputed persons (B), will give the net undercount (C) i.e.: A - B = C.

12 Census imputation can impact on net undercount estimates in two ways:

• If the Census count (B) increases due to a higher number of imputed persons but all else remains the same, net undercount (C) will decrease.
• If the Census count (B) decreases due to a lower number of imputed persons but all else remains the same, net undercount (C) will increase.

CENSUS LATE RETURNS AND IMPUTED DWELLINGS, State/territory-Person records(a)
	2006 Census count	2006 Non-contact sector(b)	2006 Non-contact sector	2011 Census count	2011 Non-contact sector(b)	2011 Non-contact sector
	no.	no.	%	no.	no.	%
New South Wales	6 549 177	309 261	4.7	6 917 654	286 575	4.1
Victoria	4 932 422	203 639	4.1	5 354 043	195 002	3.6
Queensland	3 904 534	172 384	4.4	4 332 733	189 517	4.4
South Australia	1 514 337	47 958	3.2	1 596 567	48 545	3.0
Western Australia	1 959 087	104 431	5.3	2 239 193	115 093	5.1
Tasmania	476 479	14 476	3.0	495 355	13 625	2.8
Northern Territory	192 900	15 778	8.2	211 959	17 131	8.1
Australian Capital Territory	324 037	12 843	4.0	357 217	13 203	3.7
Australia	19 852 973	880 770	4.4	21 504 721	878 691	4.1
(a) Data refer to state/territory of usual residence.
(b) Data include people from late-return dwellings and imputed persons.