One Number Census

**This information has been copied across from the SCROL website and some of it may be out-of-date. This will be updated in due course**

A One Number Census

Census 2001 results are the first Census results to represent the entire population. This was achieved through a project known as the 'One Number Census' (ONC). There were two key elements of the ONC, an independent follow-up survey (CCS) and then estimation and imputation processes.

The Census Coverage Survey (CCS) involved face to face interviews with a sample of 40,000 households from every Council Area in Scotland. In the past, the total population given by a census was the raw count, but by combining the results of the 2001 Census and the CCS, it was possible to estimate the total resident population - the 'One Number' - to a high level of precision, about ± 0.33 per cent in Scotland. It was also then possible to impute synthetic people into synthetic households or enumerated households so that the Census database was fully adjusted for biased under enumeration at a local level.

Introduction to the One Number Census

It was clear from the evaluation of the 1991 Census that there was biased under-enumeration. Certain groups of people such as young men aged 20-29 were undercounted. However, the 1991 Census follow-up survey for estimating undercount was not large enough to identify fully the extent and distribution of under-enumeration. As a result, the national population estimates for 1991 were based on demographic estimates. Census counts did not give national and local authority level totals consistent with the population estimates.

We knew the 2001 Census would not get a 100% response. Indeed, it was expected that the response rate would be lower in 2001 than in 1991. The pattern of increasing difficulty of obtaining response to a census is also evident in other countries. Users were clear that for 2001 they wanted a fully adjusted set of counts covering 100% per cent of the population. The One Number Census project (ONC) was designed to meet this need.

Therefore, a much larger post-enumeration survey (the Census Coverage Survey, CCS) was carried out. In Scotland, the survey included about 40,000 households and 90,000 people. The results from the CCS were compared to the results of the Census so that we could determine the proportion and the characteristics of people missed by the Census.

The data collected in the CCS allowed the One Number Census Project to estimate and adjust the Census database for under-enumeration so that all statistics add up to 'One Number'. It also ensured that robust results could be obtained for Council Areas.

The ONC methodologies were researched and developed over a number of years by a joint team of Government Statisticians and Academics from the University of Southampton. The work was overseen by a steering committee that included experts from central government, statistical agencies overseas, other academic institutions and local government. In addition, census users were consulted at several stages in the methodological development process through census user group meetings and workshops. Detailed information on the methodology is available via the ONS website.

How the CCS worked

The CCS was specifically designed to allow Census population counts to be adjusted for under-enumeration at the national, local and small area level. It was an independent interview survey of a sample of about 2,400 postcodes containing 40,000 households drawn from all Council Areas in Scotland. The sample design took into account the uneven distribution of under-enumeration across the country in 1991 by stratifying a 'Hard to Count' index based upon 1991 characteristics likely to be associated with under-enumeration, such as the number of multi-occupied addresses.

The CCS was as operationally independent from the 2001 Census as practicable. The CCS postcode sample was confidential and was not known to census field staff. CCS interviewers did not have Census enumerator address lists. They did not see the Census forms for the area where they were interviewing nor worked in the same areas for the Census and the CCS.

The interviewers made as many calls as necessary to achieve an interview but within a 3-week period. The timing of these calls was varied to maximise the probability of making contact. The CCS in Scotland achieved a response from 95 per cent of the households identified by interviewers.

Step by step outline of the ONC

The One Number Census process involved a number of stages:

  • A Census Coverage Survey was conducted during May/June 2001;

  • Records from the CCS were matched to those from the 2001 Census;

  • From the results of the matching and using dual system estimation techniques, an estimate of those persons missed by both the Census and the CCS was made;

  • The 'missing' population combined with the Census population gave an estimate of the true population of the sample areas;

  • Populations for each local authority by age and sex were then estimated using a combination of standard regression and small area estimation techniques;

  • Households and persons estimated to have been missed by the Census were then imputed to produce a fully adjusted Census database; and finally

  • All population estimates were quality assured using demographic analysis and comparison with aggregate level administrative data.

Quality Assurance

All ONC population estimates were quality assured. The population of each local authority by age and sex were compared to diagnostic ranges derived from rolled-forward population estimates and aggregated administrative sources (such as Birth Registration and Pensions data). These ranges gave a set of values within which we expected, prior to the Census, the ONC estimates to fall. Where the age/sex ONC estimates fell outside of the diagnostic ranges, checks of the ONC results were undertaken with respect to sample sizes, outliers, etc and contingency action was taken if necessary.

The quality assurance process included analysis for each local authority of a number of specific population subgroups known from 1991 to be prone to under-enumeration. These were full-time students, armed forces and prisoners. The estimates for these subgroups were compared with data from other official sources to determine whether the results were plausible. This separate quality assurance was necessary as the CCS did not cover large communal establishments. Adjustments were made where significant under-enumeration was identified. This resulted in about 3,450 Armed forces personnel being added to the estimates for Scotland.

Dependence between the Census and CCS

For the ONC process to produce unbiased estimates of the population it is necessary for the Census and the Census Coverage Survey to be as independent of each other as practicable. As described above, there were arrangements in place to achieve this - with Census and CCS operations being kept entirely separate in the field. If the two attempts at enumerating the same population are independent, it is possible to not only estimate those missed by either the Census or the CCS but to also estimate those missed by both - the dual system approach.

Nevertheless, people who are difficult to count in a census are also difficult to count in a post-enumeration survey such as the CCS. A methodology was used to identify areas where such dependency was marked and to adjust for that dependence. An additional 40,600 people were accordingly added to the population estimates for Scotland.

Over count

The ONC methodology was principally concerned with identifying and adjusting for Census under-enumeration. However, part of the CCS interview was also aimed at identifying any potential over count in the 2001 Census, that is persons enumerated as resident at more than one address. The expectation was that over-enumeration only occurs accidentally. Examples of such possibilities include people recorded at second homes and their main residence and children who live a proportion of time with separated parents. Analysis of responses to the CCS in England and Wales by ONS indicated that the level of overcount in the 2001 census was negligible - less than 0.1 per cent of the population were estimated to have been counted twice. This is well within the estimated precision of the ONC estimates (± 0.2 per cent for England and Wales) and has therefore been taken as not significant in calculating the ONC estimates.

Precision of the ONC results

The quality assurance process means that the Census figures are the best estimates we can make of the population. However, they are estimates and therefore subject to a margin of error. A 95 per cent confidence interval is a range within which the true population would fall for 95 per cent of the times the sample survey was repeated. For Scotland, the confidence interval is ± 0.33%. A confidence interval of 0.33% is equivalent to ± 16,700.

For Council Areas, the percentage margins of error are larger, ranging from ± 1.6% in Argyll & Bute to ± 0.5% in North Lanarkshire and South Lanarkshire. This is the first time it has been possible to estimate the level of precision for a census with any confidence. It should be noted that, as with all statistical analysis, these standardised calculations do not capture all sources of variation and there will also be, for example, response, capture and coding errors - these will be outlined in reports on Data Quality available from 2003. However, our assessment is that, having made an adjustment for dependency, the ONC results remain the best central estimates possible of the population on Census Day 2001.

Census response

In 1991, the estimated coverage of the Census in Scotland was 98 per cent. This was the proportion of the population accounted for in the Census results. It included some 2 per cent estimated by enumerators to be resident in identified households but from whom no completed Census form was collected. Thus Census response in 1991, defined as the proportion of the population counted on returned Census forms, was 96 per cent in Scotland.

If the 2001 Census had been conducted in the same way as it was in 1991, it is estimated that 97 per cent of the population in Scotland would have again been covered. This includes some 2 per cent of the population estimated to be resident in households identified by enumerators but from who no completed Census form was returned. Census response in 2001 for Scotland is therefore estimated to be 95 per cent, 1 per cent lower than in 1991. This decline in response rates is in line with changes observed for large-scale Government Surveys during the 1990s.

Census response rates indicate that under enumeration in the 2001 Census varied across all areas or age-sex groups. The patterns of Census response were as expected, that is response rates were lowest for persons in their twenties, particularly men. Response rates by age and sex are shown in the following Chart 1. 2001 Census response by age-sex group for Scotland as a whole varied from 98.7 per cent for men aged 65-69 years old to 90.1 per cent for males aged 20-24.