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Appendix C:
Data quality, confidentiality and random rounding

Data quality


The 2011 Census was a large and complex undertaking and, while considerable effort was taken to ensure high standards throughout all collection and processing operations, the resulting estimates are inevitably subject to a certain degree of error. Users of census data should be aware that such error exists, and should have some appreciation of its main components, so that they can assess the usefulness of census data for their purposes and the risks involved in basing conclusions or decisions on these data.

Errors can arise at virtually every stage of the census process, from the preparation of collection materials through data processing, including the listing of dwellings and the collection of data. Some errors occur at random, and when the individual responses are aggregated for a sufficiently large group, such errors tend to cancel out. For errors of this nature, the larger the group, the more accurate the corresponding estimate. It is for this reason that users are advised to be cautious when using small area estimates. There are some errors, however, which might occur more systematically, and which result in 'biased' estimates. Because the bias from such errors is persistent no matter how large the group for which responses are aggregated, and because bias is particularly difficult to measure, systematic errors are a more serious problem for most data users than the random errors referred to previously.

For census data in general, the principal types of error are as follows:

  1. coverage errors, which occur when dwellings or individuals are missed, incorrectly enumerated or counted more than once

  2. non-response errors, which result when responses cannot be obtained from a certain number of households and/or individuals, because of extended absence or some other reason or when responses cannot be obtained from a certain number of questions in a complete questionnaire

  3. response errors, which occur when the respondent, or sometimes the census representative, misunderstands a census question, and records an incorrect response or simply uses the wrong response box

  4. processing errors, which can occur at various steps including data capture, when responses are transferred from the census questionnaire in an electronic format, by optical character recognition methods or key-entry operators; coding, when 'write-in' responses are transformed into numerical codes; and imputation, when a 'valid,' but not necessarily correct, response is inserted into a record by the computer to replace missing or 'invalid' data ('valid' and 'invalid' referring to whether or not the response is consistent with other information on the record).

The above types of error each have both random and systematic components. These components may be significant.

Coverage errors

Coverage errors affect the accuracy of the census counts, that is, the sizes of the various census universes: population, families, households and dwellings. While steps have been taken to correct certain identifiable errors, the final counts are still subject to some degree of error because persons or dwellings have been missed, incorrectly enumerated in the census or counted more than once.

Missed dwellings or persons result in undercoverage. Dwellings can be missed because of the misunderstanding of collection unit boundaries, or because either they do not look like dwellings or they appear uninhabitable or they have recently been built or they are difficult to detect. Persons can be missed when their dwelling is missed or is classified as unoccupied, because the respondent misinterprets the instructions on whom to include on the questionnaire or because the respondent was away during the census period. Some individuals may be missed because they have no usual residence and did not spend census night in a dwelling.

Dwellings or persons incorrectly enumerated or double-counted result in overcoverage. Overcoverage of dwellings can occur when structures unfit for habitation are listed as dwellings (incorrectly enumerated), when there is a certain ambiguity regarding the collection unit boundaries or when units (for example, rooms) are listed separately instead of being treated as part of one dwelling (double-counted). Persons can be counted more than once because their dwelling is double counted or because the guidelines on whom to include on the questionnaire have been misunderstood. Occasionally, someone who is not in the census population universe, such as a foreign resident or a fictitious person, may, incorrectly, be enumerated in the census. On average, overcoverage is less likely to occur than undercoverage and, as a result, counts of dwellings and persons are likely to be slightly underestimated.

For the 2011 Census, three studies are used to measure coverage error; the Dwelling Classification Survey, the Reverse Record Check Study, and the Census Overcoverage Study. Only the Dwelling Classification Survey is used to adjust the census counts.

In the Dwelling Classification Survey, a sample of dwellings listed as unoccupied were revisited to verify that they were correctly classified on Census Day. In addition, dwellings whose households were classified by census collection as not having responded and where classification had not been established were revisited to confirm whether they were occupied on Census Day or not. If either type were occupied, then the number of usual residents living there on Census Day was obtained. Subsequently, the misclassification of occupancy status of dwellings in the census counts was estimated.

Based on the results of the Dwelling Classification Survey, adjustments have been made to the final census counts to account for households and persons missed because their dwelling was incorrectly classified as unoccupied. The census counts are also adjusted for dwellings whose households were classified as non-respondent or unclassifiable. Despite these adjustments, the final counts are still subject to some undercoverage. The undercoverage tends to be higher for certain segments of the population, such as young adults (especially young adult males) and recent immigrants.

The Reverse Record Check Study is used to measure the residual undercoverage for Canada, and each province and territory. The Census Overcoverage Study is designed to investigate overcoverage errors from person enumerated more than once. The results of the Reverse Record Check and the Census Overcoverage Study, when taken together, furnish an estimate of net undercoverage.

Other sources of errors

While coverage errors affect the number of units in the different census universes, other errors affect the characteristics of those units.

Sometimes it is not possible to obtain a complete response from a household, even though the dwelling was identified as occupied. The household members may have been away throughout the census collection period or, in rare instances, the householder may have refused to complete the questionnaire. More frequently, the questionnaire is returned by mail or submitted through Internet but no response is provided to certain questions. Effort is devoted to ensure as complete a questionnaire as possible. An analysis is performed to detect significant cases of partial non-response and follow-up interviews are attempted to get the missing information. Despite this, at the end of the collection stage, a small number of responses are still missing. Although missing responses are eliminated during processing by replacing each one of them by the corresponding response for a 'similar' record, there remain some potential imputation errors. This is particularly serious if the non-respondents differ in some respects from the respondents; this procedure will then introduce a non-response bias.

Even when a response is obtained, it may not be entirely accurate. The respondent may have misinterpreted the question or may have guessed the answer, especially when answering on behalf of another, possibly absent, household member. The respondent may also have entered the answer in the wrong place on the questionnaire. Such errors are referred to as response errors. While response errors usually arise from inaccurate information provided by respondents, they can also result from mistakes by the census representative who completed certain parts of the questionnaire, or who followed up to obtain a missing response.

The images of the questionnaire pages are scanned and the information on the images is captured into a computer file. To monitor and to ensure that the number of data capture errors is within tolerable limits, a sample of fields is sampled and reprocessed. Analysis of the two captures is done. Unsatisfactory work is identified, corrected and appropriate feedback is done to the system in order to minimize their occurrence.

Some of the census questions require a written response. During processing, these 'write-in' entries are given a numeric code, either through an automated system that matches them to a coded set of write-ins from previous censuses, or manually by coders. Coding errors can occur when the written response is ambiguous, incomplete, or difficult to read. A quality assurance process is used to detect coding errors and measure quality. This involves selecting and re-coding an ongoing sample of coded responses. Discrepancies between the first and second code are sent to a third coder for arbitration. Feedback on errors is provided to help reduce further occurrences.

The data are edited where they undergo a series of computer checks to identify missing or inconsistent responses. These are replaced during the imputation stage of processing where either a response consistent with the other respondents' data is inferred or a response from a similar donor is substituted. Imputation ensures a complete database where the data correspond to the census counts and facilitate multivariate analyses. Although errors may have been introduced during imputation, the methods used have been rigorously tested to minimize systematic errors.

Various studies are being carried out to evaluate the quality of the responses obtained in the 2011 Census. For each question, non-response rates and edit failure rates have been calculated. These can be useful in identifying the potential for non-response errors and other types of errors. Also, tabulations from the 2011 Census have been or will be compared with corresponding estimates from previous censuses, from sample surveys (such as the Labour Force Survey) and from various administrative records (such as birth registrations and municipal assessment records). Such comparisons can indicate potential quality problems or at least discrepancies between the sources.

In addition to these aggregate-level comparisons, there are some micro-match studies done, in which census responses are compared with another source of information at the individual record level. For certain 'stable' characteristics (such as age, sex, mother tongue), the responses obtained in the 2011 Census, for a sample of individuals, are being compared with those for the same individuals in the 2006 Census.

Confidentiality and random rounding

The figures shown in the tables have been subjected to a confidentiality procedure known as random rounding to prevent the possibility of associating statistical data with any identifiable individual. Under this method, all figures, including totals and margins, are randomly rounded either up or down to a multiple of '5,' and in some cases '10.' While providing strong protection against disclosure, this technique does not add significant error to the census data. The user should be aware that totals and margins are rounded independently of the cell data so that some differences between these and the sum of rounded cell data may exist. Also, minor differences can be expected in corresponding totals and cell values among various census tabulations. Similarly, percentages, which are calculated on rounded figures, do not necessarily add up to 100%. Order statistics (median, quartiles, percentiles, etc.) are computed in the usual manner.

Users should be aware of possible data distortions when they are aggregating these rounded data. Imprecision as a result of rounding tend to cancel each other out when data cells are re-aggregated. However, users can minimize these distortions by using, whenever possible, the appropriate subtotals when aggregating.

For those requiring maximum precision, the option exists to use custom tabulations. With custom products, aggregation is done using individual census database records. Random rounding occurs only after the data cells have been aggregated, thus minimizing any distortion.

In addition to random rounding, area suppression has been adopted to further protect the confidentiality of individual responses. Area suppression is the deletion of all characteristic data from the census for geographic areas with populations below 40 persons. However, if the census data refer to six-character postal codes or to groups of either dissemination blocks or block-faces, they are suppressed if the total population in the area is less than 100 persons.

In all cases, suppressed data are included in the appropriate higher aggregate subtotals and totals. The suppression technique is being implemented for all products involving subprovincial data (i.e., Profile series, basic cross-tabulations, semi-custom and custom data products).

For further information on the quality of census data, contact Statistics Canada's National Contact Centre at 1-800-263-1136.

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