A Census survey gathers information from every member (unit) of the Target Population. A random sample survey, on the other hand, collects data from randomly selected units of the target population. Every census is a survey, but not every survey is a census.
Census data have no statistical sampling errors, margins of error, or confidence intervals.
The data are the data. If the census data contain errors, they are unrelated to sampling.
(It is only with a random sample from a Target Population, that data have an associated statistical sampling error. Any data point derived from a random sample is likely not perfectly accurate. Statistical calculations provide the numerical range (margin of error) around the sample data in which the accurate (true) number is expected to be found with a specified level of confidence.)
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Real World Example
Academic Article: Sex-Based Disparities in the Hourly Earnings of Surgeons in the Fee-for-Service System in Ontario, Canada
The authors of this academic article (published in the prestigious JAMA journal) use Census data for their analysis, and yet they describe their findings using confidence intervals (CIs) and p-values. By using CIs and p-values, they are implying there is some measurable uncertainty in their data (as one would have with data from a random sample survey).
The authors examined “surgeons’ earnings for operative procedures performed in Ontario, Canada, from January 1, 2014, to December 31, 2016.”
The data for the study come from the Government of Ontario ICES Data Repository, which contains all data for surgeons’ earnings for these operative procedures performed in Ontario, Canada. That is, the authors reported on all units of their Target Population. Their data is a Census, not a random sample.
Having used census data, the data are the data. There is no sampling error, CI, margin of error, or any other measurable uncertainty associate with the data and findings. It is possible there could be some anomaly in the data so that the data are not perfectly accurate (e.g., inaccurate reporting), but without random selection of a sample from a Target Population, there is no statistical sampling error.
JAMA is a prestigious peer-reviewed journal. It is surprising that this error was not caught and corrected before publication.