Perturbation (small-cell adjustment)

How the ABS adjusts Census counts

Under the Census and Statistics Act 1905 it is an offence for the ABS to release information that could identify a person. To protect respondents in published tables, the ABS randomly adjusts cell values, a technique it calls introduced random error or perturbation. All values are adjusted slightly, including the totals, and the ABS describes the effect on the underlying pattern of the statistics as negligible.

The adjustments are made in a controlled way, so the same information is adjusted by the same amount. The ABS states that it is not possible to tell which figures were affected, and that this method lets it release very large tables with many small cells. In its guide to the 2016 Census products, the ABS added that perturbation includes the suppression of small counts, which is why counts of 1 or 2 didn't appear in that Census's output, and that the size and characteristics of the adjustments were unchanged from 2011.

Totals that don't add up

Because each cell and each total is adjusted on its own, the rows or columns of a table can differ by small amounts from the table's total. Tables for a larger area may also differ from the sum of the same tables for the smaller areas inside it. The ABS advises that these small differences can mostly be ignored.

In TableBuilder, the ABS calculates each total from the unadjusted data and then perturbs it, rather than summing the adjusted cells inside the table. It recommends building totals in TableBuilder for that reason, because summing many perturbed cells adds up their adjustments. For the same reason, the ABS advises using the published figure for a larger standard area wherever one exists, rather than adding up the figures for the small areas inside it.

Small areas and small counts

The adjustment is independent of the size of the count, so its relative effect is greatest on small values. A small adjustment is immaterial in a count of 5,000 and large in a count of 5. The ABS states that no reliance should be placed on small cells, because they are affected by random adjustment as well as by respondent and processing errors. For percentages and ratios the random error can usually be ignored, though the ABS warns that the effect can be significant when very small cells are involved.

For site work, the risk sits in the finest detail, such as a single age group or birthplace in an SA1, or a narrow income range in a small suburb. Combining small areas into a catchment, or using a broader category, gives each figure a larger base.

Perturbation and Censible

Censible can't undo the ABS's adjustments, so it shows how much each figure rests on instead. Every figure carries its base, the count it's calculated from, and the app notes that the ABS adjusts small counts for privacy wherever a place has fewer than 1,000 people.

Censible's figures are built up from SA1s, except those for Australia and the states, which are added up from councils. Medians built that way run slightly above the ABS's own national figures (household income by 0.9%), which appears to come from the adjustments accumulating across thousands of SA1s. Where the ABS publishes its own figure for an area, API responses include it alongside Censible's.

Sources: ABS, 2021 Census methodology, How the data is processed (Introduced random error / perturbation); ABS, TableBuilder user guide, Confidentiality and relative standard error (1406.0.55.005); ABS, Census QuickStats, Community Profiles and DataPacks User Guide, 2016: Census data products and the effect of perturbation on counts.