AI Glossary / Statistics and probability / Intermediate

Random rounding

Definition

Random rounding is a statistical disclosure-control technique that replaces a value, often a table count, with a nearby rounding-base value chosen using a random rule. Unlike ordinary deterministic rounding, the same original value can have more than one possible rounded result. A common unbiased scheme chooses between the adjacent multiples with probabilities that preserve the original value in expectation. Particular implementations can include additional constraints, so the exact rounding rule must be documented.

What it means

The method introduces uncertainty about the exact published count while retaining a broadly similar scale. For example, a count between two multiples of five may be rounded either down or up. Preserving the original count on average across hypothetical repetitions does not preserve it in each release. Rounding can also change totals, percentages and comparisons, especially for small cells. Random rounding offers a form of perturbation, but it is not automatically a complete confidentiality guarantee.

How it works

Choose a base and identify the permitted rounded values for each count. Under the usual unbiased adjacent-multiple rule, let the lower multiple be L, the upper multiple be U, and the original value be x. Round upward with probability (x - L)/(U - L) and downward with the complementary probability. Values already on a base multiple can remain unchanged under this version. Decide whether cells and margins are rounded independently or through a controlled procedure designed to preserve specified consistency relationships.

Three practical examples

Example 1: A statistical publisher rounds frequency-table cells before releasing a public summary. Example 2: A research-access system applies a documented controlled rounding procedure to requested tabulations. Example 3: An analyst explains why rounded components and a separately rounded total do not add exactly. These uses require clear release notes. Readers should not reverse-engineer small differences as exact changes in the underlying population when those differences may be introduced by the protection method.

Think of it this way

Think of placing a count between two permitted stepping stones and randomly choosing which stone represents it. The probabilities can be chosen so that repeated choices balance around the original position. One published choice is still only one stone, not the original count. If several counts make their choices separately, their combined position need not match the stone chosen for their total.

Worked example

Use unbiased random rounding to base five. An original count of 12 lies between 10 and 15, so the probability of rounding up is (12 - 10)/5 = 0.40. It rounds down with probability 0.60. The expected published count is 0.60 × 10 + 0.40 × 15 = 12. The rounding error is -2 or +3, giving variance 0.60 × 4 + 0.40 × 9 = 6. An original count of 8 rounds to 5 with probability 0.40 or 10 with probability 0.60. If these cells independently round upward, their published sum is 15 + 10 = 25, even though the original total is 20 and remains 20 under this rule. This illustrates why independent rounding does not ensure additivity.

Illustrative case study

Fictional case study: Birch Statistics prepares a small public table and notices that independently rounded subtotals disagree with a rounded grand total. The publication team explains the discrepancy rather than silently changing numbers to force agreement. For a later product, it evaluates a controlled method that targets particular consistency requirements. The example is fictional and does not claim that either method is sufficient for every release. Confidentiality review still considers related outputs and information available to recipients.

Common misconceptions and mistakes

Common mistakes include assuming that random means arbitrary, expecting every rounded table to be unbiased in its realized values, and treating rounding as the same as suppression. Unbiasedness is a property over the random mechanism's repetitions. Releasing many independently rounded versions of the same count can reveal more information through averaging. Small published differences may reflect rounding rather than underlying change. Random rounding is also distinct from similarly named optimization techniques used to convert fractional algorithmic solutions.

Business use

Business use: Random rounding can support publication of useful aggregate statistics while obscuring exact counts. Before using it, specify the base, rounding probabilities, treatment of totals and repeated-release policy. Assess the effects on small cells, ratios and downstream analyses. Make the protection method visible in documentation so users understand non-additivity and precision limits. Choose confidentiality measures through an assessment of the whole release environment rather than relying on the presence of random noise alone.

People also ask

Does random rounding always select the nearest multiple?

No; the standard random scheme can select either adjacent multiple. Q: Does unbiased rounding mean the released count is correct? A: No; it means the mechanism's expected output equals the original count. Q: Will components sum to their published total? A: Not necessarily, especially when cells and margins are rounded independently; controlled procedures address specified consistency conditions.

Check your understanding

Why does 12 round up only 40% of the time in the example?

Answer: It is two-fifths of the distance from 10 to 15, which gives the stated unbiased probabilities.

Is a published sum of 25 proof that the original cells totaled 25?

Answer: No. The example's original cells totaled 20, and independent rounding produced the discrepancy.

Learn next

Enumerate the four possible rounded outcomes for the two cells in the example and calculate their probabilities under independence. Verify the expected sum while inspecting its possible deviations. Then compare independent rounding with a controlled design and study how repeated releases alter confidentiality. Keep statistical utility and privacy claims separate throughout the comparison.

More in Statistics and probability

• Random model Anova - A random model ANOVA, more commonly called a random-effects analysis of variance, treats the effects of factor levels as draws from a population of possible...
• Random perturbation - Random perturbation, in statistical disclosure control, deliberately changes data using a random mechanism before release.
• Random (probability) sample - A random, or probability, sample is selected through a chance-based design in which every unit in the target population covered by the design has a known...
• Random start - A random start is an initial position chosen by a specified random mechanism before a systematic sampling sequence is followed.
• Random surfer model - The random surfer model represents movement through a linked network as a probabilistic process.
• Random variable - A random variable is a function that assigns a numerical value to each outcome of a random experiment or other probability model.

Sources

Sources: Statistics Canada, Controlled rounding: https://www.statcan.gc.ca/en/microdata/rtra/training/controlled ; Handbook on Statistical Disclosure Control, Frequency tables: https://sdctools.github.io/HandbookSDC/05-frequency-tables.html . These institutional and specialist project sources describe random and controlled rounding. The base-five probabilities, variance calculation and fictional publication case are original illustrations of an explicitly specified rounding mechanism.

Previous: Random-restart hill climbing Next: Random sample consensus