Can a record be unique on one key but not another?

Yes; adding or removing detail changes the groups.

Is a sample-unique percentage a re-identification probability?

No; additional assumptions and context are required.

AI Glossary / Statistics and probability / Intermediate

Sample unique

Definition

A sample unique is a record whose combination of specified key-variable values occurs only once within a dataset. The term is used in statistical disclosure control to identify records that may require closer confidentiality assessment. Uniqueness is relative to the selected key and the dataset; it does not automatically mean that the person or organization is unique in the wider population or has been identified.

What it means

A record can stand out because of a combination of otherwise ordinary characteristics. Each characteristic may be common on its own, yet their joint pattern may appear only once in the released sample.
The chosen key matters. A record can be unique on a detailed key and non-unique when the same variables are grouped more broadly. A database's artificial row identifier is usually unique by construction, but that is different from evaluating uniqueness on attributes relevant to disclosure risk.

How it works

Define the dataset and the key variables under assessment. The purpose is to understand whether combinations in the proposed data release can distinguish records, not to assume every available column has the same relevance.
Group records by the exact key combinations and count the records in each group. These groups are often called equivalence classes. A record in a class of size one is sample unique for that key.
Check coding and data quality. Inconsistent category labels, typographical errors, or mishandled missing values can create apparent uniqueness. Cleaning may change the counts, while missingness itself can sometimes contribute to a distinctive pattern.
Distinguish sample uniqueness from population uniqueness. A combination observed once in a sample may occur many times among unobserved population units. Conversely, a population-unique unit that is included once in an accurately recorded sample will be sample unique on the same key.
Assess the release context. Potentially available auxiliary information, knowledge of participation, key reliability, access controls, and sensitive attributes affect risk. A count of sample uniques is a diagnostic input, not a complete probability of successful identification or disclosure.
Consider suitable disclosure-control measures when needed. Broader categories, selective suppression, perturbation, or restricted access can alter risk and data usefulness. Their effects should be evaluated on the intended analyses rather than assuming that one modification solves every problem.
Reassess after changes or combined releases. A record that is not unique on one limited key can become distinguishable when additional attributes or linked periods are available. Longitudinal trajectories can reveal patterns that are not evident in a single-period table.
Document the key, dataset version, treatment of missing values, counts, and protective decisions. Removing sample uniques does not by itself establish privacy: records in larger groups may still reveal sensitive attributes or become identifiable with other information.

Three practical examples

Survey release: a statistical team reviews rare combinations of broad demographic categories before sharing microdata.
Business data sharing: analysts assess whether establishment characteristics distinguish individual organizations in a proposed dataset.
AI research preparation: a team checks the disclosure implications of releasing evaluation records, beyond merely deleting direct identifiers.

Think of it this way

Think of sorting anonymous cards into piles according to a chosen combination of labels. A pile containing one card marks a sample unique for those labels. It does not tell you whether another matching card exists outside the stack or whether anyone can connect the card to a real identity.

Worked example

Consider six fictional establishment records classified only by region and size: North-small, North-small, North-large, South-small, South-large, and South-large.
Using the two-variable key, the four combination counts are 2, 1, 1, and 2. North-large and South-small each occur once, so there are two sample-unique records among six, a sample-unique share of 2/6, approximately 33.3%.
If size is removed from the key, only region remains. North has three records and South has three, so no record is unique on that coarser key.
This reduction in uniqueness says nothing by itself about the true population counts or the safety of releasing other columns. The example contains invented categories and records and demonstrates only the counting definition, not a real identification procedure.

Illustrative case study

Fictional case: Juniper Research prepares a business survey dataset for external model evaluation. Direct names have been removed, but a confidentiality review finds several unique combinations among the planned descriptive fields.
The team assesses disclosure context, revises some category detail, and checks how the changes affect analytical usefulness. It documents remaining limitations and the appropriate access arrangement rather than declaring the file anonymous solely because the unique-combination count fell.

Common misconceptions and mistakes

A sample unique is not necessarily a population unique.
A unique combination does not prove that a real identity is known.
Deleting names alone does not make every remaining record non-identifying.
The absence of sample uniques on one key is not a universal confidentiality guarantee.
Uniqueness counts depend on variable selection, category detail, missing-value treatment, and the dataset being examined; they are not immutable properties of the people represented.

Business use

Use sample-unique analysis as one part of responsible data-sharing review. It helps identify combinations that deserve attention while keeping the distinction between rarity, identification, and sensitive-information disclosure clear. For AI projects, the same care applies to evaluation datasets, supporting examples, and repeated releases that may be combined.

Check your understanding

Why are there two sample uniques in the worked example?

Answer: Two region-size combinations each appear once.

Why do they disappear when the key contains only region?

Answer: Each region then has three matching records.

Does that prove the full dataset is safe to publish?

Answer: No; other attributes and contextual risks remain relevant.

Related terms

Statistical Disclosure Control (SDC)
k-anonymity
Population unique
key variable
equivalence class
statistical disclosure control
microdata
data minimization

Learn next

Using only synthetic records, compare uniqueness counts under two different category schemes. Explain the tradeoff between analytical detail and distinguishability without treating either count as a complete privacy assessment.

Sources

OECD Glossary of Statistical Terms, Sample unique: https://www.oecd.org/content/dam/oecd/en/publications/reports/2008/09/oecd-glossary-of-statistical-terms_g1gh9ad7/9789264055087-en.pdf UK Government Analysis Function, Statistical Disclosure Control for microdata produced from social survey data: https://analysisfunction.civilservice.gov.uk/policy-store/sdc-for-microdata-produced-from-social-survey-data/ The counting example and case are entirely fictional.

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