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Random design and sample balance

A probability design can produce an imbalanced realized sample; a balanced-looking sample can lack a valid probability mechanism.

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Ask how the units were chosen

A design can be audited by its frame and randomization rules. A photograph or table showing a pleasing mix of groups does not reveal the selection probabilities. Hand-picked observations can appear balanced on one recorded feature while being selected on other unrecorded features.

Inspect the observed composition

A simple random sample does not force every subgroup to appear in every draw. If a study requires positive samples in defined subgroups, a stratified allocation can enforce that coverage. The rule then belongs in the design, with appropriate estimation weights.

Keep claims about features separate

Evidence and scope
EvidenceWhat it establishes
Recorded random selection ruleHow selection can occur
Matched group percentagesBalance on those measured groups
Every subgroup sampledCoverage of those defined subgroups
Large stored row countA record count, not automatic representativeness

Report both design and limitations

Document unexpected imbalances, response patterns and missing frame units. The design’s uncertainty calculation and the sample’s substantive limitations answer different questions. Neither should be hidden behind a generic claim that the sample is representative.

Further references