Skill type: DISCIPLINE-ENFORCING. Before a single case is collected, this gate fixes three things — the frame, the method, and the size logic — and ties the generalization claim to them. It does not run the study or pick the test; it refuses to let sizing and recruitment happen by habit.
The Core Rule
WHO YOU SAMPLE AND HOW MANY MUST FOLLOW THE INFERENCE YOU WANT —
POWER FOR TESTS, PRECISION FOR ESTIMATES, SATURATION FOR THEORY.
A BIGGER N NEVER FIXES A BROKEN FRAME.
Sample size is not one calculation; it is whichever logic matches the inference. A hypothesis test needs an a-priori power analysis (effect size + alpha + power ⇒ N). An estimation goal needs a precision target (a margin of error at a confidence level). A qualitative study is governed by saturation / information power, not a formula. And none of these matters if the frame — the list you actually draw from — omits or over-represents part of the target population. Coverage error and self-selection are not cured by collecting more.
When to Use This Skill
- "How many participants / interviews / respondents do I need?"
- "Is my sample big enough to detect the effect?" (← a-priori power)
- "I surveyed 300 students; can I generalize to all adults?" (← frame + method)
- "My result was not significant — should I just collect more until it is?" (← no; pre-specify)
- "What sampling method should I use — stratified, cluster, quota…?"
Does NOT Trigger
| The request is really about… | Route to | Why not this skill |
|---|---|---|
| Writing / wording the questionnaire items | alterlab-survey-design |
Instrument construction, not sampling. |
| Which statistical test to run once data are in | alterlab-test-selection-guard |
Test choice, downstream of sampling. |
| Executing the power analysis / analysis in software | alterlab-statistical-analysis |
Computation; this gate sets the logic, hands execution off. |
| Deep grounded-theory / coding mechanics | alterlab-qualitative-methods |
This gate sets saturation logic; that skill does the qual depth. |
| Choosing the design & identifying assumption | alterlab-ssci-design-gate |
Design routing, upstream of sampling. |
Three sizing logics — pick by the inference, not by habit
| Inference goal | Sizing logic | Inputs | Common failure |
|---|---|---|---|
| Test a hypothesis | a-priori power analysis | expected effect size, α, target power (usually .80/.90), test | powering off an inflated pilot effect; post-hoc "observed power" |
| Estimate a quantity | precision / margin of error | desired half-width, confidence level, expected variance/proportion | reporting N with no CI target |
| Build/refine theory (qual) | saturation / information power | scope, sample specificity, dialogue quality, analysis strategy | quoting a fixed "N=12" as a rule instead of arguing information power |
A stdlib calculator for the first two (two-group mean or two-proportion designs):
scripts/sample_size.py. Full logic, stratified/cluster design effects, and finite-population
correction: references/sampling_and_power.md.
Frame and method before size
- Frame vs target population. Name the target population, then the frame you can actually draw from. The gap between them is coverage error — state it. A sample of your university's students is not a sample of adults.
- Probability vs non-probability. Only a probability sample (each unit a known non-zero selection probability: SRS, stratified, cluster, systematic) supports statistical generalization with a sampling-error quantification. Non-probability samples (convenience, quota, snowball, purposive) support only analytical/theoretical generalization — say so and do not attach a margin of error as if it were random.
- Non-response & attrition. A high non-response rate reintroduces selection bias even from a good frame. Plan for it; report it; consider weighting.
Excuse vs Reality
| Excuse | Reality |
|---|---|
| "I'll collect as many as I can get." | Convenience size is not power. Name the target effect and compute N — or state you are estimating, not testing. |
| "It wasn't significant, so I'll add data until it is." | Optional stopping inflates the false-positive rate. Pre-register N (or a sequential design with corrected boundaries). |
| "300 is a big sample, so it generalizes." | Generalization comes from the frame and method, not the count. 300 self-selected students still only speak for self-selected students. |
| "Observed (post-hoc) power shows the test was fine." | Post-hoc power is a deterministic function of the p-value; it carries no new information. Use a-priori power. |
| "For qualitative work I'll do N=12 because that's standard." | Saturation/information power is argued from scope and data quality, not a fixed number copied from another study. |
The Design Passport (hand-off)
Append: target_population, sampling_frame (+ named coverage gap), sampling_method
(probability/non-probability + specific design), size_logic (power | precision |
saturation) with its inputs and resulting N (or saturation argument), expected_nonresponse,
and generalization (statistical | analytical). alterlab-ssci-inference-gate later audits
the final generalization claim against sampling_method + generalization.
Self-Check Before Advancing
- Is the sizing logic the one that matches the inference (power / precision / saturation)?
- For a test, is N from an a-priori power analysis on a defensible effect size — not a pilot's inflated one?
- Is the frame stated, with its coverage gap from the target population named?
- Is the sample probability or non-probability, and is the generalization claim scoped to match?
- Is non-response/attrition planned for, not ignored?
References
references/sampling_and_power.md— sizing logics, design effects, finite-population correction, reporting templates.scripts/sample_size.py— stdlib a-priori N for two-group mean and two-proportion designs.
Part of the AlterLab Academic Skills suite.