Minimum Detectable Effect Table¶
Design reference table — instantiates Hypothesis Test Power Calibration
Reverses the sample-size question — for a design whose size is already fixed by budget or population, tabulates the smallest effect it can detect at the target power.
The single idea that makes this mechanism itself and not its curve-drawing twin: it runs the power relation backwards from a fixed design. Most power tools ask "how many units do I need to detect this effect?" — but often the units are not negotiable. The population is capped, the budget is set, the survey window closes on a date. Minimum Detectable Effect Table starts from that fixed, feasible design and asks the inverted question: given this N, this allocation, this alpha and target power, what is the smallest effect I could reliably detect? It solves the power relation for the effect axis instead of the sample axis and lays the answers out as a table — one row per plausible design constraint (response rate, group split, budget tier), each reporting its minimum detectable effect. That single number per row is a reality check: if the smallest effect the design can catch is larger than any effect anyone would act on, the study is decorative before it begins.
Example¶
An HR team wants to know whether a new manager-coaching program moves employee engagement, measured on an annual survey. The catch is that the whole company is 850 employees — there is no "recruit more" lever, and only about 70% typically respond. Rather than pretend they can choose N, they build a minimum-detectable-effect table over the constraints they do control: response rates of 60/70/80%, an even versus a two-thirds/one-third split between coached and uncoached managers' teams, and the survey's known score spread. Each cell inverts the power formula at 80% power and 5% alpha to report the smallest engagement shift detectable. The table is sobering: even at the best response rate and balanced split, the design can only reliably catch a shift of about 0.3 points on the five-point scale — and the leadership team had hoped to detect half that. The table converts a vague "let's just run the survey" into a concrete choice: accept that only a large effect is visible, oversample the coached teams, or pool two years of data before claiming anything.
How it works¶
- Fix the design, free the effect. Take N, allocation, alpha, target power, and the noise level as given, and treat the effect size as the unknown to solve for.
- Invert a supplied power relation. Using a power relation produced elsewhere (a formula or a simulation), solve for the effect that yields exactly the target power at the fixed design — it does not build that relation, it reads it in reverse.
- Tabulate over feasible constraints. Repeat across the design variations that are actually on the table — response rate, split, budget tier, follow-up window — so each row is a design a decision-maker could truly choose.
- Compare against the meaningful threshold. Set each row's minimum detectable effect beside the smallest effect worth acting on; rows whose MDE exceeds that threshold are flagged as under-instrumented.
Tuning parameters¶
- Fixed power level — the power at which the MDE is quoted; a higher bar reports a larger (harder-to-beat) minimum detectable effect, an honest but less flattering number.
- Constraint axes tabulated — which feasibility levers become table rows (response rate, split, budget); more axes surface options but bloat the table.
- Allocation split — the group ratio per row; imbalance forced by feasibility inflates the MDE.
- Effect metric — raw units versus standardized; raw units read plainly to stakeholders, standardized ones travel across studies.
- Meaningful-effect marker — where the "worth acting on" line is drawn on the table; move it and different rows flip from adequate to decorative.
When it helps, and when it misleads¶
Its strength is honesty under constraint: when the sample cannot grow, it refuses the fiction that any effect is detectable and shows exactly which effects the fixed design can and cannot see — the ideal antidote to convenience-N studies that never ask what they could catch. It misleads when the meaningful threshold is set loosely: an MDE looks acceptable only relative to the smallest effect size of interest, and if no one has committed to that number, a large MDE can be waved through as "fine."[n1] The classic misuse is reading the table as a promise — treating the minimum detectable effect as the effect the study will find, rather than the floor below which it goes blind. The guarding discipline is to fix the meaningful-effect line before reading the table, and to treat any row whose MDE sits above it as a design that must change or be relabeled exploratory.
How it implements the components¶
decision_relevant_effect_threshold— its output is expressed in effect units and read directly against the smallest effect worth acting on, making that threshold the pivot of the whole table.sample_size_and_allocation_plan— the fixed N and allocation are the table's inputs; each row is a concrete plan whose sensitivity is being priced.feasibility_and_ethics_constraint— the table exists precisely because size is bounded by budget, population, or burden; those constraints define its rows.
It does not build an operating_characteristic_model — it inverts one supplied by Closed-Form Power Calculation or Simulation-Based Power Analysis. Its nearest twin is Operating Characteristic Curve: both read a fixed design's sensitivity, but the curve owns the full operating_characteristic_model and traces detection probability across every effect, whereas this table holds power fixed and reports the single boundary effect per feasible design.
Related¶
- Instantiates: Hypothesis Test Power Calibration — the reversal used when the sample is fixed and the effect is unknown.
- Consumes: Closed-Form Power Calculation or Simulation-Based Power Analysis — supplies the power relation the table inverts.
- Sibling mechanisms: Closed-Form Power Calculation · Simulation-Based Power Analysis · Operating Characteristic Curve · Power Sensitivity Grid · Pre-Analysis Power Statement · Pilot Variance Estimation
Editorial Notes¶
Form Classification¶
Form family: Analysis, Modeling & Optimization
Rationale: Minimum Detectable Effect Table operates as a computation, comparison, model, or analytic representation used to infer, estimate, or choose because it reverses the sample-size question — for a design whose size is already fixed by budget or population, tabulates the smallest effect it can detect at the target power.
Independent corroboration: The frozen evidence defines Minimum Detectable Effect Table as 'Reverses the sample-size question — for a design whose size is already fixed by budget or population, tabulates the smallest effect it can detect at the target power', so its operative form is Analysis, Modeling & Optimization.
Review outcome: Independent reviewer agreement; high confidence.
Origin Attribution¶
Primary origin: Statistics & Experimental Design
Origin pattern: Cross-disciplinary synthesis
Present-day reach: Multi-domain
Rationale: Minimum detectable effects are standard statistical power and study-design quantities.
Related originating lineages:
- Medicine & Healthcare — Clinical research institutionalized tabular effect thresholds under fixed samples and budgets.
Review resolution: Both independent reviews place the primary provenance in statistics_experimental_design. The queued differences (alternate_origin_disagreement, origin_mode_disagreement) concern secondary metadata, not primary lineage. The final retains medicine_healthcare only where a reviewer supplied a formative-lineage rationale; downstream use or broad applicability by itself is not treated as origin. origin_mode=cross_disciplinary_synthesis because the supplied rationales identify formative contributions that are composed in the mechanism's present form. domain_reach=multi_domain records established application breadth separately from provenance. confidence=high preserves the more cautious evidence assessment. encyclopedia_synthesis=false records whether either reviewer identified deliberate corpus-level composition.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
[n1] The smallest effect size of interest is the pre-committed line below which an effect would not change any decision. A minimum detectable effect is only interpretable against it: an MDE means little in the abstract and everything once you can say whether it sits above or below the effect anyone actually cares about. ↩