The Certainty Bound — Interactive Instruments

Certainty Bound Diagnostic

Given prior probability, significance threshold, power, and reliability target, computes the positive predictive value, the infeasibility index Ψ, and the structural regime.

PPV = πΛ / (πΛ + 1−π) Ψ = Λ_req / Λ Λ_req = (τ/1−τ)·(1−π)/π Ceiling = π / (π + α(1−π))

Prior probability π

0.10

Significance α

0.050

Power 1−β

0.80

Target reliability τ

0.95

—

PPV

—

Infeasibility index Ψ —

Leverage Λ —

Required leverage —

Ceiling PPV —

Critical prior π_crit —

Min. α for feasibility —

Adjust the parameters above to diagnose the reliability regime.

Replication Pipeline

The minimum pipeline depth k* required to achieve target reliability τ. Leverage compounds multiplicatively: Λ^k = ((1−β)/α)^k.

Λ^(k) = Λ^k α^(k) = α^k PPV(k) = πΛ^k / (πΛ^k + 1−π)

Prior π

0.10

Significance α

0.050

Power 1−β

0.80

Target τ

0.95

Single-study PPV (k = 1) —

Min. pipeline depth k* —

Pipeline α at k* —

Pipeline leverage at k* —

k	α^k	Power^k	Λ^k	PPV	≥ τ?

Adjust parameters above.

Reliability Landscape

The feasibility boundary Ψ = 1 on the (Λ, π) plane. Plot your own field alongside calibrated reference points from the literature.

Field name

Prior π

0.150

Significance α

0.050

Power 1−β

0.80

Majority-false

Infeasible

Feasible

Your field

Feasibility boundary (τ = 0.95)

Majority-false boundary

Adjust the sliders to place your field on the landscape.