Repeated Significance Tests on Accumulating Data.¶
Armitage, P., McPherson, C. K., & Rowe, B. C. (1969). Repeated Significance Tests on Accumulating Data. Journal of the Royal Statistical Society, Series A, 235-244.
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Primes¶
- Termination Condition
- Termination condition supports several portable inferences. Halting requires a separate argument: proving that an iterative process terminates is structurally distinct from proving that it does the right thing while iterating, and conflating the two is a recurring engineering bug. Monotone-progress plus bounded-state implies termination: if each step monotonically changes a state variable that lives in a bounded set, termination is forced, which is the underlying form of nearly every classical termination proof — loop variants, well-founded recursion, decreasing measure functions. No-progress conditions are dangerous near optima: a stopping rule based on "the objective stopped improving" can halt arbitrarily close to or far from the optimum depending on the landscape, with the cross-domain symptom of solvers converging to wrong answers and early-stopped models acquiring avoidable bias. Optional stopping inflates false positives: a rule allowed to look at the data and choose when to stop violates fixed-design statistical guarantees, the same structural fact appearing in p-hacking, mid-game concession in negotiation, and early stopping for non-inferiority.
This sourceFoundational demonstration that repeated significance testing on accumulating data inflates the Type I error above the nominal level — the basis for stopping rules in sequential testing.
- Termination condition supports several portable inferences. Halting requires a separate argument: proving that an iterative process terminates is structurally distinct from proving that it does the right thing while iterating, and conflating the two is a recurring engineering bug. Monotone-progress plus bounded-state implies termination: if each step monotonically changes a state variable that lives in a bounded set, termination is forced, which is the underlying form of nearly every classical termination proof — loop variants, well-founded recursion, decreasing measure functions. No-progress conditions are dangerous near optima: a stopping rule based on "the objective stopped improving" can halt arbitrarily close to or far from the optimum depending on the landscape, with the cross-domain symptom of solvers converging to wrong answers and early-stopped models acquiring avoidable bias. Optional stopping inflates false positives: a rule allowed to look at the data and choose when to stop violates fixed-design statistical guarantees, the same structural fact appearing in p-hacking, mid-game concession in negotiation, and early stopping for non-inferiority.
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