Predeclare review triggers across repeated observations

Define the decision and evidence boundary

A monitoring plan should specify what observation triggers review, what confirms the signal and who is authorized to revise action. Looking repeatedly for an unusual result creates more opportunities for a false alarm. That statistical issue is distinct from the ecological consequences of missing a true problem.

Reconstruct the transparent method

If m looks are independent and each has false-alarm probability α when no change exists, the probability of at least one alarm is 1−(1−α)^m. Without independence, the union bound gives an upper limit min(1,mα). Environmental records are often serially correlated, so independence must not be assumed merely because measurements have different dates.

Interpret the comparison

For a total family target α across m predeclared looks, a Bonferroni allocation uses per-look levelα/m. The bound does not require independence, but may be conservative. A more elaborate sequential procedure needs its own justified design; repeatedly resetting the monitoring family after an inconvenient result changes the original error accounting.

Predeclare limitations and revision

A review trigger is not automatic permission for a physical intervention. A responsible plan retains raw data, verifies measurement quality, assesses effect size and ecological relevance, checks safety/legal constraints and records the authorized decision. Urgent safety signals may require separate escalation rules rather than waiting for a statistical threshold.

Worked original packet

At per-look 0.05 and six independent looks, at-least-one false alarm is 1−0.95⁶≈0.26491. The dependence-agnostic union bound is 0.30. For a total target 0.05, Bonferroni per-look level is 0.05/6≈0.008333.

Investigation

Compare one,six and twelve looks at 0.05. Explain the independence limitation, then write a review/confirmation/escalation rule without presenting this toy alpha as a regulatory threshold.

Changed-case transfer

At per-look 0.02 and ten looks, calculate independent family probability, union bound and per-look level for total target 0.02.

Feedback

Independent probability 1−0.98¹⁰≈0.182927; union bound 0.20. Bonferroni level 0.002 gives a family upper bound 0.02 under valid per-look tests; it does not establish power or practical importance.

Sources and evidence boundary

Original prose, dataset and numerical exercises. Primary method/mechanism source, checked 30 October 2026. The versioned packet is synthetic, not observed fieldwork. No treatment implementation, site access, pollutant handling or real management authorization is requested. Preserve first reasoning and critique in the course workspace.