Chapter map

1. 1. Target series
2. 2. Reference stations
3. 3. Reference weights
4. 4. Relative series
5. 5. Standardization
6. 6. Candidate splits
7. 7. First mean
8. 8. Second mean
9. 9. Weighted contrast
10. 10. Second contribution
11. 11. Tk statistic
12. 12. Maximum search
13. 13. Null calibration
14. 14. Reference sensitivity
15. 15. Metadata investigation
16. 16. Adjustment decision

Visit the How Mathematics Works hub for the wider series and its connections to education, reasoning, science, computing, design and careers.

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1. Target series

This is where modelling choices begin to affect evidence. Define the station or process under review.

A concrete situation

Annual target values are aligned.

What the mathematics does not license

Missing years distort ratios. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Audit completeness. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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2. Reference stations

The central mathematical idea is concrete. Choose comparable surrounding records.

A concrete situation

Several neighbours form one reference.

What the mathematics does not license

Shared instrument changes contaminate it. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Check metadata. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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3. Reference weights

Here the geometry becomes operational. Declare how stations are combined.

A concrete situation

Weights reflect correlation and availability.

What the mathematics does not license

Outcome-based weights overfit. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Freeze rules. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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4. Relative series

This step deserves a careful pause. Form target-to-reference ratios or differences.

A concrete situation

One value compares local with regional level.

What the mathematics does not license

Near-zero references destabilize ratios. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Choose a safe form. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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5. Standardization

The useful question is not only how to calculate, but what the calculation assumes. Centre and scale the relative series.

A concrete situation

z values are used.

What the mathematics does not license

Contaminated scale weakens contrast. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Report estimators. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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6. Candidate splits

A small example makes the mechanism visible. Evaluate k from 1 to n-1 with safeguards.

A concrete situation

k=3 separates five values.

What the mathematics does not license

Tiny edge segments are unstable. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Use minimum lengths. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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7. First mean

This is where modelling choices begin to affect evidence. Average z1 through zk.

A concrete situation

First mean=-.816.

What the mathematics does not license

One outlier can dominate. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Inspect influence. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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8. Second mean

The central mathematical idea is concrete. Average remaining z values.

A concrete situation

Second mean=1.225.

What the mathematics does not license

Short second segments are noisy. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Report n-k. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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9. Weighted contrast

Here the geometry becomes operational. Compute k zbar1 squared.

A concrete situation

First contribution≈1.997.

What the mathematics does not license

Weights reward segment size. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Show components. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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10. Second contribution

This step deserves a careful pause. Compute (n-k) zbar2 squared.

A concrete situation

Second contribution≈3.001.

What the mathematics does not license

Rounding changes totals slightly. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Keep precision. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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11. Tk statistic

The useful question is not only how to calculate, but what the calculation assumes. Add both contributions.

A concrete situation

T3≈4.999.

What the mathematics does not license

It is not yet a probability. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Use calibrated maxima. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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12. Maximum search

A small example makes the mechanism visible. Find T0=max Tk.

A concrete situation

The largest split is the candidate.

What the mathematics does not license

Searching many k inflates tails. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Calibrate the full search. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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13. Null calibration

This is where modelling choices begin to affect evidence. Use appropriate tables or simulation.

A concrete situation

Reference-quality uncertainty is included if possible.

What the mathematics does not license

Fixed-reference simulation can be optimistic. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Rebuild references. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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14. Reference sensitivity

The central mathematical idea is concrete. Remove one station at a time.

A concrete situation

The candidate remains near k=3.

What the mathematics does not license

A single neighbour may drive it. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Report leave-one-out results. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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15. Metadata investigation

Here the geometry becomes operational. Check station history around the candidate.

A concrete situation

An instrument change is found.

What the mathematics does not license

Metadata may be incomplete. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Keep uncertainty visible. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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16. Adjustment decision

This step deserves a careful pause. Model any correction separately.

A concrete situation

Before and after levels are estimated.

What the mathematics does not license

Detection does not determine adjustment size. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Document the correction model. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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A seven-day practice lab

1. Day 1: define the decision, observation unit, X variables and Y or reference condition.
2. Day 2: reproduce the smallest worked example and check every dimension, unit and sign.
3. Day 3: build a transparent baseline and write what it assumes.
4. Day 4: fit the main method inside a training-only pipeline; record every parameter.
5. Day 5: challenge one assumption with a deliberately difficult dataset or operating regime.
6. Day 6: compare validation metrics with the practical workload created by errors.
7. Day 7: present one supported conclusion, one unresolved uncertainty and one safe next experiment.

Questions for a student, parent or mentor

• Which part of the model is a mathematical definition, and which part is a choice?
• What small calculation would catch a sign, scale or dimension error?
• What evidence comes from training, validation and the untouched test?
• What benign condition could look like a fault or prediction failure?
• How would the answer change for another response, asset, school project or time period?
• What should a human review before acting on the score?

A method-specific audit before deployment

The Standard Normal Homogeneity Test, usually called SNHT, compares the mean of the standardized series before each candidate split with the mean after it. The candidate with the largest weighted squared contrast becomes the suspected break. In climate quality control, the original relative version compares a target station with surrounding reference stations to separate local measurement changes from regional weather.

For standardized values zi and split k, let z̄1 be the mean of the first k values and z̄2 the mean of the remaining n−k. The statistic Tk=k z̄1²+(n−k)z̄2², and T0=max Tk. Weighting by segment length rewards a contrast supported by more observations while the square makes either direction count.

Consider z values −0.816, −0.816, −0.816, 1.225 and 1.225. At k=3, the segment means are −0.816 and 1.225, giving T3=3(0.816²)+2(1.225²)≈4.999. This almost perfectly separated toy series illustrates the calculation; a real conclusion requires the correct standardization, reference construction and null calibration.

SNHT can be distorted by a poor reference series, simultaneous regional changes, serial dependence, seasonality, metadata gaps and multiple breaks. A statistical maximum should be investigated alongside station history, instrument changes and neighbouring records. Homogenization adjustments require an additional documented model, not an automatic edit at every detected maximum.

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Frequently asked questions

What is SNHT?

It is a maximum test based on standardized segment means before and after each candidate break.

Why use a reference series?

A good surrounding reference helps distinguish a local measurement change from weather shared across the region.

What is Tk?

It is k times the squared first-segment mean plus n−k times the squared second-segment mean.

Why square the segment means?

Squaring counts departures in either direction and forms the likelihood-based contrast under the standard model.

Does the maximum automatically justify adjustment?

No. It identifies a candidate that must be checked with station history, references and alternative explanations.

Can several breaks be found by one basic SNHT run?

The basic maximum targets one break; multiple-break procedures need separate search and multiplicity controls.

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Primary source and fact-check note

Hans Alexandersson, “A Homogeneity Test Applied to Precipitation Data,” Journal of Climatology 6(6), 661–675 (1986), DOI 10.1002/joc.3370060607. Definitions and core claims in this article were checked against this primary publication. Calculations shown here were independently recomputed. Examples are educational illustrations; they are not reported industrial performance results.

Useful next reading

• Buishand range test
• Pettitt change-point test
• How Mathematics Works

Keep the options open. Mathematics education supports clearer questions, transferable problem-solving skills and informed choices across science, engineering, computing, AI, statistics, design and many other careers. It does not guarantee intelligence, income, admission or employment; those outcomes depend on far more than one subject or model.

Extended laboratory: topic-specific validation and responsible use

Reference audit

Publish station choice, weights and missing-data rules.

Ratio audit

Verify relative-series construction.

Standardization audit

Reproduce centres and scales.

Split audit

Calculate Tk for every eligible k.

Maximum audit

Calibrate the complete search.

Sensitivity audit

Leave out each reference in turn.

Metadata audit

Investigate instruments and procedures.

Final claim

Separate break detection from adjustment.

Mechanism workshop: calculate, challenge and transfer

Workshop 1: Target series

Begin with this mechanism: Define the station or process under review. Recreate the concrete case: Annual target values are aligned. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Missing years distort ratios. Complete the transfer step: Audit completeness. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 2: Reference stations

Begin with this mechanism: Choose comparable surrounding records. Recreate the concrete case: Several neighbours form one reference. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Shared instrument changes contaminate it. Complete the transfer step: Check metadata. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 3: Reference weights

Begin with this mechanism: Declare how stations are combined. Recreate the concrete case: Weights reflect correlation and availability. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Outcome-based weights overfit. Complete the transfer step: Freeze rules. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 4: Relative series

Begin with this mechanism: Form target-to-reference ratios or differences. Recreate the concrete case: One value compares local with regional level. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Near-zero references destabilize ratios. Complete the transfer step: Choose a safe form. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 5: Standardization

Begin with this mechanism: Centre and scale the relative series. Recreate the concrete case: z values are used. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Contaminated scale weakens contrast. Complete the transfer step: Report estimators. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 6: Candidate splits

Begin with this mechanism: Evaluate k from 1 to n-1 with safeguards. Recreate the concrete case: k=3 separates five values. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Tiny edge segments are unstable. Complete the transfer step: Use minimum lengths. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 7: First mean

Begin with this mechanism: Average z1 through zk. Recreate the concrete case: First mean=-.816. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: One outlier can dominate. Complete the transfer step: Inspect influence. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 8: Second mean

Begin with this mechanism: Average remaining z values. Recreate the concrete case: Second mean=1.225. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Short second segments are noisy. Complete the transfer step: Report n-k. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 9: Weighted contrast

Begin with this mechanism: Compute k zbar1 squared. Recreate the concrete case: First contribution≈1.997. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Weights reward segment size. Complete the transfer step: Show components. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 10: Second contribution

Begin with this mechanism: Compute (n-k) zbar2 squared. Recreate the concrete case: Second contribution≈3.001. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Rounding changes totals slightly. Complete the transfer step: Keep precision. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 11: Tk statistic

Begin with this mechanism: Add both contributions. Recreate the concrete case: T3≈4.999. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: It is not yet a probability. Complete the transfer step: Use calibrated maxima. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 12: Maximum search

Begin with this mechanism: Find T0=max Tk. Recreate the concrete case: The largest split is the candidate. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Searching many k inflates tails. Complete the transfer step: Calibrate the full search. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 13: Null calibration

Begin with this mechanism: Use appropriate tables or simulation. Recreate the concrete case: Reference-quality uncertainty is included if possible. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Fixed-reference simulation can be optimistic. Complete the transfer step: Rebuild references. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 14: Reference sensitivity

Begin with this mechanism: Remove one station at a time. Recreate the concrete case: The candidate remains near k=3. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: A single neighbour may drive it. Complete the transfer step: Report leave-one-out results. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 15: Metadata investigation

Begin with this mechanism: Check station history around the candidate. Recreate the concrete case: An instrument change is found. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Metadata may be incomplete. Complete the transfer step: Keep uncertainty visible. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 16: Adjustment decision

Begin with this mechanism: Model any correction separately. Recreate the concrete case: Before and after levels are estimated. Write target values, reference values, station weights, relative ratios, standardized values, split points, segment sizes, segment means, weighted squared contrasts, maximum statistics, calibrated probabilities and metadata events with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Detection does not determine adjustment size. Complete the transfer step: Document the correction model. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.