A rising nominal home-price index does not by itself show whether housing became more or less affordable. Affordability depends on the price faced by the relevant household, disposable income, financing terms, taxes, subsidies, rents, location and the definition of the dwelling basket.
This guide develops one focused reader question within the Urban Economics subject guide. It adds a complete mechanism, original worked decisions, changed-context transfer checks and explicit limits. Read it with The Gold Standard of Education | Learning That Transfers into Life and the How X Works.
All numerical examples are invented teaching cases. They are not operational measurements, production records, financial advice, conservation findings or compliance results.
In a fictional year, a matched-home price rises from 500,000 to 540,000, or 8%, while disposable income rises from 80,000 to 83,200, or 4%. The simple price-to-income ratio moves from 6.25 to 6.49, an increase of about 3.85%, so affordability worsens on that narrow measure even though income rose. If the mortgage rate also rises, required payments may move more sharply; if a subsidy changes, the household result can differ again. OECD housing prices distinguishes nominal and real house-price indices and defines price-to-income as a measure of affordability. Its methodology also notes that this ratio does not include borrowing costs.
Continue with Separating Matched-Home Price Change from a Changing Sales Mix, Avoiding Double Counting When Accessibility Gains Appear in Property Values and the Urban Economics root.
The short answer is to keep the target quantity, observation and reporting rule separate. Name what the system intends to estimate, what was actually observed, how the summary was formed and which conditions make the inference defensible. If one field is missing, keep the ambiguity visible.
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A rising nominal home-price index does not by itself show whether housing became more or less affordable. Affordability depends on the price faced by the relevant household, disposable income, financing terms, taxes, subsidies, rents, location and the definition of the dwelling basket.
ROUTE 4 · CHAPTERS 19–22
Audit and continue
Repair claims, answer questions and follow verified routes.
Chapter contents
Define the question · Chapters 1–6
2. Separate the two target quantities
4. Protect the denominator and boundary
Protect the method · Chapters 7–12
7. Check units before interpretation
8. Keep method settings visible
10. Recognise saturation and censoring
Test the claim · Chapters 13–18
13. Separate mechanism from appearance
16. Change one consequential condition
Audit and continue · Chapters 19–22
19. State what it cannot establish
20. Repair an overconfident sentence
Ask whether the claim concerns market price, real value, purchase burden, monthly payment, rent burden or access to suitable homes.
Write an evidence ledger before calculating: target quantity, object, unit, boundary, observation rule, transformation and decision limit. Mark every input as observed, stipulated, fitted or assumed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “define the reader question”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Nominal price growth is a price-index change; affordability relates housing cost to resources and financing for a defined population.
Draw the mechanism in order. Separate the underlying state, the measurement, the mathematical summary and the claim. Then name one rival explanation and the additional observation that could distinguish it.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “separate the two target quantities”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Name the house-price index, income measure, household, location, tenure and time interval.
Keep the comparison fair by holding the specimen, interval, protocol and denominator constant. If one changes, state that the new number answers a different question even when the label looks familiar.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “name the observation rule”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
A national mean, city median and matched-home index have different populations and composition effects.
Use two checks that can fail differently: reconstruct a total, test a limiting case, repeat the result from definitions or inspect a shared control. Two calculations that reuse one assumption are only one check.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “protect the denominator and boundary”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Record price 500,000 to 540,000 and income 80,000 to 83,200 before ratios or interpretations.
Separate measurement from decision. A correct number can still be too local, uncertain or method-dependent for the intended action. Report it with its conditions and say what stronger evidence would be needed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “build the fictional evidence ledger”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Price growth is 8%; income growth is 4%; price-to-income rises from 6.25 to about 6.49.
| Fictional quantity | Start | End |
|---|---|---|
| Home price | 500,000 | 540,000 |
| Income | 80,000 | 83,200 |
| Price/income | 6.25 | 6.49 |
Preserve identity and order. Equal totals can hide different mechanisms when records come from different specimens, resources, homes or viewing geometries. Aggregate only after the question no longer depends on that identity.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “work the central calculation”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Index points, currency, annual income and monthly payments cannot be swapped without definitions and conversions.
Run a changed-context transfer check. Change one consequential condition while holding the remaining basis fixed, calculate again and explain why the result moves or stays stable.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “check units before interpretation”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Interest rate, term, deposit, taxes, maintenance and eligibility rules shape the household payment path.
Put the boundary of inference beside the answer. Name the system, representation and interval to which the result applies, then name the nearest tempting conclusion the evidence does not establish.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “keep method settings visible”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Check whether prices and incomes cover comparable geographies, dwelling types, households and seasons.
Use uncertainty as structure. Vary the input most capable of changing the conclusion over a defensible range and show whether the ranking or interpretation changes.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “locate the usable range”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
A price index can rise while some segments fall; a median income can rise because population composition changes.
Finish with a reproducible evidence package: source records, definitions, exclusions, calculations, validation result and revision rule.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “recognise saturation and censoring”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Use matched-home measures, income distributions, payment calculators and rental measures as independent checks.
Write an evidence ledger before calculating: target quantity, object, unit, boundary, observation rule, transformation and decision limit. Mark every input as observed, stipulated, fitted or assumed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “use controls that can fail differently”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Carry sampling error, index revision and plausible financing terms into the affordability range.
Draw the mechanism in order. Separate the underlying state, the measurement, the mathematical summary and the claim. Then name one rival explanation and the additional observation that could distinguish it.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “carry uncertainty into the claim”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Price growth may reflect supply limits, amenities, rates, credit, incomes or expectations. The ratio alone does not identify cause.
Keep the comparison fair by holding the specimen, interval, protocol and denominator constant. If one changes, state that the new number answers a different question even when the label looks familiar.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “separate mechanism from appearance”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Compare the same dwelling and household definition or state every mismatch.
Use two checks that can fail differently: reconstruct a total, test a limiting case, repeat the result from definitions or inspect a shared control. Two calculations that reuse one assumption are only one check.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “compare like with like”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
A lower price-to-income ratio can coexist with poor access if suitable supply is scarce or deposits bind.
Separate measurement from decision. A correct number can still be too local, uncertain or method-dependent for the intended action. Report it with its conditions and say what stronger evidence would be needed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “test a rival explanation”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Change income growth to 10% while keeping the 8% price rise; the simple ratio then improves.
Preserve identity and order. Equal totals can hide different mechanisms when records come from different specimens, resources, homes or viewing geometries. Aggregate only after the question no longer depends on that identity.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “change one consequential condition”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
End income 88,000 gives price-to-income about 6.14, below 6.25. The price still rose while the narrow affordability ratio improved.
Run a changed-context transfer check. Change one consequential condition while holding the remaining basis fixed, calculate again and explain why the result moves or stays stable.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “recalculate the changed case”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
The original case establishes that prices outpaced income under a simple matched definition.
Put the boundary of inference beside the answer. Name the system, representation and interval to which the result applies, then name the nearest tempting conclusion the evidence does not establish.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “state what the result establishes”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
It does not establish monthly payment, distributional access, welfare or a policy cause.
Use uncertainty as structure. Vary the input most capable of changing the conclusion over a defensible range and show whether the ranking or interpretation changes.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “state what it cannot establish”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Replace “prices rose 8%, so homes became 8% less affordable” with the calculated ratio and stated exclusions.
Finish with a reproducible evidence package: source records, definitions, exclusions, calculations, validation result and revision rule.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “repair an overconfident sentence”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Are real prices affordability? No. Inflation adjustment and household resources answer different questions.
Does price-to-income include interest rates? Usually not. Add financing evidence.
Can one city average describe every buyer? No. Distribution and eligibility matter.
Write an evidence ledger before calculating: target quantity, object, unit, boundary, observation rule, transformation and decision limit. Mark every input as observed, stipulated, fitted or assumed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “answer focused reader questions”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Use OECD definitions, local housing data and financing evidence, then follow matched-home and accessibility branches.
Draw the mechanism in order. Separate the underlying state, the measurement, the mathematical summary and the claim. Then name one rival explanation and the additional observation that could distinguish it.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For Urban Economics, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “continue through verified routes”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.