Count facilities, then investigate access

Count facilities, then investigate access

Start with the question

Does having more facilities mean better service?

Inspect the teaching record

Fictional East has four facilities and 20000 residents. West has three and 10000 residents. Each East facility has 100 places; each West facility has 50.

This is fictional teaching evidence. It is not an observation about an actual community or economy.

Explain the mechanism

Per-person availability, service capacity and travel are separate access dimensions. A population denominator permits comparison across unequal places. Even a high facility rate may coexist with long journeys, poor accessibility or unavailable appointments. Never interpret zero residents as a zero rate.

Follow the worked example

East has 4/20000 × 10000 = 2 facilities per 10000. West has 3. East capacity is 400/20000 × 1000 = 20 places per 1000; West has 15.

Challenge the first explanation

East residents are assigned a uniform 20-minute journey and West residents a 40-minute journey. These are simplifying assumptions, not measured travel distributions; prices and opening hours are missing.

Make and revise your evidence

Capture East and West settings in the access lab. Compare the three indicators and recommend one missing measurement before choosing a location.

Revise your answer to “Does having more facilities mean better service?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.

Name the idea

Denominator: The population or other reference quantity used to form a rate.

Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.

Extend the investigation

Whose journey does the average describe?

A fictional town can open one library at X or Y. A and B each have100 residents; C has800. Compare the same population under two proposed sites. Every resident of a neighborhood shares its stated journey time, for one fixed travel mode/time setting. These are original teaching assumptions, not observed trips or a geographic route map.

Predict a site and state your criterion Evidence caseOriginal journey timesTransfer: A-to-Y journey becomes 8 minutesAudit: C-to-Y journey time is missing Mean weightingOne equal weight per residentOne equal weight per neighborhood Coverage threshold10 minutes or less15 minutes or less20 minutes or less40 minutes or less

One proposed site at a time; same1,000 residents

Site	Known times for residents	Mean minutes, resident weights	Worst neighborhood minutes	Residents at or below15min
X	1000/1000	17.500	20.000	20.0%
Y	1000/1000	10.000	40.000	80.0%

Reconstruct the weights and inspect the assumptions

The resident mean is (100×A minutes +100×B minutes +800×C minutes)/1000. The neighborhood mean is (A minutes+B minutes+C minutes)/3. Changing this rule changes the question; it does not move people. Coverage always counts residents, regardless of the mean selector. Threshold equality is included. Worst journey is the largest of three stated times, not a measured within-neighborhood maximum.

• SiteX: A: 5 min × weight100, B: 10 min × weight100, C: 20 min × weight800; mean denominator1000. Confirmed covered residents200 of1000.
• SiteY: A: 40 min × weight100, B: 20 min × weight100, C: 5 min × weight800; mean denominator1000. Confirmed covered residents800 of1000.

A missing time blocks the complete-population mean and worst journey. We do not drop those residents from the denominator. Coverage bounds assign all unknown-time residents either outside or inside the threshold; these are logical bounds, not confidence intervals. Missing does not mean unreachable.

Methodological context: DfT2019 journey-time definitions distinguish average journey time and the share of users within a time threshold. NAO2020 technical guide explains that travel time alone omits other barriers. We use original library numbers, not their measured outputs or a reproduction of their routing model. Fares, physical accessibility, opening hours, capacity and user eligibility remain unmodeled. A site with a better mean is not automatically the best public decision.

Transfer: compare the improved A-to-Y journey with the original case. Then inspect the missing-time audit. Write a recommendation that names the weighting and criterion, identifies the neighborhood disadvantaged by it, and names a measurement that could change the choice.

Revised decision and missing evidence

Compare your decision reasoning

Originally resident means favor Y:10 minutes versus X17.5. Equal-neighborhood means favor X:11.667 versus Y21.667. Worst journey favors X20 versus Y40, while15-minute resident coverage favors Y80% versus X20%. No single site wins every criterion. After A-to-Y becomes8, Y's resident mean6.8 and neighborhood mean11 both beat X; worst journeys tie20, but B still travels20 to Y versus10 to X. Missing C-to-Y blocks a complete mean; original15-minute Y coverage is only bounded0–80%.

Copy your access analysis

{ "activity": "GEO-04.b access distributions", "fictional": true, "audit": { "mode": "baseline", "weight": "people", "threshold": 15, "neighborhoods": [ { "id": "A", "population": 100, "x": 5, "y": 40 }, { "id": "B", "population": 100, "x": 10, "y": 20 }, { "id": "C", "population": 800, "x": 20, "y": 5 } ], "sites": [ { "id": "x", "rows": [ { "id": "A", "population": 100, "minutes": 5, "weight": 100 }, { "id": "B", "population": 100, "minutes": 10, "weight": 100 }, { "id": "C", "population": 800, "minutes": 20, "weight": 800 } ], "complete": true, "denominator": 1000, "knownPopulation": 1000, "mean": 17.5, "worst": 20, "covered": 200, "coverageLow": 0.2, "coverageHigh": 0.2 }, { "id": "y", "rows": [ { "id": "A", "population": 100, "minutes": 40, "weight": 100 }, { "id": "B", "population": 100, "minutes": 20, "weight": 100 }, { "id": "C", "population": 800, "minutes": 5, "weight": 800 } ], "complete": true, "denominator": 1000, "knownPopulation": 1000, "mean": 10, "worst": 40, "covered": 800, "coverageLow": 0.8, "coverageHigh": 0.8 } ], "totalPopulation": 1000 }, "worksheet": { "prediction": "", "revision": "" }, "feedbackSeen": false, "limits": "Original fixed journey-time matrix for one proposed library site at a time. Not measured travel, routing or actual service provision. All residents of a neighborhood share its stated time. Population threshold coverage remains person-weighted under either mean rule. Missing is unknown, not zero or unreachable. No capacity, fares, eligibility or opening hours modeled. Temporary practice." }

Reset access practice

Temporary practice: reset clears writing and restores the original case/resident weighting/15-minute threshold; guide/report exposure remains during this visit. Reload clears it. No independent mastery is awarded.

Independently extend the investigation “Count facilities, then investigate access” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.