When the ward choropleth disagrees with the water office
Class XII students survey household water supply in five municipal wards. They select 12 households per ward by standing at a corner and walking to every third house, interview whoever is at home on a Wednesday between 9 a.m. and 12 noon, and record hours of piped supply per day. Ward 3 yields only 8 completed interviews because several houses were locked. The students use a ward map at 1:10,000, a hand-held GPS with ±8 m accuracy, and plot ward averages as a choropleth. They conclude that Ward 3 is the worst-served and recommend a new pipeline. Their teacher notices that the municipal water office's own records, based on valve-opening times, rank Ward 3 second-best. The ward boundaries on the students' map also differ from those used by the water office, and one ward includes a large unauthorised settlement not in the municipal register.
1. Identify two sampling or measurement problems in the survey and state the likely direction of bias each introduces.
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First, the sample is not random and is taken at a time when many working people are away. Starting at a corner and taking every third house, then interviewing whoever is at home on a weekday morning, over-represents non-working residents, often women and the elderly, and under-represents locked, working households. The direction is not certain, but it is a real bias: households with someone at home during supply hours may store water differently or report supply more accurately. Ward 3's eight completed interviews make its mean especially unstable. Second, there is coverage error: the ward boundary differs from the water office's boundary and the unauthorised settlement is omitted from the register. If that settlement is poorly served, the survey excludes some of the worst-served households and understates the problem in that ward. The GPS error of ±8 m is also comparable to a house plot, so near boundaries households can be assigned to the wrong ward.
2. Was a ward-level choropleth an appropriate choice? Justify your answer and propose a better map design and scale for the purpose.
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A ward-level choropleth of average hours is weak here. It treats each ward as internally uniform, hides variation between households, and maps a derived statistic based on small and unequal samples; Ward 3's eight households make its average unreliable. It also invites the ecological fallacy and is sensitive to the boundary mismatch, the classic modifiable areal unit problem. A better design is a household-level symbol map: proportional circles for recorded supply hours placed at each household, with ward boundaries and the unauthorised settlement shown as a separate polygon, supported by a bar chart of ward means with confidence intervals. This shows both the general pattern and the local exceptions. At 1:10,000, 1 cm represents 100 m, so a 10 m house is only 1 mm across; a ward map at 1:2,500 to 1:5,000 is more appropriate, and household plotting should use tape offsets from permanent features rather than GPS alone.
3. Design a short improved field procedure that would let the class test whether the municipal records or their own survey is closer to reality.
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The class should draw a stratified random sample within each ward from the municipal register, plus a transect sample of the unauthorised settlement, aiming for at least 20–25 households per ward. Visits should be made on two days and at two times, morning and evening, with repeat visits to locked houses. For each household, record valve opening and closing times as reported, measure flow directly with a 10-litre container and a stopwatch, and note storage capacity and whether supply was actually received that day. Plot households using a tape and offset from a permanent boundary or lane junction, and use the water office's boundary file. Finally, compare the household data with the office's valve logs and consumer complaints, and report ward means with confidence intervals. This design tests the two sources against measured flow and reduces the timing, coverage and sample-size weaknesses of the original survey.