The 68% That Became a Coin Toss
A barangay of 4,000 registered voters is deciding whether to impose a 10 p.m. curfew on minors. A councilor surveys 400 residents at the plaza between 2 p.m. and 5 p.m. on a weekday. Of the 400 respondents, 240 are aged 60 or over, although seniors are only 18% of the barangay. Overall, 272 respondents (68%) say they support the curfew; within the sample, 85% of seniors support it, while only 68 of the 160 non-senior respondents do. The councilor announces that "68% of the barangay supports the curfew." A second councilor proposes instead surveying people leaving a bar at 11 p.m., expecting the opposite result.
1. Recompute the support estimate using the barangay's actual age structure, and compare it with the announced 68%.
Read the worked answer
Step 1 - Get within-group support rates.
- Seniors: 85% support (given).
- Non-seniors: 68 / 160 = 42.5% support.
Step 2 - Weight by the population, not the sample. Seniors are 18% of the barangay and non-seniors 82%. The sample's 60/40 split is the distortion.
Step 3 - Reweight: 0.18 × 85 = 15.3 0.82 × 42.5 = 34.85 Total = 50.15% ≈ 50%
Comparison: the announced 68% is not the barangay's view; it is the view of a sample that is 60% seniors in a barangay that is 18% seniors. The reweighted estimate flips a "clear majority" into a statistical tie.
Shortcut check: the raw sample average (0.60 × 85 + 0.40 × 42.5 = 51 + 17 = 68) reproduces the reported figure exactly, confirming the over-weighting of seniors is the whole gap.
2. Identify the specific defect in each proposed survey and state what a defensible design would require.
Read the worked answer
Survey A (plaza, 2–5 p.m., weekday):
- Defect: selection bias via time and place. Weekday afternoons systematically over-represent retirees (the 60% senior share), and plaza users are not a random draw of residents.
- Consequence: the estimate is biased, not merely noisy - the error has a direction, and reweighting fixes only what is measured (age), not what is unmeasured (employment, health, disability).
Survey B (bar exit, 11 p.m.):
- Defect: the same bias with the sign reversed. It samples people whose behaviour is directly at odds with the policy under study, guaranteeing an under-count of curfew support. Predicting the result before sampling is the tell that the design is chosen to produce an answer.
Defensible design: a sampling frame of registered voters with random selection, contact attempted at multiple times of day and on weekends, an age/sex quota monitored against barangay records, neutral wording, and a reported margin of error. Neither street-corner survey can support a claim about 4,000 people.
3. The reweighted figure of about 50% relies on one assumption that the data cannot verify. State it, and say how the council should present the result.
Read the worked answer
The fragile assumption: that the 85% (senior) and 42.5% (non-senior) support rates are accurate for all seniors and all non-seniors in the barangay. Reweighting corrects only the mix of groups; it cannot correct for who within each group chose to answer. The 160 non-seniors are a small, self-selected group, so 42.5% carries a wide uncertainty - roughly ±8 percentage points at 95% confidence - and the seniors' 85% is measured on people who were at the plaza on a weekday afternoon, plausibly the most available and most curfew-favourable seniors.
How to present it: report it as "approximately 50%, with the estimate sensitive to assumptions," show the range rather than a point figure, and state plainly that the original 68% came from a sample that over-represented seniors threefold.
Judgement: at a 50/50 estimate, the honest conclusion is that the barangay is divided. Presenting 68% would misstate the evidence, and commissioning the bar survey to "confirm" the opposite would simply repeat the same mistake facing the other way.