The Library Survey Mandate
The Northvale Library Service circulated an online survey and left paper copies at its two busiest branches, Fenwick and Alder. Of the 48,000 residents in the catchment, 1,240 replied. The council bulletin headline read: 'Over 70% of residents back later opening.' The underlying table shows that 874 respondents (70.5%) said they would use a branch after 6 p.m. on at least one weekday. Of those 874, 601 named Fenwick or Alder as their usual branch. The remaining three branches - Corrie, Bramble and Dean - sit in villages with one evening bus per hour, and the service's transport review found that 18% of residents in those villages have no car. The library director proposes extending evening hours at all five branches for twelve months, citing 'clear public demand'. A councillor has asked whether the survey can bear that weight.
1. Identify the main unstated assumption in the director's inference and explain, using the figures, why it is unsafe.
Read the worked answer
The inference is: 874 respondents said they would use evening opening; therefore all five branches should open in the evening. That requires at least two unstated assumptions: that the 1,240 respondents are representative of the 48,000 residents, and that a stated intention to use a branch becomes actual attendance at every branch.
The response rate is 1,240/48,000 = 2.6%, and the survey was available online and at the two busiest branches, so it is self-selecting. Within the supportive group, 601/874 = 68.8% named Fenwick or Alder, the two branches where paper copies were available. Only 273 supporters (22% of respondents, 0.57% of residents) are associated with Corrie, Bramble or Dean. The evidence is therefore concentrated where the survey was distributed. The transport figures make the leap to the three villages especially weak: hourly evening buses and 18% car-free households could suppress actual use even among people who support the idea. Intention is not attendance.
2. The bulletin says 'Over 70% of residents back later opening.' Is that statement accurate as written? State what a defensible wording would be.
Read the worked answer
No. The 70.5% figure is a proportion of respondents, not residents; it is 874/1,240. The 1,240 people who replied are 2.6% of the 48,000 residents, and because participation was voluntary and paper copies were placed only at two branches, the respondents are not a random or representative sample. The statement also changes 'would use a branch after 6 p.m.' into 'back later opening'; support for a policy and intended use are different claims.
A defensible wording would be: 'Of the 1,240 people who chose to respond, 70.5% said they would use a branch after 6 p.m. on at least one weekday; 68.8% of those named Fenwick or Alder as their usual branch.' That wording keeps the sample, the question asked and the concentration of responses visible, and it does not imply a majority of residents.
3. The council proposes a 12-month trial at all five branches. Propose one change to the evidence-gathering design that would most improve the decision, and explain the trade-off.
Read the worked answer
The most useful change is a stratified random sample by branch catchment, with a target number of completed responses per branch (for example 150 at each of the five), followed by a small behavioural pilot at one village branch. Stratification fixes the main defect: the current sample over-represents Fenwick and Alder and cannot estimate demand at Corrie, Bramble or Dean. A pilot measures attendance rather than intention, which is the outcome the council actually cares about.
The trade-off is time and cost. A random sample with five strata needs address-level sampling or intercepts, reminder calls and weighting, and a pilot delays the twelve-month rollout. The council could instead weight the existing responses by catchment population, but that only reweights a self-selected sample and cannot repair the missing village evidence. If the decision cannot wait, the safer option is to extend hours only at Fenwick and Alder and run a separate village trial, rather than treat the 70.5% as a mandate for all five.