What the Canteen Data Can and Cannot Show
Read this extract from a school newsletter.
'Since Term 1, the canteen has been cash-free. Lunch queue waiting times fell from an average of 6 minutes 40 seconds to 4 minutes 10 seconds. Principal Adeyemi says the change "has made lunchtime calmer for everyone". However, the canteen also stopped selling hot soup in the same week and closed one of its two serving windows for repairs. A survey of 40 students found that 29 preferred the new system; all 40 were drawn from Year 11, whose lunch break begins 25 minutes before the rest of the school.'
No further information is available.
1. A student writes: 'The data proves that going cash-free cut queue times by more than a third.' Identify precisely what is wrong with this claim.
Read the worked answer
Two separate faults.
1. The arithmetic describes the drop accurately but the causation is unsupported.
- 6 min 40 s = 400 s; 4 min 10 s = 250 s. A fall of 150 s is 37.5% of 400 s - so 'more than a third' is a fair description of the change.
- But the extract supplies two other changes in the same week: no hot soup (fewer items, faster transactions) and one serving window closed (which would normally slow service). With three changes at once, the fall cannot be credited to the cash-free system alone.
2. 'Proves' overstates the design. This is a before-and-after observation with no control group; it can support 'is consistent with' but not 'proves'.
Model answer: the percentage is defensible, the causal claim is not - the soup change and the window closure are uncontrolled alternatives.
2. What is the weakness in the survey evidence, and why does the Year 11 detail matter?
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Weakness of the sample: 40 students is small, but size is the lesser problem.
Why the Year 11 detail is decisive: Year 11 students eat 25 minutes before the rest of the school. They therefore never experience the peak congestion the change was meant to fix. Their preference tells you about a group who had the least to gain from shorter queues.
Consequence: the survey can be reported as '29 of 40 surveyed preferred the new system' but not as evidence that students generally prefer it, and certainly not as support for a queue-time claim, since the respondents were not queuing at the busiest time.
Model answer: the sample is unrepresentative of the lunchtime population in a way that is directly relevant to the claim being made. A larger sample drawn from the same early break would not fix this; only sampling across both breaks would.
3. Which single piece of additional evidence would most strengthen the case that the cash-free system caused the shorter queues?
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Rank the options by what they rule out.
- Asking students whether they like the system: measures preference, not speed. Weak.
- Counting how many students use the canteen: useful context, but does not separate the causes.
- Reopening the second serving window and reintroducing soup while keeping the system cash-free, then re-measuring queue times: this holds the other two changes constant and isolates the cashless variable.
- Comparing with a school that kept cash: helpful, but the two schools differ in too many ways to be conclusive.
Model answer: the controlled re-measurement. It is the only option that removes the competing explanations the extract itself raises - which is why the extract mentions the soup and the closed window at all.