No-Show Data and an Over-Optimistic Projection
A rural clinic reviewed four weeks of appointment data. Bookings and no-shows by weekday were: Monday 120 booked, 18 no-shows; Tuesday 90 booked, 9 no-shows; Wednesday 100 booked, 8 no-shows; Thursday 110 booked, 7 no-shows; Friday 130 booked, 26 no-shows. The overall no-show rate was reported to the board as 12%. In weeks 5 to 8 the clinic sent SMS reminders on Wednesday and Thursday only. Those days then recorded 100 booked with 4 no-shows (Wednesday) and 110 booked with 3 no-shows (Thursday); Monday, Tuesday and Friday were unchanged in rate. The clinic manager wants to extend reminders to all five days and expects the overall no-show rate to fall to about 6%. A board member notes that Friday alone accounts for about a third of all missed appointments and asks whether the projection is safe.
1. Check the reported 12% figure and the board member's claim about Friday. What do the weekday rates show?
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Total bookings: 120 + 90 + 100 + 110 + 130 = 550. Total no-shows: 18 + 9 + 8 + 7 + 26 = 68.
Overall rate = 68 ÷ 550 = 0.1236, i.e. 12.4%, so 12% is a fair rounding but slightly understates it.
Weekday rates:
- Monday 18 ÷ 120 = 15.0%
- Tuesday 9 ÷ 90 = 10.0%
- Wednesday 8 ÷ 100 = 8.0%
- Thursday 7 ÷ 110 = 6.4%
- Friday 26 ÷ 130 = 20.0%
Friday's share of all no-shows is 26 ÷ 68 = 38.2%, closer to two-fifths than to a third. The board member's point stands and is if anything understated. Friday is also the busiest day (130 of 550 bookings, 23.6%), so it contributes disproportionately: its share of no-shows is about 1.6 times its share of bookings.
The important pattern is the spread: rates range from 6.4% to 20.0%. An overall 12.4% conceals a low-risk midweek and a high-risk Friday, which matters for any prediction built on an average.
2. Evaluate the manager's 6% target. What assumption does it require, and what overall rate results under a proportional versus an absolute reduction?
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Observed changes on the pilot days:
- Wednesday: 8.0% to 4.0%, a fall of 4.0 percentage points, or a 50% relative reduction.
- Thursday: 6.4% to 2.7% (3 ÷ 110 = 2.73%), a fall of 3.6 points, or about 57% relative.
Proportional assumption. If reminders halve the rate on every day, apply roughly a 53% relative reduction to the overall 68 no-shows: 68 × 0.47 ≈ 32, giving about 32 ÷ 550 = 5.8%, which rounds to the manager's 6%.
Absolute assumption. If reminders remove about 3.8 percentage points on every day, the overall rate becomes 12.4 − 3.8 = 8.5%, or about 47 no-shows.
So 6% is not wrong arithmetic; it depends on an unstated assumption that the effect is proportional and transfers to days with very different baseline rates. That is the weak link. Friday's rate is 20%, two and a half times Wednesday's pre-pilot rate, and 26 of the 68 no-shows sit there. If Friday's cause is different, such as end-of-week transport, payday commitments or a particular clinic list, a reminder may not halve it. If Friday stays at 20% while the others halve, total no-shows would be about 9 + 5 + 4 + 3 + 26 = 47, again near 8.5%. Presenting 6% as the expected outcome is therefore optimistic; a range of 6% to 9% is more honest.
3. The board asks what evidence would justify the manager's target. Outline the weaknesses in the current comparison and the cheapest way to test the claim before rolling out reminders everywhere.
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The comparison has three weaknesses.
- No control. Wednesday and Thursday in weeks 5 to 8 are compared with Wednesday and Thursday in weeks 1 to 4. Anything else that changed in that period, such as season, staffing, a new booking system or weather, is bundled into the 'reminder effect'.
- Day selection. Reminders were piloted on the two days with the lowest baseline rates. Low-rate days have less room to fall in absolute terms, yet they fell most; that could be a genuine strong effect, or regression to the mean after an unusual four weeks.
- Transportability. There is no evidence that Friday, with a 20% rate, behaves like Wednesday at 8%. The extrapolation is the manager's assumption, not a finding.
A cheap test: continue reminders on Wednesday and Thursday, add them to Friday only, and leave Monday and Tuesday as a comparison. Run it for at least six to eight weeks so each weekday has several observations, and record a reason for each missed appointment (forgot, transport, work, illness) rather than only a count. If Friday's no-shows are mostly forgetfulness, reminders should work; if they are transport failures, a reminder will not move the rate much.
Until that runs, the board should treat 6% as a hypothesis with a plausible range, and should not promise a target that depends on Friday behaving like midweek.