Verbal - Later start times: what three schools can and cannot prove
A district changed the first bell at two of its three high schools, moving it from 7:15 to 8:30. School A adopted the later start and also began a free breakfast program in the same year. School B kept the 7:15 start and made no other change. School C adopted the later start but not the breakfast program. Compared with the previous year, average grades rose 6 points at A, 1 point at B and 4 points at C, while absence rates fell 18%, 2% and 11% respectively. The district's press release says: "Moving the first bell to 8:30 raised grades by six points and cut absences by nearly a fifth." Parents have asked the board to justify that sentence before the policy is extended to middle schools.
1. Separate the part of the press release the comparison supports from the part it does not, using the three schools.
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The three schools form a partial experiment, not a complete one.
Supported: the later start alone has an effect. Comparing C with B isolates the change, since both added nothing else: grades +4 versus +1 gives roughly +3 points, and absences −11% versus −2% gives roughly −9 percentage points attributable to the timing change.
Not supported: the full +6 and −18% at School A. A adds a breakfast program on top of the later start, so the extra +2 points and extra −7 points of absence reduction coincide with breakfast rather than being shown to be caused by it. The design has schools with (late start, no breakfast) and (early start, no breakfast), but there is no school with an early start plus breakfast, so breakfast's contribution cannot be isolated at all.
So a defensible sentence is: "Moving the first bell to 8:30 was associated with about a three-point grade gain and a nine-point fall in absences; the larger gains at one school coincided with a new breakfast program." A second caveat: one year of data per school cannot rule out a pre-existing trend.
2. A board member says the fix is to 'collect more data'. Which single additional comparison would most sharpen the conclusion, and which would be merely more of the same?
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Most valuable: complete the 2 × 2 design. Introduce the breakfast program at School B, which keeps the early start and currently has neither intervention. That gives four cells - late/breakfast, late/no breakfast, early/breakfast, early/no breakfast - and separates the two factors cleanly. Running the breakfast program at a fourth school with the early start would do the same job.
Second most valuable: prior-year trend data for the same three schools. If A and C were already improving faster than B before the change, the gains attributed to the later start shrink.
Merely more of the same: larger samples within each school. Adding thousands of student records to A, B and C improves precision but does nothing about confounding, because the missing cell stays missing. Likewise, asking parents whether they like the new schedule produces opinion, not evidence about grades.
3. A board member argues: 'Absences fell most where grades rose most, so attendance causes higher grades.' Evaluate that inference.
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The pattern is real but the inference is not forced. Across three schools, absences fell most at A (−18%, grades +6) and least at B (−2%, grades +1), so the two measures move together. Three data points, however, cannot distinguish between three explanations:
- Better attendance → more instruction → higher grades.
- The schedule or breakfast → better sleep and nutrition → both better attendance and higher grades.
- A third change (a new test, a grading adjustment) that lifted grades everywhere, with attendance moving for its own reasons.
Explanation 2 is especially plausible here, because the later start is a known route to both outcomes. The board member has also compared schools rather than students: nobody has shown that the individual pupils whose attendance improved are the ones whose grades improved.
A fair statement: the association is consistent with a causal role for attendance, but it is equally consistent with a shared cause, and school-level averages cannot settle which is operating.