Morning Habits Report: Group Averages and Causal Claims
Ms. Tanaka's class is reading a one-page report in a Nara public high school newsletter. The report says, 'Our school surveyed 240 students about morning habits. Students who study before school tend to sleep less.' A table gives grade-level results. Grade 1 has 80 students: 25% study before school, 40% eat breakfast daily, average sleep 7.2 hours. Grade 2 has 80 students: 30% study before school, 35% eat breakfast daily, average sleep 6.8 hours. Grade 3 has 80 students: 45% study before school, 50% eat breakfast daily, average sleep 6.3 hours. The report adds, 'Grade 3 students are the most serious about study and sleep.' Sora writes a summary: 'The table proves that if a student studies before school, that student will sleep less.' Emi says the report is wrong because Grade 3 eats breakfast more often, so breakfast must cause less sleep. The teacher asks the class to judge which conclusions the data can and cannot support, and to calculate one number from the table. No student may use a calculator.
1. Evaluate Sora's sentence. State what the table actually shows and what it cannot show.
Read the worked answer
- What the table shows: as the grade goes up, the percentage who study before school rises (25% → 30% → 45%) and average sleep falls (7.2 → 6.8 → 6.3 hours). That is a group-level trend across three grade groups.
- What the table cannot show: it cannot prove that 'if a student studies before school, that student will sleep less.' That is an individual-level causal claim. The table gives only grade averages, not individual students' study times and sleep times.
- Even at group level, correlation is not causation. Grade 3 students may sleep less because of exams, longer commutes, club activities, or later bedtimes, not because they study in the morning.
- The word proves is too strong. A careful answer would say: 'The table is consistent with a negative association between grade-level morning study and average sleep, but it does not prove a causal effect on individuals.'
2. Evaluate Emi's reasoning and calculate how many Grade 3 students study before school. Show the calculation.
Read the worked answer
- Calculation: Grade 3 has 80 students, and 45% study before school.
45% of 80 = 0.45 × 80 = 36 students. - Emi's causal claim is not supported. She notices that Grade 3 has the highest breakfast rate (50%) and the lowest average sleep (6.3 hours), then concludes that breakfast causes less sleep. But Grade 3 also has the highest morning-study rate (45%), so breakfast is not isolated.
- A simple check across grades weakens her claim: from Grade 1 to Grade 2, the breakfast rate falls (40% → 35%), but average sleep also falls (7.2 → 6.8). If breakfast caused less sleep, lower breakfast should be linked to more sleep, not less.
- The table can support only a description of grade-level patterns. It cannot separate breakfast, study, age, exams, or other factors. Emi is treating one group-level pattern as proof of a cause.