Breakfast and Quiz Scores: Confounding Variable
A school wellness committee wants to know whether eating breakfast is associated with higher math quiz scores. They surveyed 60 students: 30 who reported eating breakfast on the morning of the quiz and 30 who did not. The breakfast group had a mean score of 82 and a median of 84; the no-breakfast group had a mean of 76 and a median of 78. The quiz was out of 100. The committee also found that 18 of the 30 breakfast students were enrolled in an advanced math class, compared with 9 of the 30 no-breakfast students. The committee wants to make a claim in a school newsletter, but the principal asks them to avoid causal language and to account for the advanced-class difference.
1. Compare the two groups using the mean and median. What does the pattern of medians being higher than means suggest?
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The breakfast group's mean is 82 and median is 84; the no-breakfast group's mean is 76 and median is 78. In both groups the median is 6 points higher than the mean. That pattern suggests the means are pulled downward by a few unusually low scores, while the middle score is higher. The breakfast group scores higher by 6 points at both the mean and the median, but that difference alone does not show why.
2. Identify the confounding variable in the setup and explain how it could affect the conclusion.
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The confounding variable is enrollment in an advanced math class. The breakfast group has 18 advanced students out of 30, while the no-breakfast group has 9 out of 30. Advanced-class enrollment could raise quiz scores independently of breakfast. Because the groups differ on this variable, the 6-point score gap may partly reflect class placement rather than breakfast. A stronger study would compare students within the same class level or randomly assign breakfast conditions.
3. Write a cautious one- or two-sentence conclusion for the newsletter that uses the data but avoids a causal claim.
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Students who reported eating breakfast also tended to score higher on this math quiz, with a mean of 82 compared with 76. However, the breakfast group had more students enrolled in advanced math, so this survey does not show that eating breakfast causes higher scores.