Reasoning About Sample Size and an Outlier in a Plant Growth Study
A student grows 30 bean plants: 15 in plain soil and 15 in soil with a worm castings amendment. After 4 weeks, mean height is 18.2 cm (plain) and 21.0 cm (amended). The plain group heights range from 15 to 22 cm; the amended group ranges from 12 to 30 cm. One amended plant is 30 cm tall; without it, the amended mean is 20.4 cm. The student reports that castings increase growth by about 2.8 cm and that the effect is clear. She did not report variability or a statistical test, and plants were assigned to groups by position on the bench (left half plain, right half amended).
1. Explain how the outlier and the assignment method affect the strength of the conclusion.
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The 30 cm plant raises the amended mean by about 0.6 cm (from 20.4 to 21.0), so the reported 2.8 cm difference partly depends on one unusual plant; the difference without it is about 2.2 cm. More importantly, group assignment by bench position confounds treatment with location: light, temperature, or draft differences across the bench could cause the height difference. The wide amended range (12–30 cm) also suggests high variability. Without random assignment and a measure of variability, the claim of a clear 2.8 cm effect is not well supported.
2. What should the student report or do to make the comparison more defensible?
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She should randomly assign plants to treatments, report means with a measure of variability (e.g., standard deviation or standard error), and report the effect with and without the outlier. A statistical test (e.g., a t-test) would indicate whether a difference of about 2–3 cm is larger than expected from variability. She should also check whether the outlier is a measurement error or a real plant. If bench position cannot be randomized, she could swap positions or include position as a factor. The defensible conclusion is that amended plants were somewhat taller on average in this trial, with uncertainty noted.