The Fertilizer Trial and the Sunny Windowsill
A student investigates whether a liquid fertilizer increases mung bean growth. She plants six seedlings in six identical pots with the same soil and the same seed variety. Three pots receive 50 mL of fertilizer diluted in water every morning; three receive 50 mL of plain water. After 14 days she measures stem height: fertilized pots 12, 15 and 13 cm; control pots 10, 9 and 11 cm. Because the sunny windowsill has room for only three pots, she keeps the fertilized pots there and the control pots on a shaded shelf. She concludes that the fertilizer increased growth by about 33%, and a fertilizer company asks permission to cite her result in an advertisement.
1. Compute the mean height of each group and check the student's "about 33%" figure.
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Means:
- Fertilized: (12 + 15 + 13) ÷ 3 = 40 ÷ 3 ≈ 13.3 cm
- Control: (10 + 9 + 11) ÷ 3 = 30 ÷ 3 = 10.0 cm
Percent increase relative to the control: (13.3 − 10.0) ÷ 10.0 × 100 ≈ 33%
The arithmetic is correct. But the number measures a difference between two groups, not necessarily an effect of the fertilizer. Also note the spread: fertilized heights range 12–15 cm (range 3 cm), control heights range 9–11 cm (range 2 cm). The 3.3 cm gap between means is only slightly larger than the spread inside a group of three - which is a warning sign that the sample is too small to support a confident claim on its own.
2. Identify the flaw in the experimental design and describe the minimum change that would fix it.
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The design confounds the treatment with light. Fertilized pots sat on a sunny windowsill; control pots sat on a shaded shelf. Light is a well-known driver of stem growth, so any difference could be caused by light, by fertilizer, or by both acting together. Nothing in the data separates these.
There is a second, smaller problem: with three pots per group, one unusual seedling shifts the mean substantially.
Minimum fix - randomisation plus rotation:
- Assign the six pots to positions at random rather than by group.
- Rotate pot positions every few days so each pot receives comparable light over the 14 days.
- Measure a second response variable (leaf count or dry mass), since stem height alone can reflect light-seeking elongation rather than healthy growth.
Repeating the trial with a larger number of pots per group would strengthen the result, but randomisation and equal light exposure are the changes that must happen first, because without them the comparison is not a fair test at all.
3. The fertilizer company wants to quote the 33% figure in an advertisement. What should the student answer, and on what grounds?
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The student should decline to have the figure used as an advertising claim, and may permit a carefully worded mention only if the study is described honestly.
Grounds for declining:
- Confounded design. Because light differed between groups, the 33% cannot be attributed to the fertilizer. An advertisement stating "increases growth by 33%" would assert causation the experiment did not establish.
- Tiny, unreplicated sample. Six plants, one trial, one school. The result is a classroom observation, not evidence about the product's general performance.
- Selection of a favourable number. Advertising quotes a single percentage with no context; the spread within groups (12–15 cm vs 9–11 cm) disappears.
- Consent and accuracy. A student's name attached to a commercial claim implies endorsement of the product, not merely of the method.
A defensible response: offer to let the company cite the study only as a description - "a 14-day classroom trial of six seedlings reported taller stems in fertilized pots" - with the confound disclosed, and only with the school's and the student's permission. If the company wants the 33% headline, it should fund a properly randomised, replicated trial first.