The Fertilizer Experiment
A student investigates whether fertilizer increases bean growth. Three trays are planted with 10 bean seeds each. Tray A sits on a south-facing windowsill, gets 50 mL of water daily, and receives fertilizer. Tray B sits on a north-facing shelf, gets 50 mL of water daily, and receives no fertilizer. Tray C sits on the south-facing windowsill, gets 30 mL of water daily, and receives fertilizer. After 21 days, the average seedling heights are: A = 14.2 cm, B = 8.6 cm, C = 9.1 cm. The student writes, "Fertilizer made the plants grow 65% taller, since 14.2 is about 65% more than 8.6."
1. The student's arithmetic is correct but the conclusion is not. Explain the difference.
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The arithmetic: 14.2 / 8.6 = 1.651, so tray A's seedlings are about 65% taller than tray B's. That computation is fine.
The conclusion: comparing A and B does not isolate fertilizer, because two variables differ between those trays -- fertilizer and light exposure (south windowsill vs. north shelf). The 5.6 cm gap could be produced by fertilizer, by extra light, or by some combination. Attributing all of it to fertilizer is an uncontrolled comparison.
A second, subtler issue: even if light were controlled, the claim is about height only. "Growth" in the student's hypothesis might mean height, mass, leaf count, or time to germination; a single height measurement at day 21 does not test all of them.
What the student actually has: a correlation between a tray's conditions and its height. The causal claim needs a comparison in which only fertilizer changes.
2. What does comparing trays A and C tell you, and why is that comparison more informative than A versus B?
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A and C share the south windowsill and both receive fertilizer. The only planned difference is water: 50 mL daily versus 30 mL daily.
Result: 14.2 cm versus 9.1 cm -- a 5.1 cm gap attributable to the watering difference alone, since everything else is held constant.
Why it matters more:
- It is a controlled comparison, so the difference in outcome can be tied to the difference in treatment.
- It shows water is a large factor. The gap from water (5.1 cm) is nearly as large as the gap the student credited entirely to fertilizer (5.6 cm).
- It undermines the original conclusion in a specific way: tray C had fertilizer but only 30 mL of water, and it grew no better than tray B, which had no fertilizer but 50 mL of water. So fertilizer alone, without adequate water, did not produce a visible advantage here.
The honest summary: this design cannot separate fertilizer from light, and its one clean comparison suggests water is doing much of the work.
3. Redesign the experiment so that the fertilizer question can actually be answered. State the trays you would use and what each comparison would show.
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Core fix: change one variable at a time, and add replication.
Proposed design -- all four trays on the same south windowsill, all watered 50 mL daily, 10 seeds each:
- Tray 1: fertilizer
- Tray 2: no fertilizer
- Tray 3: fertilizer (repeat of Tray 1)
- Tray 4: no fertilizer (repeat of Tray 2)
What it buys you:
- 1 vs. 2 isolates fertilizer, because light and water are now identical. Any consistent difference is attributable to the treatment.
- The repeats guard against the possibility that one tray happened to get better soil or a draft; a single tray per condition cannot show whether a difference is real or noise.
- Trays should be rotated along the windowsill, since light varies even across one sill.
Optional second factor: if the student also wants to study water, run a second set of trays at 30 mL. That turns the study into a two-factor design rather than a confounded one.
Also fix the measurement: record height on the same days for all trays, and add a second measure (e.g., dry mass at the end) so "growth" is not defined by height alone.