The Fertilizer Trial
Four groups of ten bean seedlings were grown for three weeks in the same potting mix, watered on the same schedule, and given the same volume of liquid each week. The only intended difference was fertilizer concentration: 0% (plain water), 1%, 2%, 4%, and 8%. Mean heights after three weeks: 0% → 12.1 cm; 1% → 15.4 cm; 2% → 18.2 cm; 4% → 11.9 cm; 8% → 4.3 cm. Unknown to the students, the 4% and 8% pots were placed on the bottom shelf of the rack, while the other pots sat on the top shelf, which receives direct sunlight. A classmate concludes: "Fertilizer makes bean plants grow taller."
1. Describe the pattern in the data and state precisely what the numbers do and do not support about fertilizer concentration.
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Pattern: mean height rises from 12.1 cm (0%) to 15.4 cm (1%) to a peak of 18.2 cm (2%), then falls to 11.9 cm (4%) and collapses to 4.3 cm (8%).
What is supported:
- Low concentration helps: 1% and 2% both beat the control by 3.3 cm and 6.1 cm.
- The relationship is not "more is better." Beyond 2% the trend reverses, and at 8% the plants are less than half the height of the untreated control, which suggests toxicity or root damage rather than mere lack of benefit.
- The optimum lies at or near 2%. The data cannot narrow it further - no concentration between 2% and 4% was tested, so "the optimum is exactly 2%" overstates the evidence; "between 2% and 4%, probably closer to 2%" is defensible.
What is not supported: the classmate's blanket claim. "Fertilizer makes bean plants grow taller" is true only in a narrow band and is false at the two highest doses tested, where fertilizer is associated with shorter plants.
2. Explain why the 4% and 8% results may not be attributable to fertilizer at all, and say what that does to the conclusion.
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The 4% and 8% pots sat on the bottom shelf; every other pot sat on the top shelf in direct sun. Concentration and light exposure therefore changed together: every pot with a high dose also got less light.
Light is a primary driver of photosynthesis and stem elongation, so shade alone can stunt seedlings. Two competing explanations fit the same numbers:
- High fertilizer concentration is harmful, or
- Reduced light is harmful, or some mix of the two.
Because the two variables were never separated, the experiment cannot distinguish them - this is a confounded design, and confounded variables cannot be untangled by looking harder at the same data.
Effect on the conclusion: the low-dose half of the result (0%, 1%, 2%, all in sun) is still usable, since light was constant across those pots. The dramatic 8% figure must be treated as uninterpretable until the confound is removed. Any claim about high concentrations is premature.
3. Propose the minimum changes that would make this experiment capable of supporting a causal claim, and name one measurement issue the mean heights conceal.
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Fix the confound by design, not by argument:
- Put all pots on a single shelf, or if shelves must differ, rotate pot positions every few days and randomise which concentration sits where - then light exposure is spread across all groups instead of locked to two of them.
- Add concentrations between 2% and 4% (e.g. 2.5%, 3%) to locate the optimum rather than guessing between two widely spaced points.
- Keep at least the current replication (10 per group) and add a true zero-dose control that is handled identically in every respect, including shelf position.
Measurement issue: only means are reported. Without the spread of individual plant heights, a 1–2 cm difference between groups cannot be judged meaningful - it could be ordinary variation. The report should give per-plant data or a measure of variability, plus the number of seeds that failed to germinate, since a high-dose group might show a "tall" mean produced by two survivors out of ten.