The Fertilizer Fair: A 40% Claim Built on Confounded Trays
At a district science fair, a high school junior presents a project titled 'GrowBoost Increases Radish Growth by 40%.' She mixed three nutrient concentrations: 0 mL, 5 mL, and 10 mL of GrowBoost per liter of water. For each concentration she filled one tray with four radish seedlings, watered all trays with 50 mL every other day, and measured stem height after 21 days. Mean heights were 6.2 cm, 7.8 cm, and 8.7 cm. The 10 mL tray sat at the front of a south-facing windowsill; the 0 mL tray sat at the back. One seedling in the 0 mL tray died and was excluded. The student reports the 8.7 cm versus 6.2 cm difference as a 40% increase and concludes that GrowBoost causes greater growth. As a judge and science teacher, you must decide what feedback and rating the project deserves, and how to respond when the student says, 'But I kept everything else the same.'
1. Evaluate the extent to which the data support the student's causal claim. Identify the most serious design flaws and explain how each could produce the reported pattern.
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The data show an association, not a causal effect. The most serious flaw is confounding by tray position: the highest concentration sat at the front of a south-facing window and the control sat at the back, so light intensity and temperature differ systematically with treatment. The 40% difference could be a light effect. Second, there is no independent replication at the treatment level: one tray per concentration means the tray, not the treatment, is the experimental unit. Excluding one dead seedling in the control also biases the control mean upward or downward depending on why it died, and the decision was not pre-specified. Third, the student did not randomize seedlings to trays, so initial size differences are uncontrolled. The arithmetic 8.7/6.2 = 1.40 is correct, but the uncertainty is unknown and likely large. A defensible conclusion is that the 10 mL treatment group was taller in this one placement, not that GrowBoost caused greater growth.
2. Rewrite the investigation as a feasible high school revision that would allow a causal inference. Specify replication, controls, and at least one measurement decision.
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A feasible revision uses at least three trays per concentration, with four matched seedlings per tray, for 12 trays total. Randomly assign trays to concentrations and randomize tray positions on the windowsill; rotate positions daily or use a grow-light rack so light is uniform. Keep soil batch, pot size, water volume, watering time, and seedling starting height as consistent as possible. Treat the tray mean as the unit of analysis, not each seedling. Measure stem height at days 0, 7, 14, and 21, and pre-specify that a seedling dying is recorded but not silently dropped. Have someone measure without knowing the treatment label, or use a ruler placed consistently. If the windowsill cannot be made uniform, use a simple randomized block design with position blocks. This design still fits a school budget and gives the student a genuine reason to average tray means and report variability rather than one dramatic percentage.
3. The student's parent asks why the project did not place first despite 'clear numbers.' Draft a response that is honest about the flaw and still encourages the student.
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Thank the parent and be specific: the student asked a testable question, measured carefully, and did the percentage calculation correctly. The issue is not the arithmetic but the comparison. Because each nutrient level had only one tray and the trays sat in different light positions, the judges could not tell whether GrowBoost or window light caused the height difference. In science, a strong number does not fix a comparison that changes two things at once. Explain that this is a common and teachable design issue, not misconduct. Offer a concrete next step: revise with multiple trays per concentration and rotated positions, then report means with spread. Praise the student's persistence and suggest presenting the redesign as the next iteration. This keeps the feedback honest while modeling how scientists improve claims rather than defend them.