Confounded Fertilizer Trial
A student tests a new organic fertilizer on tomato plants. Twenty seedlings of the same variety are potted in identical soil. Ten pots are placed on a bench near a south-facing window; these receive 200 mL of fertilizer solution weekly. Ten pots are placed on a bench 3 m away from the window; these receive 200 mL of water weekly. After 8 weeks, fertilized plants produce an average of 12 tomatoes each, versus 7 in controls. A t-test gives p = 0.03. The student concludes the fertilizer increases yield. However, the near-window bench averages 26°C and 450 µmol m^-2 s^-1 light, while the far bench averages 22°C and 200 µmol m^-2 s^-1. The student did not rotate pots or blind the harvesters. The fertilizer solution also contains 2% nitrogen, while the water contains none.
1. Identify the main confounding variables in this experiment. Explain how each could produce the observed yield difference independently of the fertilizer.
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Light and temperature are confounded with fertilizer treatment: the fertilized pots are near the window (450 vs. 200 µmol m^-2 s^-1; 26°C vs. 22°C). Higher light and temperature increase photosynthesis and tomato yield, so the 12 vs. 7 difference could be due to environment, not fertilizer. The fertilizer also adds nitrogen, while water does not, so nutrient supply is confounded. Lack of blinding at harvest could bias tomato counts. Any of these could produce the result without a fertilizer effect.
2. Propose a revised experimental design that controls for light, temperature, and harvest bias. Include randomization, blocking, and blinding.
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Use a randomized complete block design. Place many pots across several benches; within each block (for example, bench section), randomly assign fertilizer vs. control. Rotate pots regularly to equalize light. Use a control solution matched for nitrogen (for example, add an inert nitrogen source) so only the organic fertilizer differs. Blind harvesters to treatment codes. Increase replication and measure light, temperature, and soil moisture. This separates fertilizer effects from position effects.
3. Interpret the p-value of 0.03 correctly. Does it prove the fertilizer caused the yield increase? Explain.
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p = 0.03 means that if the null hypothesis (no difference between treatments) were true and the test assumptions held, there is a 3% chance of observing a difference this large or larger. It is not the probability that the fertilizer works, nor does it prove causation. Because light, temperature, and nitrogen are confounded and harvest was not blinded, the low p-value does not establish that the fertilizer caused the yield increase. A controlled, randomized experiment is needed.