Testing a Fertilizer Claim
A student reads that a new liquid fertilizer increases tomato plant height. She designs an experiment: 10 plants get fertilizer, 10 get plain water, all in the same greenhouse. She measures height after four weeks. Her results show the fertilized plants averaged 3 cm taller, and she concludes the fertilizer works. Her teacher notices that the fertilized plants were placed on the sunnier side of the greenhouse, that the fertilizer group included the largest seedlings at the start, and that she did not measure starting heights. The teacher asks her to identify flaws and redesign the study.
1. Identify the confounding variables and explain how each could produce the observed difference without the fertilizer having any effect.
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Two confounds stand out. First, light: the fertilized plants were on the sunnier side, so greater photosynthesis from more light could explain the extra 3 cm, independent of fertilizer. Second, initial size: the fertilizer group started with the largest seedlings, and larger seedlings tend to grow more, so the difference may reflect starting conditions rather than treatment. A third issue is that starting heights were not recorded, so the groups cannot be shown to be equivalent at the start. Any of these could produce a 3 cm difference with no real fertilizer effect. The design lacks a control for these variables, so the conclusion is not justified.
2. Describe a stronger design, including how to reduce confounding and how to judge whether a 3 cm difference is meaningful.
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Randomly assign plants to fertilizer and water groups so initial size is balanced on average, and record starting height for every plant so growth (final minus initial) can be compared rather than final height alone. Place all plants in the same light conditions, or rotate positions regularly, so light is not confounded with treatment. Keep water, soil, pot size, and temperature identical except for the fertilizer. Increase sample size if possible and have the person measuring height unaware of group assignment to reduce bias. To judge meaning, compare the average growth of the two groups and consider variability: if the difference is small relative to the spread within groups, it may be due to chance. A statistical test or repeat trials would help. Only if fertilized plants consistently grow more under controlled conditions can the claim be supported.