Fertilizer, Windowsills, and Confounded Variables
Two Grade 11 students test a claim that a new liquid fertilizer increases bean plant height. They use 20 seedlings. Ten pots are placed on a classroom windowsill; the other ten are placed on a shelf 3 metres away. Both groups receive 100 mL of water every second day. The windowsill group also receives 50 mL of diluted fertilizer as directed; the shelf group receives 50 mL of plain water. After four weeks, the windowsill group has a mean height of 18.2 cm (range 15.1–21.0 cm), and the shelf group has a mean height of 15.4 cm (range 12.8–17.9 cm). The students conclude that the fertilizer caused a 2.8 cm increase in growth. Their teacher notes that the windowsill receives about four more hours of direct sunlight per day and is 2–3°C warmer than the shelf. The students have one week left before the project is due and 20 unused seedlings. They want to know whether their conclusion is defensible and what they can realistically do to improve the investigation.
1. Identify the main flaw in the investigation and explain precisely why the students cannot conclude that the fertilizer caused the 2.8 cm difference.
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The main flaw is confounding: fertilizer treatment is completely tied to location. All fertilized pots are on the windowsill; all control pots are on the shelf. The windowsill also gets about four more hours of sunlight and is 2–3°C warmer. Sunlight and temperature affect plant growth, so the observed 2.8 cm difference could be caused by light, temperature, fertilizer, or an interaction. The design has no way to separate these.
The ranges also overlap: the windowsill range 15.1–21.0 cm overlaps the shelf range 12.8–17.9 cm, so the group difference is not clean even descriptively. The conclusion that fertilizer caused a 2.8 cm increase is therefore not defensible; at most, the data show an association between the windowsill treatment package and greater mean height. A second problem is that the students may have known which pots were fertilized, which can bias measurement, although height is fairly objective. The fundamental issue is not sample size but lack of a controlled comparison. A valid conclusion requires fertilized and unfertilized plants to be exposed to the same light, temperature, water, soil, and pot conditions, with treatment assigned randomly.
2. Describe an improved design that could be completed with the 20 unused seedlings and would allow a causal conclusion.
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Use all 20 seedlings in one location with the same light and temperature. Randomly assign 10 to fertilizer and 10 to water only. Keep pot size, soil, watering volume, watering time, and measurement method identical. Rotate pot positions every two days so that no pot stays at the brightest edge. Measure height at the same time of day, by the same person, without knowing which treatment each pot received; label pots by code.
Record temperature and light daily to confirm that the location is uniform. If the students also want to test whether light matters, they could use a 2×2 design: fertilizer versus water in each of two light locations, with 5 seedlings per cell. That uses all 20 and separates the fertilizer effect from the light effect, but each cell is small. The simpler randomized single-location design gives a cleaner test of the fertilizer claim, while the 2×2 design gives more information but less power per condition. Either way, the key is that treatment is not confounded with location.
3. The students have one week and 20 seedlings left. Which improvement is most realistic, and what limitation should they report?
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With one week, a full four-week growth experiment cannot be repeated from seed. The most realistic improvement is to use the remaining seedlings for a short randomized trial in one location, measuring change over the week rather than final height. Randomly assign 10 to fertilizer and 10 to water, keep all pots together, rotate positions daily, and measure at day 0 and day 7 with coded labels.
This controls location and gives a fair comparison, but the short duration limits the conclusion: a one-week change may not predict four-week height, and the seedlings may already differ. The students should report the original result as inconclusive and describe the confound explicitly. They should not claim that the fertilizer works. If the short trial shows no difference, that does not disprove the original claim either; it only fails to support it under better control. The best scientific move is to state the limitation, present the improved design as a pilot, and recommend a full repeat with more plants and a longer period. This is honest and still earns credit for understanding experimental design.