Fertiliser and Duckweed Growth: A Flawed Growth Experiment
A student investigates whether a liquid fertiliser increases duckweed growth. In trial 1, ten fronds are placed in a 200 cm³ beaker containing 150 cm³ of pond water plus 2.0 cm³ of fertiliser; ten fronds are placed in a second beaker with 150 cm³ of pond water and no fertiliser. Both beakers stand on the same windowsill for 14 days, but the fertiliser beaker is placed closer to the window because the other position was occupied by a thermometer. At the end, the student counts fronds: 46 in the fertiliser beaker and 21 in the control, and concludes that fertiliser roughly doubles growth. Two repeats give fertiliser counts of 44 and 61, and control counts of 20 and 19. A classmate notices that the fertiliser beaker's water looks greener and that the student counted every small detached frond, including ones that had broken off larger fronds. Each condition had only one beaker per trial.
1. Identify the main confounding variables and state, for each, the direction in which it would bias the conclusion.
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Several variables differ between the two beakers besides fertiliser, so the comparison is not a controlled experiment.
Light. The fertiliser beaker is closer to the window and receives more light, which directly increases photosynthesis and growth. This biases the result in favour of fertiliser, and it cannot be separated from the fertiliser effect.
Algae. The fertiliser adds nutrients, and the water looks greener, so algae are probably growing. Algae affect duckweed in two opposing ways: they compete for nutrients and can shade the fronds (reducing apparent growth), but the extra nutrients also directly benefit duckweed. Either way, the green colour shows the treatment changed more than the duckweed, so 'fertiliser increases duckweed' is not a clean claim.
Counting method. Counting detached fronds inflates the count, and if fertiliser caused more fragmentation rather than more growth, the 46 versus 21 difference partly measures breakage, not biomass.
No replication within a trial. One beaker per condition means beaker position, water batch and container effects are confounded with treatment, and the effective sample size is 3 beakers, not 30 fronds.
Each flaw, taken alone, weakens the causal claim; the light and counting problems both push the result toward the student's hypothesis.
2. Design an improved experiment, specifying replication, randomisation, controls and the measurement to record.
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Treat the beaker, not the frond, as the experimental unit and replicate it.
Design: use six beakers per treatment (12 total), each with the same volume of water from the same source, the same initial number of healthy fronds, and the same fertiliser volume for the treatment. Randomly assign beakers to positions on the windowsill, and rotate or shuffle positions every two days so that no treatment consistently receives more light. Include a water-only control and, ideally, a nutrient control without algae to separate fertiliser nutrients from algal growth. Use lids or a mesh to reduce evaporation and contamination, and keep temperature and day length as constant as the room allows.
Measurement: count only attached fronds at days 0, 7 and 14, or better, harvest at day 14 and measure dry mass after drying, since mass is less sensitive to fragmentation than counting. Count blind (the counter does not know which beaker is which), and record a contamination check such as water chlorophyll or a visual algae score. Report the mean and standard deviation across the six beakers for each treatment, and compare with an appropriate test rather than eyeballing one pair.
This design gives the fertiliser effect a fair comparison and makes the variability visible.
3. Interpret the three trials (fertiliser 46, 44, 61; control 21, 20, 19) and judge how strongly the conclusion 'fertiliser roughly doubles growth' is supported.
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Means: fertiliser (46 + 44 + 61)/3 = 50.3; control (21 + 20 + 19)/3 = 20.0. Ratio = 2.5, so the direction is consistent and the magnitude is large.
The spread matters. Control counts are tightly clustered (SD ≈ 1), while fertiliser counts range from 44 to 61. The 61 trial is 11 above the mean; with only three values this is a substantial outlier. A larger variance in the treatment group suggests an uncontrolled factor acting there - light position, algal bloom, or temperature - rather than a stable fertiliser effect. So the data support 'fertiliser increases growth' reasonably well, but the precise figure 'roughly doubles' is not established: the three trials give ratios of 2.2, 2.2 and 3.2, and the mean ratio is 2.5.
With one beaker per condition per trial, the beakers are the replicates (n = 3), which is too few to separate treatment from position effects, and the light confound remains. The honest conclusion is that the result is suggestive and consistent in direction but the design cannot support a causal, quantitative claim. Replication with randomised positions and attached-frond or dry-mass measurements would be needed before accepting the doubling claim.