Fertiliser trial with a confounded paddock
A student runs a data-test-style analysis on a nitrogen trial. A paddock is split into two halves by a farm track. The north half receives 120 kg N/ha; the south half receives 0 kg N/ha. Each half is harvested as a single strip and weighed. North yields 6.8 t/ha; south yields 5.9 t/ha. Soil tests show the north half has 18 mg/kg nitrate-N and the south 11 mg/kg nitrate-N before sowing, and the north half also has a darker soil colour and better drainage. The student calculates a response of 0.9 t/ha and reports that 120 kg N/ha produced a 0.9 t/ha yield increase, worth $270/ha at $300/t, against a fertiliser cost of $180/ha, concluding a profit of $90/ha.
1. Identify the main threats to the internal validity of this trial and explain how each affects the reported 0.9 t/ha response.
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Several factors are confounded with the nitrogen treatment, so the 0.9 t/ha figure cannot be attributed to nitrogen alone.
- No replication. Each treatment is applied to one strip only. There is no way to separate treatment effect from paddock variation; the 0.9 t/ha could be entirely site difference.
- Pre-existing soil nitrogen. The north half starts with 18 mg/kg versus 11 mg/kg nitrate-N. Some of the yield difference reflects the higher starting N, not the applied N. The true response to applied N is therefore likely smaller than 0.9 t/ha.
- Soil and drainage differences. Darker colour and better drainage suggest different soil type or organic matter, which affect water-holding, mineralisation and yield independently of fertiliser.
- Track as a boundary. The track may coincide with a soil or drainage boundary, so the split is not random; the halves are systematically different.
- No measurement of other variables. Rainfall, weed pressure, sowing date and plant density are not reported, so any of these could differ between halves.
Because treatment is completely confounded with location, the 0.9 t/ha is an association, not a demonstrated causal effect. The economic conclusion inherits this uncertainty: the $90/ha profit could be zero or negative once the pre-existing N and soil differences are accounted for.
2. The student wants to keep the same paddock. Propose a modified design and explain how it would fix the main problem.
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The core fix is to break the link between treatment and location by replicating within a randomised design.
- Randomised complete block design: divide the paddock into several blocks that run across the track (e.g. blocks oriented east–west so each block contains both soil types), and within each block randomly allocate replicated plots to 0 and 120 kg N/ha. Randomisation ensures soil differences are spread across treatments rather than tied to one treatment.
- More than two rates: include intermediate rates (e.g. 0, 60, 120, 180 kg N/ha) so the response curve, not just a single difference, can be estimated. This also allows identification of the economic optimum.
- Baseline measurement: record pre-sowing nitrate-N, soil colour or type, drainage and plant density for every plot, so these can be used as covariates or to check that randomisation balanced them.
- Consistent management: same variety, sowing date, density, irrigation and weed control across all plots; harvest each plot separately.
- Analysis: compare treatment means with replication-based statistics and report variability, so the yield response and its confidence can be stated.
With replication and randomisation, the treatment effect is estimated against a measure of background variation, and the economic conclusion can be stated with an appropriate margin of error rather than from a single strip comparison.