Tomato Compost Trial: Method of Difference and Confounding
The agriculture unit of a junior college wants to test whether a new organic compost increases tomato yield. Eight equal plots are available. Four plots receive compost; four receive the usual fertilizer. The compost plots are next to the greenhouse and receive 20 minutes more watering each day because the greenhouse sprinkler overlaps them. Harvesting is done by two groups: the compost plots are weighed by the project leader, the control plots by a first-year volunteer. One control plot is damaged by stray cattle and excluded. Results: compost plots average 4.8 kg per plant; control plots average 4.1 kg per plant. The unit concludes the compost caused a 0.7 kg increase. A teacher asks the students to evaluate the strength of the inductive inference, identify the method of causal reasoning being used, and propose a better design. The unit has one more season and can reassign plots and watering.
1. Identify the method of causal reasoning the unit is relying on and assess the strength of the conclusion. Mention at least two weaknesses.
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The unit is using the method of difference: it compares two groups that differ with respect to compost and observes a difference in yield. The inference is weak to moderate, not strong enough for the causal conclusion. First, watering is confounded with compost: the compost plots receive 20 extra minutes daily, so the yield difference could be caused by water rather than compost. Second, assignment to plots is not random and the greenhouse position may differ in light, soil, or temperature. Third, the compost plots are weighed by the project leader and the controls by an inexperienced volunteer, creating a possible measurement bias. Fourth, one control plot is lost, reducing the control group to three and introducing attrition. The 0.7 kg difference is a correlation under uncontrolled conditions; it does not establish causation.
2. How should the design be changed to support a causal claim? Give specific controls.
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Randomly assign compost and control treatments to plots, preferably within blocks that share soil and light conditions. Equalize watering so every plot receives the same amount and timing, or install separate sprinklers. Keep greenhouse distance similar across treatments or include position as a blocking variable. Use one weighing protocol for all plots and, if possible, have the weigher blind to treatment. Retain all eight plots or replace the lost control with a similarly positioned plot, and record why any plot is excluded. Increase the number of replicates and take a pre-season baseline yield or soil measurement. These changes reduce confounding and make the comparison support a causal inference more strongly.
3. State a testable hypothesis and one prediction. Distinguish the observed correlation from causation.
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Testable hypothesis: under equal watering, soil, and measurement conditions, tomato plants treated with the new organic compost produce a higher mean marketable yield per plant than plants given the usual fertilizer. Prediction: if the hypothesis is true, the mean yield of compost plots will exceed that of control plots by a difference larger than the study's estimated margin of error. The observed 0.7 kg difference is a correlation between compost and yield in this sample. Causation would require ruling out watering, plot position, measurement bias, and loss of the control plot, ideally through randomization and controlled watering.