The Finger Millet Plot Trial in Mandya
An agricultural science student at a PU college in Mandya compares four 0.4-hectare plots of finger millet, all sown with the same variety (ML-365) on the same date in the same red sandy loam, and all receiving 42 mm of measured irrigation. The only difference is the input package: Plot 1: compost + recommended NPK - 22 q/ha Plot 2: no compost + recommended NPK - 18 q/ha Plot 3: compost + no NPK - 15 q/ha Plot 4: no compost + no NPK - 11 q/ha She then interviews 15 farmers at a compost-training workshop; 12 report yields above 20 q/ha, and she concludes that compost training raises yield by about 10 q/ha across the district. Her teacher points out that the four plots were not replicated and that the survey design may not support the district-level claim. The student must defend or revise each conclusion using Mill's methods and the canons of inductive generalisation.
1. Which of Mill's methods does the four-plot design use? State the causal conclusion it licenses and the size of each effect.
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The design is the method of difference, with an element of the method of agreement supporting it. Each comparison differs in exactly one input:
| Comparison | Plots | Arithmetic | Effect |
|---|---|---|---|
| Compost, NPK held constant | 1 vs 2 | 22 − 18 | +4 q/ha |
| Compost, no NPK | 3 vs 4 | 15 − 11 | +4 q/ha |
| NPK, compost held constant | 1 vs 3 | 22 − 15 | +7 q/ha |
| NPK, no compost | 2 vs 4 | 18 − 11 | +7 q/ha |
The compost effect agrees across both NPK levels (4 and 4), and the NPK effect agrees across both compost levels (7 and 7); this joint pattern is the joint method of agreement and difference. Within these plots the licensed conclusion is: compost raises yield by about 4 q/ha and NPK by about 7 q/ha, other things equal.
A method of residues check fits: 11 (baseline) + 4 + 7 = 22, exactly Plot 1, so no residual interaction is visible. But with a single plot per cell, interaction and hidden confounders cannot be excluded, and the conclusion is confined to these four plots.
2. The student generalises to 'about 10 q/ha across the district' from 15 farmers at a compost workshop. Evaluate this inference and say what design would support the claim.
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There are several distinct gaps:
- The number is wrong before any generalisation. Her own controlled comparison gives a 4 q/ha compost effect. The figure of 10 q/ha is Plot 1 minus Plot 4 (22 − 11), which bundles compost and NPK together; she is attributing a joint effect to one factor - a case of false cause through an unremoved confounder.
- The survey cannot support a district claim. The 15 respondents were recruited at a compost-training workshop, so they are self-selected, already committed to compost, and likely to over-report. There is no control group, no measured yield, and no matching on farm size or soil. Drawing a district-wide conclusion from them is hasty generalisation (converse accident).
- The 12-out-of-15 figure describes the room, not the district. A convenience sample gives no margin of error that could justify an extrapolation.
A defensible design: randomise compost (applied / not applied) across many farms within each NPK level; keep variety, sowing date and irrigation fixed or recorded; weigh yields rather than rely on self-report; and compare trained with untrained farmers matched on farm size and soil. Replication plus a control group, used alongside the joint method, is what turns an association into a causal claim.
3. Rewrite her claim as a testable hypothesis and state what evidence would confirm or refute it.
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Hypothesis: under fixed variety (ML-365), soil and irrigation, applying compost raises finger millet yield by about 4 q/ha at each level of NPK and does not change the size of the NPK response.
Testable predictions:
- P1: compost plots out-yield matched no-compost plots by roughly 4 q/ha - already met in the two pairwise comparisons (22 vs 18; 15 vs 11).
- P2: the compost × NPK interaction is close to zero, i.e. the 4 q/ha gap appears at both NPK levels - met here, but with only one replicate per cell.
- P3: the effect reappears on other farms and in another season.
Confirming evidence: replicated, randomised trials with a consistent positive difference; a dose–response pattern (0, 2, 4 and 6 t/ha of compost producing steadily rising yields) would add support through Mill's method of concomitant variation.
Refuting evidence: no difference in replicated trials; the gap vanishing once plots are matched for drainage or organic carbon, which would expose confounding; the effect appearing only in the un-irrigated season; or the outcome reversing at high NPK, which would indicate interaction. One failed prediction would not destroy the hypothesis at once, but a consistent pattern of failure would.