The Premium Fertilizer Pays Off, But Only in Bright Light

At low light it does nothing. At high light it adds nearly eight centimetres of growth.

To Head Grower

From Trial Analytics

Re Fertilizer × light greenhouse trial

Where this comes from

Chapter Chapter 166 · Two-Way ANOVA: Fertilizer and Sunlight

Part Part XXVII · Capstone Projects: Statistical Testing

Dataset capstone-plant-growth-two-factors.xlsx

Notebook View the analysis

Recommendation

Bottom line

Buy the Premium fertilizer for your high-light houses only. In bright conditions it added about 7.7 cm of growth per plant, a large and reliable gain. In low light it added nothing (if anything the plants did slightly worse), and at medium light the gain was too small to be sure of. Spending on Premium across the whole operation would waste most of the money.

What we found

We grew 68 plants across six combinations: two fertilizers by three light levels. Light is by far the biggest driver of growth under either fertilizer. The fertilizer itself is a conditional story. Comparing Premium against Standard separately at each light level: at low light the difference was -1.05 cm (not meaningful), at medium light +2.31 cm (still not conclusive), and at high light +7.68 cm, which is both large and statistically certain.

Individual plant growth by light level and fertilizer, beside an interaction plot whose two lines start together at low light and fan apart at high light. — Figure 1. Left: every plant in the trial. Right: average growth for each fertilizer across the three light levels. The two lines start together and pull apart as light increases, which is the whole finding in one picture.

Bar chart: minus 1.05 cm in low light, plus 2.31 in medium, plus 7.68 in high. — Figure 2. The premium fertilizer's advantage over standard, at each light level.

Why the average number would have misled you

If we had simply compared all Premium plants against all Standard plants, ignoring light, Premium would have come out significantly ahead, and that headline would have been technically true and practically wrong. That average blends a small loss, a small gain, and a large gain into one number that matches no growing condition you actually have. This is why the trial crossed the two factors instead of testing them separately.

Premium minus Standard growth at each light level with confidence intervals; only the high-light difference is clear of zero and marked significant. — Figure 3. The Premium advantage measured separately at each light level, with the range we are 95 percent confident contains the truth. Only the high-light bar clears zero.

Before you scale this up

Three cautions. The trial ran in a greenhouse with uniform water, soil, and temperature, so field conditions may differ. Our 'high' light is one specific intensity, and we cannot promise the pattern keeps improving beyond it. And the recommendation is a cost decision as much as a growing one: the gain is real only in bright conditions, so the purchase should follow the light, not the label.

← Back to Chapter 166 📓 Companion notebook 📊 Download dataset

From Statistics, Data Science and AI: A Visual Handbook by John Fisher. Every statistic, table, and figure in this report is reproduced by the companion notebook.