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Agrochemistry

Analysis of variance of the results of a single-factor field experiment with rice

For students

3 min read

AGROCHEMISTRY A

Any field trial is accompanied by the natural variation of soil fertility and accidental errors during sowing or harvesting. To understand whether new fertilizer application rates have truly increased the yield or if it is a result of a random combination of circumstances, analysis of variance is used. Let us examine this method using the example of a field trial of mineral nutrition for the Liman rice cultivar.

How to verify the significance of a yield increase using the LSD criterion

The trial studied six nutrition variants for the Liman rice cultivar in four replicates. After harvesting, the yield from each plot was recalculated to standard humidity and grain purity. Mathematical analysis of this data allows for obtaining key indicators of the field trial's precision.

  • Overall trial mean (M) — 54.14583 centners/ha
  • Standard error of the mean (m) — 0.4261932
  • Trial error — 0.75 %
  • LSD05 — 1.30 centners/ha

The LSD05 criterion (least significant difference at the 5% significance level) is the agronomist's main guideline. If the difference between the experimental variant and the control is less than the LSD, then the increase is random and cannot be attributed to the effect of fertilizers.

Actual rice yield data across all replicates and mean indicators per trial variant are summarized in the table:

Nutrition variant 1st replicate, centners/ha 2nd replicate, centners/ha 3rd replicate, centners/ha 4th replicate, centners/ha Mean, centners/ha Deviation from control, centners/ha
Without fertilizers (control) 46.2 43.7 47.1 44.8 45.45 —
N50P40K40 50.3 51.6 52.4 51.2 51.37 +5.92
N80P60K60 53.9 54.4 55.2 54.8 54.57 +9.12
N120P80K80 56.2 57.3 58.1 57.0 57.15 +11.67
N150P90K90 59.9 59.1 61.4 62.7 60.77 +15.32
N180P100K100 55.3 54.8 56.4 55.7 55.55 +10.10

To confirm that the increase was obtained specifically due to fertilizers, perform a comparison using the following algorithm:

  1. Take the mean yield of the control (without fertilizers) — 45.45 centners/ha.
  2. Add the LSD05 value (1.30 centners/ha) to it: 45.45 + 1.30 = 46.75 centners/ha.
  3. Compare the resulting sum with the yield of the experimental variant (for example, N50P40K40 — 51.37 centners/ha). Since the actual yield (51.37 centners/ha) is higher than the control threshold (46.75 centners/ha), the difference is mathematically significant.
  4. To double-check, subtract the LSD05 from the yield of the experimental variant: 51.37 - 1.30 = 50.07 centners/ha. The resulting value exceeds the control (45.45 centners/ha), which also confirms the significance of the increase (the difference of 5.92 centners/ha is significantly greater than the LSD 1.30 centners/ha).

If the difference between the mean indicators of the experimental variant and the control is less than the LSD05 value, then the increase is not mathematically proven. Using such a nutrition scheme in production makes no sense — it does not guarantee a result.

Evaluating the contribution of factors: what influenced the rice yield more strongly

To determine the structure of yield variability and the share of influence of each factor, a statistical matrix of variance analysis is calculated. This allows for separating the useful signal (effect of fertilizers) from the influence of the background and random errors of the trial.

Type of variance Variance Degrees of freedom Mean square LSD of pairwise means F-ratio calculated F-ratio table
Total 574.58 23 24.98 — — —
Replicates 9.98 3 3.33 — — —
Variants 553.7 5 110.74 1.304 / 0.841 152.4 2.9
Error 10.90 15 0.73 — — —

Based on this data, the contribution share of each source of variation to the rice yield is calculated. To do this, the error value (10.90) is subtracted from the total variance (574.58), variant variance (553.7), and replicate variance (9.98). The percentage contribution is determined relative to the adjusted sum of variances (1105.56):

  • Contribution of overall variation (weather, climate, and genetic potential of the Liman cultivar): (574.58 - 10.90) = 563.68, which accounts for 51.0% of the influence.
  • Contribution of mineral nutrition variants (fertilizer application rates): (553.7 - 10.90) = 542.8, which accounts for 49.1% of the influence.
  • Contribution of replicates in the trial (soil non-uniformity across different replicates): (9.98 - 10.90) = -0.92, which accounts for -0.1% of the influence.

The extremely small negative contribution share of the replicates (-0.1%) proves that soil variegation on the experimental plot was practically absent and had no influence on the rice yield. The formation of the Liman cultivar's yield in the trial was determined exclusively by the general ecological background (51.0%) and the doses of applied mineral fertilizers (49.1%).

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