Methodology of conducting and variance analysis of a two-factor field experiment with rice

For a two-factor analysis of variance in an experiment, the following conditions must be met:

• for factor A (fertilizer rates, tillage methods, predecessors), at least three gradations (variants) of the experiment are necessary, as the results may not be accurate with only two variants;
• for factor B (cultivars, fertilizer rates), there must also be at least three variants;
• the experiment must be conducted in 3, 4, or 5 replications.

We compile a yield matrix for rice cultivars in a two-factor experiment. Yield results can be presented as decimal fractions (58.7; 65.4; 66.2, etc.). We enter the yield results into any PC file and check for errors after entry.

Using the two-factor analysis of variance program, we obtain a matrix of statistical yield results on the monitor screen, which includes: type of variance, variance value, degrees of freedom, mean square, least significant difference (LSD05) pairwise and in comparison with the mean, as well as the F-test (Fisher's criterion).

For each variant with fertilizer rates, the cultivars are compared pairwise with the standard. For factor A, the averaged values of all cultivars in the variant without fertilizer are compared with the corresponding values with fertilizer.

Table 236 – Yield matrix for rice cultivars in a two-factor experiment, c/ha

Table 237 – Matrix of statistical values for the result of the two-factor analysis of variance of rice yield LSD F-test Type of variance Variance Degrees of freedom Mean square pairwise average table calculated

 Total 950.11 5 16.10 Replications 9.97 3 2.66 Variants 830.11 14 59.29 2.36 1.62 22.2 1.9 Factor A 260.31 2 130.16 1.06 0.61 48.8 3.2 Factor B 538.61 4 134.65 1.37 0.86 50.5 2.6 Interaction AB 31.19 8 3.90 2.36 1.62 1.5 2.1 Errors 112.03 42 2.67

Taking into account the variance value, one can determine the share of influence of each factor and its components on the expression of the studied trait (grain yield of rice cultivars). To do this, we subtract the errors (112.03) from each variance type value:

– total: 950.11–112.03 = 838.08;

– replications: 9.97–112.03 = –102.06;

– variants: 830.11–112.03 = 718.08;

– factor A: 260.31–112.03 = 148.28;

– factor B: 538.61–112.03 = 426.58;

– interaction AB: 31.19–112.03 = –80.84.

We obtain the sum of these values: [838.08+(–102.06)+718.08+148.28+ +426.58+(-80.84)] = 1948.12.

We determine the share of influence (contribution) of each type of variability (variance) on yield formation in the entire population of variation according to the ratios. The total sum of variation values minus errors (1948.12) is taken as 100% of the influence.

Share of contribution of total variation in yield formation:

838.08 — x x = 838.08·100/1948.12 = 43.01 %;

Share of contribution of replications:

-102.06 — x x = –102.06·100/1948.12 = –5.23 %;

Share of contribution of variants:

718.08 — x x = 718.08·100/1948.12 = 36.86 %;

Share of contribution of factor A:

148.28 — x x = 148.28·100/1948.12 = 7.61 %;

Share of contribution of factor B:

426.58 — x x = 426.58·100/1948.12 = 21.89 %;

Share of contribution of interaction AB:

–80.84 — x x = –80.84·100/1948.12 = –4.14 %.

The sum of all values of the shares of influence (contribution) of each type of variation must always equal 100 %.

Furthermore, the researcher provides an explanation of the share of influence of each type of variation on the formation of the yield of different rice cultivars depending on the rates of mineral fertilizers. The dominant role in the formation of rice cultivar yield belongs to the total variance (43.01 %), each variant (36.86 %), and cultivar genotypes (21.89 %).

Processing the rice grain yield results using the two-factor analysis of variance method shows that in the "average by variants" column, these are the averaged data for each experimental variant from four replications. The average for factor A is obtained as a result of summing the mean values for the variants included in the experiment variant for factor A (without fertilizer: 56+54+59.5+63+61.5 = 294. There are 5 cultivars in the experiment; we divide the sum of 294 by 5, which equals 58.8. Similarly, we obtain yield values for each variant of factor A. These calculations are performed by a PC.

When planning a rice nutrition system, it is important to know how a specific cultivar responds to the application of mineral fertilizers. A two-factor field experiment helps determine if there is a real yield increase from the joint effect of factors — genetic characteristics of plants (factor B) and nutrition doses (factor A). This will prevent unnecessary expenses on expensive fertilizer mixtures if the cultivar is physiologically unable to assimilate them. Proper calculation allows for the identification of hidden patterns and optimization of costs per hectare.

Evaluation of the interaction between cultivar and fertilizer rate

To understand how effectively a cultivar utilizes fertilizers, one must first calculate its average yield across all experimental nutrition backgrounds. To do this, the yield indicators of a specific cultivar for each experimental variant are summed, and the resulting sum is divided by the number of variants. Such a calculation allows for the purification of the cultivar productivity indicator from the influence of fertilizer doses and an evaluation of its pure potential. A step-by-step methodology for this calculation is provided below.

1. Collect yield data for a specific cultivar across all mineral nutrition backgrounds.
2. Sum the obtained values. For example, for the Liman cultivar: 56.0 + 60.8 + 64.3 = 181.1 c/ha.
3. Divide the sum by the number of nutrition variants (there are 3 in this experiment). The average yield of the Liman cultivar will be: 181.1 / 3 = 60.3 c/ha.

Average yield values for all other cultivars are determined using a similar scheme. All obtained data are compiled into a final analysis of variance table. The effect of factors is considered mathematically significant only if their values exceed the least significant difference (LSD₀₅). If the AB interaction indicator is lower than the LSD, the combined effect of the cultivar and fertilizer is considered unproven.

• LSD05 for variants — 2.36 c/ha
• LSD05 for Factor A (fertilizer) — 1.06 c/ha
• LSD05 for Factor B (cultivar) — 1.37 c/ha
• LSD05 for AB interaction — 2.36 c/ha