Performing a Two-Way ANOVA with Blocks using R Studio

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I’ll upload one data in R.

if(!require(readr)) install.packages("readr")
library(readr)

github= paste0("https://raw.githubusercontent.com/agronomy4future/",
                "raw_data_practice/refs/heads/main/",
                "corn_grain_yield.csv")
dataA=data.frame(read_csv(url(github),show_col_types = FALSE))

print(head(dataA, 5))
  year      season variety population location ear   AGW   KN    GY
1 2022 Long Season     CV1     High D   Site 1   1 297.5 3550 10439
2 2022 Long Season     CV1     High D   Site 1   2 283.9 3408  9562
3 2022 Long Season     CV1     High D   Site 1   3 270.8 3834 10264
4 2022 Long Season     CV1     High D   Site 1   4 328.1 3408 11053
5 2022 Long Season     CV1     High D   Site 1   5 298.1 3692 10878
.
.
.

I have 10 corn varieties and want to analyze the impact of nitrogen treatments (N0 and N1), variety, and their interaction on grain yield. Since replicates are considered as blocks, I will conduct a two-way ANOVA analysis with blocks as the statistical model.

The statistical model for two-way ANOVA with blocks is as follows:

yijk = μ  + αi + βj + δij + γk + εijk

where
yijk: observed values for treatment (ij; i = factor 1, j = factor 2) and replicates (k)
μ: grand mean of observed values
αi: treatment effect of factor 1
βj: treatment effect of factor 2
δij: interaction effect between factor 1 (i) and factor 2 (j)
γk: block effect
εijk: residuals

Based on the statistical model for two-way ANOVA with blocks, we can conduct the analysis using R. Below is an example code:

anova2way= aov (GY ~ variety + population + variety:population, data=dataA)
summary(anova2way)

                     Df    Sum Sq   Mean Sq F value  Pr(>F)    
variety              22 9.569e+08  43496413   9.309 < 2e-16 ***
population            1 8.215e+08 821484359 175.810 < 2e-16 ***
variety:population   22 2.117e+08   9620751   2.059 0.00262 ** 
Residuals          2205 1.030e+10   4672566                    
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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