N. Uttam Singh¹

Abhishek Thakur¹*

Eric Rani¹

*Corresponding Author Email: thakurabhishek7188@gmail.com

¹ICAR Research Complex for NEH Region

Umiam, Meghalaya

Introduction

Analysis of Variance (ANOVA) is one of the most widely used statistical techniques in agricultural research. It is used to compare treatment means and determine whether significant differences exist among treatments under experimental conditions.

ANOVA helps researchers identify treatment effects and distinguish them from random experimental variation.

R Studio provides an efficient and user-friendly environment for performing ANOVA, graphical visualization, and statistical interpretation.

Objectives

The objectives of this practical tutorial are:

To understand the concept of ANOVA
To import agricultural datasets into RStudio
To perform ANOVA using R
To calculate CD, CV, SEm, and SEd
To perform DMRT for multiple comparison
To generate graphical representation of treatment means

Software Requirements

Software	Purpose
R Software	Statistical Computing
RStudio	Integrated Development Environment

Recommended Versions

R version 4.0 or above
Latest version of R Studio

Introduction to R and R Studio

R is an open-source programming language widely used for statistical analysis, data visualization, and predictive modelling.

R Studio is an Integrated Development Environment (IDE) for R.

Main Components of RStudio

Source Editor
Console
Environment/History
Files/Plots/Packages/Help

Agricultural Dataset Description

In this tutorial, agricultural experimental data consisting of treatments and replications are analysed using ANOVA techniques.

Recommended Excel Dataset Format

Treatment	Replication	Yield
T1	R1	45
T1	R2	47
T1	R3	46
T2	R1	52
T2	R2	54
T2	R3	53

Save the Excel sheet as:

rbddata.xlsx

Required Package Installation

Run these commands once in R Console:

install.packages("readxl")
install.packages("dplyr")
install.packages("ggplot2")
install.packages("agricolae")
install.packages("emmeans")
install.packages("knitr")

Library Required Packages

library(readxl)
library(ggplot2)
library(dplyr)
library(knitr)
library(agricolae)
library(emmeans)

# Import Data (Not for Users)

data <- read_excel("rbddata.xlsx")

Command to be Used (For Users)

data <- read_excel("C:/Users/Abhisek/Desktop/RBD in R studio/rbddata.xlsx")

Note 1: Use the Second command to Import the data from the Excel File by copying the file path, the First Command is provided as reference with R Markdown file.

Note 2: While specifying the file path in RStudio, use forward slashes (/) instead of backward slashes (\). For example:

C:/Users/Abhisek/Desktop/RBD in R studio/rbddata.xlsx

head(data)

## # A tibble: 6 × 3
##   Treatment Replication Yield
##   <chr>     <chr>       <dbl>
## 1 T1        R1             45
## 2 T1        R2             47
## 3 T1        R3             46
## 4 T2        R1             52
## 5 T2        R2             54
## 6 T2        R3             53

Convert Variables into Factor

data$Treatment <- as.factor(data$Treatment)
data$Replication <- as.factor(data$Replication)

Structure of Dataset

str(data)

## tibble [24 × 3] (S3: tbl_df/tbl/data.frame)
##  $ Treatment  : Factor w/ 8 levels "T1","T2","T3",..: 1 1 1 2 2 2 3 3 3 4 ...
##  $ Replication: Factor w/ 3 levels "R1","R2","R3": 1 2 3 1 2 3 1 2 3 1 ...
##  $ Yield      : num [1:24] 45 47 46 52 54 53 58 57 59 63 ...

Summary Statistics

summary(data)

##    Treatment Replication     Yield      
##  T1     :3   R1:8        Min.   :45.00  
##  T2     :3   R2:8        1st Qu.:51.75  
##  T3     :3   R3:8        Median :59.50  
##  T4     :3               Mean   :59.75  
##  T5     :3               3rd Qu.:66.00  
##  T6     :3               Max.   :77.00  
##  (Other):6

Treatment Means

aggregate(Yield ~ Treatment,
          data=data,
          mean)

##   Treatment Yield
## 1        T1    46
## 2        T2    53
## 3        T3    58
## 4        T4    64
## 5        T5    70
## 6        T6    61
## 7        T7    50
## 8        T8    76

Boxplot of Treatments

ggplot(data,
       aes(x=Treatment,
           y=Yield,
           fill=Treatment)) +
  geom_boxplot() +
  labs(title="Treatment-wise Yield",
       x="Treatment",
       y="Yield") +
  theme_minimal()

Analysis of Variance (ANOVA)

Fitting ANOVA Model

model <- aov(Yield ~ Treatment,
             data=data)

model

## Call:
##    aov(formula = Yield ~ Treatment, data = data)
## 
## Terms:
##                 Treatment Residuals
## Sum of Squares     2164.5      16.0
## Deg. of Freedom         7        16
## 
## Residual standard error: 1
## Estimated effects may be unbalanced

ANOVA Table

summary(model)

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## Treatment    7   2164   309.2   309.2 7.34e-16 ***
## Residuals   16     16     1.0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interpretation of ANOVA Table

The ANOVA table provides:

Degrees of freedom
Sum of squares
Mean squares
F-value
p-value

Decision Rule

p-value	Interpretation
p < 0.05	Significant Treatment Effect
p > 0.05	Non-significant Treatment Effect

Coefficient of Variation (CV)

cv <- (sqrt(mean(model$residuals^2)) /
         mean(data$Yield)) * 100

cv

## [1] 1.366521

Interpretation of CV

Lower CV indicates better experimental precision and reliability
Higher CV indicates greater experimental variability
In Randomized Block Design (RBD), CV values generally ranging from 5–15% are considered acceptable for agricultural experiments

Standard Error of Mean (SEm)

mse <- deviance(model)/df.residual(model)

r <- 3

SEm <- sqrt(mse/r)

SEm

## [1] 0.5773503

Standard Error of Difference (SEd)

SEd <- sqrt(2*mse/r)

SEd

## [1] 0.8164966

Critical Difference (CD)

tvalue <- qt(0.975,
             df.residual(model))

CD <- tvalue * SEd

CD

## [1] 1.730895

Duncan Multiple Range Test (DMRT)

dmrt <- agricolae::duncan.test(model,
                               "Treatment",
                               group=TRUE)

dmrt

## $statistics
##   MSerror Df  Mean      CV
##         1 16 59.75 1.67364
## 
## $parameters
##     test    name.t ntr alpha
##   Duncan Treatment   8  0.05
## 
## $duncan
##      Table CriticalRange
## 2 2.997999      1.730895
## 3 3.143802      1.815075
## 4 3.234945      1.867696
## 5 3.297445      1.903780
## 6 3.342599      1.929850
## 7 3.376283      1.949298
## 8 3.401918      1.964098
## 
## $means
##    Yield std r        se Min Max  Q25 Q50  Q75
## T1    46   1 3 0.5773503  45  47 45.5  46 46.5
## T2    53   1 3 0.5773503  52  54 52.5  53 53.5
## T3    58   1 3 0.5773503  57  59 57.5  58 58.5
## T4    64   1 3 0.5773503  63  65 63.5  64 64.5
## T5    70   1 3 0.5773503  69  71 69.5  70 70.5
## T6    61   1 3 0.5773503  60  62 60.5  61 61.5
## T7    50   1 3 0.5773503  49  51 49.5  50 50.5
## T8    76   1 3 0.5773503  75  77 75.5  76 76.5
## 
## $comparison
## NULL
## 
## $groups
##    Yield groups
## T8    76      a
## T5    70      b
## T4    64      c
## T6    61      d
## T3    58      e
## T2    53      f
## T7    50      g
## T1    46      h
## 
## attr(,"class")
## [1] "group"

Graphical Representation of Treatment Means

means <- aggregate(Yield ~ Treatment,
                   data=data,
                   mean)

ggplot(means,
       aes(x=Treatment,
           y=Yield,
           fill=Treatment)) +
  geom_bar(stat="identity") +
  labs(title="Treatment Means",
       x="Treatment",
       y="Mean Yield") +
  theme_minimal()

Applications in Agriculture

ANOVA has wide applications in agricultural sciences.

Major Applications

Crop variety evaluation
Fertilizer response studies
Irrigation management
Soil nutrient experiments
Agronomic research
Plant breeding studies
Pest and disease management trials

Conclusion

ANOVA is an important statistical tool for analysing agricultural experimental data and comparing treatment effects. RStudio provides a powerful environment for performing ANOVA, calculating statistical parameters, conducting multiple comparison tests, and generating graphical outputs. The procedures demonstrated in this tutorial can be extended to advanced experimental designs and agricultural data analysis.

Randomized Block Design in R Studio: One Factor Analysis

R Codes for ANOVA Analysis

2026-05-25