ANOVA also known as Analysis of Variance is a powerful statistical method to test a hypothesis involving more than two groups (also known as treatments). However, ANOVA is limited in providing a detailed insights between different treatments or groups, and this is where, Tukey (T) test also known as T-test comes in to play. In this tutorial, I will show how to prepare input files and run ANOVA and Tukey test in R software. For detailed information on ANOVA and R, please read this article at this link.

Step 1.0 Download and install R software and R studio

  1. Download and install the latest version of the R software from this link
  2. Download and install R studio from this link
  3. Finally, install the library qtl in R

Step 1.2 - Setup working directory following the below steps:


Step 1.3: Preparing the Input file

Create an input file as shown in the example below:

Import data

Step 2: Run ANOVA in R


2.1 Import R package

Install R package agricolae and open the library typing the below command line:

library(agricolae)



NOTE: Plesase remember to install the correct R package for ANOVA!


2.2 Import data

Import your data by typing the below command line:

data= read.table(file = "fileName.txt", header = T)

2.3 Check data

Once the data is imported, check it by typing the below command line:

head(data_pressure)
tail(data_pressure)

2.4 Conduct ANOVA

Now, Simply run ANOVA by typing the below command lines:

data.lm <- lm(data$Dependent_variable ~ data$Treatment, data = data)

data.av <- aov(data.lm)
summary(data.av)

The results should look similar as seen below:

> summary(data.av)
               Df Sum Sq Mean Sq F value   Pr(>F)    
data$Treatment  3  139.2   46.38   38.49 1.69e-08 ***
Residuals      20   24.1    1.20                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

From the summary output, one can interpret that there is a significant difference (i.e. P < 0.001) between the Treatments, however, we perfom Tukey’s Test to investigate the differences between all treaments using steps below.


3.0 Conduct Tukey test

Type below commands to run Tukey test:

data.test <- TukeyHSD(data.av)
data.test

Below is the summary of the Tukey test:

> data.test
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = data.lm)

$`data$Treatment`
           diff        lwr      upr     p adj
B-A  2.52666667  0.7527896 4.300544 0.0037260
D-A  5.74500000  3.9711229 7.518877 0.0000001
E-A  5.72583333  3.9519563 7.499710 0.0000001
D-B  3.21833333  1.4444563 4.992210 0.0003106
E-B  3.19916667  1.4252896 4.973044 0.0003326
E-D -0.01916667 -1.7930437 1.754710 0.9999897

From the above T-test, one can conclude that there is a significant difference in the most of groups, except between-groups E-D at P <0.001

Finally, one can plot the above results using the below command:

plot(data.test)

Output:

Output

--- End of Tutorial ---

Thank you for reading this tutorial. If you have any questions or comments, please let me know in the comment section below or send me an email.

Bibliography

Felipe de Mendiburu (2019). agricolae: Statistical Procedures for Agricultural Research. R package version 1.3-1. https://CRAN.R-project.org/package=agricolae