Split plot analysis in R using doebioresearch package

The blog explains split plot analysis in R along with assumption testing and LSD test for mean comparison (Reading time 9 min)

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Replication: 4

Main-plot: Variety levels 3

Sub-plot: Nitrogen levels 3

Dependent variable: Yield 

Source of problem: https://fliphtml5.com/waov/gjll/basic

 Data: excel sheet

 R-script: script

#Upload excel file into RStudio

library(readxl)

SP <- read_excel("D:/Youtube/Design of Experiments/Split plot/SP.xlsx")

View(SP)
#You can upload the data by clicking on import data set-> From Excel -> Browse -> Select your file-> #Import

#Load doebioresearch package

library(doebioresearch)

#Store split plot analysis in variable named output along with LSD test

output<-splitplot(SP[4],SP$Replication,SP$Variety,SP$Nitrogen,1)

#Store output in document outside RStudio in word file

sink("output.doc")

print(output)

sink()

Output from R:

Analysis of Variance Table

Response: dependent.var
                   Df    Sum Sq   Mean Sq   F value     Pr(>F)   
block               3   190.083   63.361    2.1836      0.190936   
main.plot           2    90.487   45.243    1.5592      0.284900   
Ea                  6   174.100   29.017                    
sub.plot            2    92.435   46.217    10.2287     0.001078 **
main.plot:sub.plot  4    9.533    2.383     0.5275      0.717003   
Eb                 18   81.332    4.518                    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


The p-value of the subplot is <0.05, so its significant. The means of all the three nitrogen levels are not same so go for LSD test. The main plot and interaction is non significant so ignore their LSD test result and all of their levels are same.  

[1] "CV(a): 30.348 , CV(b) : 11.976"

The main plot C.V. is high and out of general limit which will need a suitable justification. The C.V. for the sub plot is within a limit (less than 12-15%).

[1] "R Square 0.873"

0.873 i.e. 87.3% variation present in the dependent variable yield is explained by the model.

	Shapiro-Wilk normality test

data:  model$residuals
W = 0.97257, p-value = 0.5

[1] "Normality assumption is not violated"


$Yield[[1]][[6]]
[1] "All the main plot factor level means are same so dont go for any multiple comparison test"

[1] "The means of one or more levels of sub plot factor are not same, so go for multiple comparison test"

   MSerror Df  Mean       CV  t.value      LSD
  4.518426 18 17.75 11.97554 2.100922 1.823173


   dependent.var groups
n3      19.70833      a
n2      17.75833      b
n1      15.78333      c

The LSD test reveals that 60 kg/ha (n3) gives highest yield which is on par with/statistically different from 30 kg/ha (n2) and 0 kg/ha (n1).

Happy Learning!

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Hope you found this blog useful. If have any query or suggestions please do post it below.

If you are using "doebioresearch" for analysis. You can cite it as:

Popat, R and Banakara, K. (2020). doebioresearch: Analysis of Design of Experiments for Biological Research. R package version 0.1.0

To learn more about Agricultural Statistics follow my youtube channel

Topics you might be interested in:

CRD analysis in R

Degrees of freedom

Principles of designs of experiments-I: Replication

Principles of designs of experiments-II: Randomization
Principles of design of experiments-III: Local control