Durbin test and multiple comparison of treatments

A multiple comparison of the Durbin test for the balanced incomplete blocks for sensorial or categorical evaluation. It forms groups according to the demanded ones for level of significance (alpha); by default, 0.05.

durbin.test(
  judge,
  trt,
  evaluation,
  alpha = 0.05,
  group = TRUE,
  main = NULL,
  console = FALSE
)

Arguments

judge	Identification of the judge in the evaluation
trt	Treatments
evaluation	variable
alpha	level of significant
group	TRUE or FALSE
main	Title
console	logical, print output

Value

statistics

Statistics of the model

parameters

Design parameters

means

Statistical summary of the study variable

rank

rank table of the study variable

comparison

Comparison between treatments

groups

Formation of treatment groups

Details

The post hoc test is using the criterium Fisher's least significant difference.

References

Practical Nonparametrics Statistics. W.J. Conover, 1999 Nonparametric Statistical Methods. Myles Hollander and Douglas A. Wofe, 1999

Examples


library(agricolae)
# Example 1. Conover, pag 391
person<-gl(7,3)
variety<-c(1,2,4,2,3,5,3,4,6,4,5,7,1,5,6,2,6,7,1,3,7)
preference<-c(2,3,1,3,1,2,2,1,3,1,2,3,3,1,2,3,1,2,3,1,2)
out<-durbin.test(person,variety,preference,group=TRUE,console=TRUE,
main="Seven varieties of ice cream manufacturer")
#> 
#> Study: Seven varieties of ice cream manufacturer 
#> variety,  Sum of ranks
#> 
#>   sum
#> 1   8
#> 2   9
#> 3   4
#> 4   3
#> 5   5
#> 6   6
#> 7   7
#> 
#> Durbin Test
#> ===========
#> Value      : 12
#> DF 1       : 6
#> P-value    : 0.0619688
#> Alpha      : 0.05
#> DF 2       : 8
#> t-Student  : 2.306004
#> 
#> Least Significant Difference
#> between the sum of ranks:  2.824267 
#> 
#> Parameters BIB
#> Lambda     : 1
#> Treatmeans : 7
#> Block size : 3
#> Blocks     : 7
#> Replication: 3 
#> 
#> Treatments with the same letter are not significantly different.
#> 
#>   Sum of ranks groups
#> 2            9      a
#> 1            8     ab
#> 7            7    abc
#> 6            6    bcd
#> 5            5    cde
#> 3            4     de
#> 4            3      e
#startgraph
bar.group(out$groups,horiz=TRUE,xlim=c(0,10),density=4,las=1)
#endgraph
# Example 2. Myles Hollander, pag 311
# Source: W. Moore and C.I. Bliss. 1942
day<-gl(7,3)
chemical<-c("A","B","D","A","C","E","C","D","G","A","F","G","B","C","F",
 "B","E","G","D","E","F")
toxic<-c(0.465,0.343,0.396,0.602,0.873,0.634,0.875,0.325,0.330,0.423,0.987,
0.426,0.652,1.142,0.989,0.536,0.409,0.309,0.609,0.417,0.931)
out<-durbin.test(day,chemical,toxic,group=TRUE,console=TRUE,
main="Logarithm of Toxic Dosages")
#> 
#> Study: Logarithm of Toxic Dosages 
#> chemical,  Sum of ranks
#> 
#>   sum
#> A   5
#> B   5
#> C   9
#> D   5
#> E   5
#> F   8
#> G   5
#> 
#> Durbin Test
#> ===========
#> Value      : 7.714286
#> DF 1       : 6
#> P-value    : 0.2597916
#> Alpha      : 0.05
#> DF 2       : 8
#> t-Student  : 2.306004
#> 
#> Least Significant Difference
#> between the sum of ranks:  5.00689 
#> 
#> Parameters BIB
#> Lambda     : 1
#> Treatmeans : 7
#> Block size : 3
#> Blocks     : 7
#> Replication: 3 
#> 
#> Treatments with the same letter are not significantly different.
#> 
#>   Sum of ranks groups
#> C            9      a
#> F            8      a
#> A            5      a
#> B            5      a
#> D            5      a
#> E            5      a
#> G            5      a
plot(out)
#> Warning: NAs introduced by coercion