Friedman test and multiple comparison of treatments

The data consist of b-blocks mutually independent k-variate random variables Xij, i=1,..,b; j=1,..k. The random variable X is in block i and is associated with treatment j. It makes the multiple comparison of the Friedman test with or without ties. A first result is obtained by friedman.test of R.

friedman(
  judge,
  trt,
  evaluation,
  alpha = 0.05,
  group = TRUE,
  main = NULL,
  console = FALSE
)

Arguments

judge	Identification of the judge in the evaluation
trt	Treatment
evaluation	Variable
alpha	Significant test
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

comparison

Comparison between treatments

groups

Formation of treatment groups

Details

The post hoc friedman test is using the criterium Fisher's least significant difference (LSD)

References

Practical Nonparametrics Statistics. W.J. Conover, 1999

Examples


library(agricolae)
data(grass)
out<-with(grass,friedman(judge,trt, evaluation,alpha=0.05, group=TRUE,console=TRUE,
main="Data of the book of Conover"))
#> 
#> Study: Data of the book of Conover 
#> 
#> trt,  Sum of the ranks
#> 
#>    evaluation  r
#> t1       38.0 12
#> t2       23.5 12
#> t3       24.5 12
#> t4       34.0 12
#> 
#> Friedman's Test
#> ===============
#> Adjusted for ties
#> Critical Value: 8.097345
#> P.Value Chisq: 0.04404214
#> F Value: 3.192198
#> P.Value F: 0.03621547 
#> 
#> Post Hoc Analysis
#> 
#> Alpha: 0.05 ; DF Error: 33
#> t-Student: 2.034515
#> LSD: 11.48168 
#> 
#> Treatments with the same letter are not significantly different.
#> 
#>    Sum of ranks groups
#> t1         38.0      a
#> t4         34.0     ab
#> t3         24.5      b
#> t2         23.5      b
#startgraph
plot(out,variation="IQR")
#> Warning: NAs introduced by coercion
#endgraph