SK: The SK Test for Single Experiments

In ScottKnott: The ScottKnott Clustering Algorithm

The SK Test for Single Experiments

Description

These are methods for objects of class formula, lm, aov, aovlist and lmerMod for single, factorial, split-plot and split-split-plot experiments.

Usage

SK(x,...)

## S3 method for class 'formula'
SK(formula,
       data            = NULL,
       which           = NULL,
       fl1             = NULL,
       fl2             = NULL,
       error           = NULL,
       sig.level       = .05,
       round           = 2,
       ...)

## S3 method for class 'lm'
SK(x,
       which           = NULL,
       fl1             = NULL,
       fl2             = NULL,
       error           = NULL,
       sig.level       = .05,
       round           = 2,
       ...)

## S3 method for class 'aovlist'
SK(x,
       which           = NULL,
       fl1             = NULL,
       fl2             = NULL,
       error           = NULL,
       sig.level       = .05,
       round           = 2,
       ...)

## S3 method for class 'lmerMod'
SK(x,
       which           = NULL,
       fl1             = NULL,
       fl2             = NULL,
       error           = NULL,
       sig.level       = .05,
       round           = 2,
       ...)

Arguments

x,formula	A formula, lm, aov, aovlist and lmerMod class object. Objects of the formula class follow “response variable ~ predicted variable.
data	A object of the data.frame class. Use only objects of formula class.
which	The name of the treatment to be used in the comparison. The name must be inside quoting marks.
fl1	A vector of length 1 giving the level of the first factor in nesting order tested.
fl2	A vector of length 1 giving the level of the second factor in nesting order tested.
error	The error to be considered. If from experiment at split plot or split-split plot pay attention! See details!
sig.level	Level of Significance used in the SK algorithm to create the groups of means. The default value is 0.05.
round	Integer indicating the number of decimal places.
...	Potential further arguments (required by generic).

Details

The function SK returns an object of class SK containing the groups of means plus other necessary variables for summary and plot.

The generic functions summary and plot are used to obtain and print a summary and a plot of the results.

The error arguments may be used whenever the user want a specific error other than the experimental error. At the split plot and split-split plot experiment, combination of error may be specified with "/" in the sequence of the which argument. For example, a object of aovlist class, a possible combination would be error = 'Within/blk:plot' at case block split plot experiment with which = 'subplot:plot' argument.

Value

The function SK returns a list of the class SK with the slots:

out	A list storing the result of Scott & Knott test.
info	A list storing the descriptive statistics.
stat	A matrix with the statistics of each clustering process.
clus	A list with the groups formed in each clustering process.

Author(s)

Jose Claudio Faria ([e-mail])
Enio Jelihovschi ([e-mail])
Ivan Bezerra Allaman ([e-mail])

References

Miller, R.G. (1981) Simultaneous Statistical Inference. Springer.

Ramalho M.A.P, Ferreira D.F and Oliveira A.C. (2000) Experimentacao em Genetica e Melhoramento de Plantas. Editora UFLA.

Steel, R.G., Torrie, J.H and Dickey D.A. (1997) Principles and procedures of statistics: a biometrical approach. Third Edition.

Yandell, B.S. (1997) Practical Data Analysis for Designed Experiments. Chapman and Hall.

Examples

##
## Examples:Randomized Complete Block Design (RCBD)
## More details: demo(package='SK')
##

## The parameters can be: formula, aov, lm, aovlist and lmerMod

data(RCBD)

## From: formula
sk1 <- with(RCBD,
            SK(y ~ blk + tra,
               data=dfm,
               which='tra'))
summary(sk1)

## From: merMod
## This class is specific of the lme4 package.
## Not run: 
  if(require(lme4)){
    lmer1 <- with(RCBD,
                  lmer(y ~ (1|blk) + tra,
                       data=dfm))

    sk2 <-  SK(lmer1,
               which='tra')
    summary(sk2)
  }

## End(Not run)
##
## Example: Latin Squares Design (LSD)
## More details: demo(package='SK')
##

data(LSD)

## From: formula
sk3 <- with(LSD,
            SK(y ~ rows + cols + tra,
               data=dfm,
               which='tra'))
summary(sk3)

## From: aov
av1 <- with(LSD,
            aov(y ~ rows + cols + tra,
                data=dfm))

sk4 <- SK(av1,
              which='tra')
summary(sk4)

## From: lm
lm1 <- with(LSD,
            lm(y ~ rows + cols + tra,
               data=dfm))

sk5 <- SK(lm1,
          which='tra')
summary(sk5)

##
## Example: Factorial Experiment (FE)
## More details: demo(package='SK')
##

data(FE)
## From: formula
## Main factor: N
sk6 <- with(FE,
            SK(y ~ blk + N*P*K,
               data=dfm,
               which='N'))
summary(sk6)

## Nested: p1/N
# From: formula
n_sk1 <- with(FE,
              SK(y ~ blk + N*P*K,
                 data=dfm,
                 which='P:N',
                 fl1=1))
summary(n_sk1) 

## Nested: p2/N
# From: lm
lm2 <- with(FE,
            lm(y ~ blk + N*P*K, 
               dfm))

n_sk2 <- with(FE,
              SK(lm2,
                 which='P:N',
                 fl1=2))
summary(n_sk2) 

## Nested: n1/P
# From: aov
av2 <- with(FE,
            aov(y ~ blk + N*P*K,
                dfm))

n_sk3 <- with(FE,
              SK(av2,
                 which='N:P',
                 fl1=1))
summary(n_sk3) 

# From: merMod
## Not run: 
  if(require(lme4)){
    lmer2 <- with(FE,
                  lmer(y ~ (1|blk) + N*P*K,
                       dfm))

    n_sk4 <- with(FE,
                  SK(lmer2,
                     which='N:P',
                     fl1=1))
    summary(n_sk4)
  }

## End(Not run)

##
## Example: Split-plot Experiment (SPET)
## More details: demo(package='SK')
##
data(SPET)

## From lm
lm3 <- with(SPET,
            lm(y ~ blk*tra + tra*year,
               dfm))

# crotgrantiana/year
sp_sk1 <- SK(lm3,
             which='tra:year',
             fl1=1)
summary(sp_sk1) 

# year1/tra
# It is necessary to set year error with trat error in the order of the "which" argument.
# It is necessary to inform how to combinate the errors
sp_sk2 <-  SK(lm3,
              which='year:tra',
              error='Residuals/blk:tra',
              fl1=1)
summary(sp_sk2)

# From merMod
# Onty tra
## Not run: 
  if(require(lme4)){
    lmer3 <- with(SPET,
                  lmer(y ~ blk + (1|blk:tra) + tra*year,
                       dfm))

    # comparison only tra
    sp_sk3 <- SK(lmer3,
                 which = 'tra',
                 error = 'blk:tra')
    summary(sp_sk3)

    # year1/tra
    sp_sk4 <- SK(lmer3,
                 which='year:tra',
                 error='Residual/blk:tra',
                 fl1=1)
    summary(sp_sk4)
  }

## End(Not run)

## Example: Split-split-plot Experiment (SSPE)
## More details: demo(package='SK')
##

data(SSPE)
## From: formula
## Main factor: P
## It is necessary to inform the appropriate error for the test
ssp_sk1 <- with(SSPE,
                SK(y ~ blk + P*SP*SSP + Error(blk/P/SP),
                   data=dfm,
                   which='P',
                   error='blk:P'))
summary(ssp_sk1)

## Main factor: SP
## It is necessary to inform the appropriate error for the test
ssp_sk2 <- with(SSPE,
                SK(y ~ blk + P*SP*SSP + Error(blk/P/SP),
                   data=dfm,
                   which='SP',
                   error='blk:P:SP'))
summary(ssp_sk2)

## Main factor: SSP
ssp_sk3 <- with(SSPE,
                SK(y ~ blk + P*SP*SSP + Error(blk/P/SP),
                   data=dfm,
                   which='SSP'))
summary(ssp_sk3)

## From: aov
## Main factor: SSP
av3 <- with(SSPE,
            aov(y ~ blk + P*SP*SSP + Error(blk/P/SP),
                data=dfm))

ssp_sk4 <- SK(av3,
              which='SSP')
summary(ssp_sk4)

## Nested: p1/SP
## It is necessary to inform the appropriate error for the test
ssp_sk5 <- SK(av3,
              which='P:SP',
              error='blk:P:SP',
              fl1=1)
summary(ssp_sk5)

## Nested: p1/SSP
ssp_sk6 <- SK(av3,
              which='P:SSP',
              fl1=1)
summary(ssp_sk6)

## Nested: p1/sp1/SSP
## Testing SSP inside of level one of P and level one of SP
ssp_sk7 <- SK(av3,
              which='P:SP:SSP',
              fl1=1,
              fl2=1)
summary(ssp_sk7)

## Nested: p2/sp1/SSP
ssp_sk8 <- SK(av3,
              which='P:SP:SSP',
              fl1=2,
              fl2=1)
summary(ssp_sk8)

## Nested: sp1/P
## It is necessary to inform the appropriate error for the test
ssp_sk9 <- SK(av3,
              which='SP:P',
              error='blk:P:SP/blk:P',
              fl1=1)

summary(ssp_sk9)

## Nested: ssp1/SP
ssp_sk10 <- SK(av3,
               which='SSP:SP',
               error='Within/blk:P:SP',
               fl1=1)
summary(ssp_sk10)

## Nested: ssp1/sp1/P
## It is necessary to inform the appropriate error for the test
ssp_sk11 <- SK(av3,
               which='SSP:SP:P',
               error='Within/blk:P:SP/blk:P',
               fl1=1,
               fl2=1)
summary(ssp_sk11)

## UNBALANCED DATA
## The average are adjusted by "Least-Square-Means" methodology.
## From: formula
data(CRD2)

uCRD2 <- CRD2$dfm
uCRD2[c(3, 5, 10, 44, 45), 3] <- NA

usk1 <-  SK(y ~ x,
            data=uCRD2,
            which='x')
summary(usk1)

## From: lm
ulm1 <- lm(y ~ x,
           data=uCRD2)

usk2 <- SK(ulm1,
           which='x')
summary(usk2)

## Factorial Experiments
## Nested: p1/N
# From: lm

uFE <- FE$dfm
uFE[c(3, 6, 7, 20, 31, 32), 5] <- NA

ulm2 <- lm(y ~ blk + N*P*K,
           uFE)

## Nested: p1/N
usk3 <- SK(ulm2,
           data=uFE,
           which='P:N',
           fl1=1)
summary(usk3) 

## Nested: p2/n2/K
usk4 <- SK(ulm2,
           data=uFE,
           which='P:N:K',
           fl1=2,
           fl2=2)
summary(usk4) 

ScottKnott documentation built on Aug. 31, 2023, 1:06 a.m.