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	An object of class formula, lm, aov, aovlist, or lmerMod. Objects of the formula class follow “response variable ~ predictor variables”.
data	An object of class data.frame. Used only when the input is of class formula.
which	The name of the treatment factor to be compared. Must be quoted.
fl1	An integer of length 1 selecting the level of the first nesting factor.
fl2	An integer of length 1 selecting the level of the second nesting factor.
error	The error term to be used. For split-plot and split-split-plot experiments, see Details.
sig.level	Significance level used in the SK algorithm to form the groups of means. Default is 0.05.
round	Integer indicating the number of decimal places. Default is 2.
...	Potential further arguments (required by generic).

Details

The function SK returns an object of class SK containing the groups of means and the variables needed by summary and plot.

The error argument may be used whenever a specific error term other than the residual is required. In split-plot and split-split-plot experiments, error terms may be combined using / in the order implied by the which argument. For example, for an aovlist object from a block split-plot experiment, a valid combination would be error = 'Within/blk:plot' with which = 'subplot:plot'.

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)

Faria, J. C. ([e-mail])
Jelihovschi, E. G. ([e-mail])
Allaman, I. B. ([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='ScottKnott')
##

## Input classes accepted: formula, aov, lm, aovlist, and lmerMod.

data(RCBD)

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

## From: lmerMod
## This class requires 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='ScottKnott')
##

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='ScottKnott')
##

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: lmerMod
## 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 in Time (SPET)
## More details: demo(package='ScottKnott')
##
data(SPET)

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

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

## Nested: year1/tra
## It is necessary to set the year error with the treatment error,
## in the order of the which argument.
## It is necessary to specify how to combine the error terms.
sp_sk2 <-  SK(lm3,
              which='year:tra',
              error='Residuals/blk:tra',
              fl1=1)
summary(sp_sk2)

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

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

    ## Nested: 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='ScottKnott')
##

data(SSPE)
## From: formula
## Main factor: P
## It is necessary to specify the appropriate error term 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 specify the appropriate error term 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 specify the appropriate error term 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 within 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 specify the appropriate error term 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 specify the appropriate error term 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
## Means are adjusted using the Least-Squares Means (LSMeans) 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 May 24, 2026, 5:06 p.m.