# ssp.plot: Split-split-Plot analysis In agricolae: Statistical Procedures for Agricultural Research

## Description

The variance analysis of a split-split plot design is divided into three parts: the main-plot, subplot and sub-subplot analysis.

## Usage

 `1` ```ssp.plot(block, pplot, splot, ssplot, Y) ```

## Arguments

 `block` replications `pplot` Factor main plot `splot` Factor subplot `ssplot` Factor sub-subplot `Y` Variable, response

## Details

The split-split-plot design is an extension of the split-plot design to accommodate a third factor: one factor in main-plot, other in subplot and the third factor in sub-subplot

## Value

ANOVA: Splip Split plot analysis

## Author(s)

Felipe de Mendiburu

## References

Statistical procedures for agricultural research. Kwanchai A. Gomez, Arturo A. Gomez. Second Edition. 1984.

`sp.plot`, `strip.plot`, `design.split`, `design.strip `

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```# Statistical procedures for agricultural research, pag 143 # Grain Yields of Three Rice Varieties Grown under #Three Management practices and Five Nitrogen levels; in a #split-split-plot design with nitrogen as main-plot, #management practice as subplot, and variety as sub-subplot #factores, with three replications. library(agricolae) f <- system.file("external/ssp.csv", package="agricolae") ssp<-read.csv(f) model<-with(ssp,ssp.plot(block,nitrogen,management,variety,yield)) gla<-model\$gl.a; glb<-model\$gl.b; glc<-model\$gl.c Ea<-model\$Ea; Eb<-model\$Eb; Ec<-model\$Ec par(mfrow=c(1,3),cex=0.6) out1<-with(ssp,LSD.test(yield,nitrogen,gla,Ea,console=TRUE)) out2<-with(ssp,LSD.test(yield,management,glb,Eb,console=TRUE)) out3<-with(ssp,LSD.test(yield,variety,glc,Ec,console=TRUE)) plot(out1,xlab="Nitrogen",las=1,variation="IQR") plot(out2,xlab="Management",variation="IQR") plot(out3,xlab="Variety",variation="IQR") # with aov AOV<-aov(yield ~ block + nitrogen*management*variety + Error(block/nitrogen/management),data=ssp) summary(AOV) ```

### Example output

```ANALYSIS SPLIT-SPLIT PLOT:  yield
Class level information

nitrogen 	:  0 50 80 110 140
management 	:  m1 m2 m3
variety 	:  1 2 3
block 	:  1 2 3

Number of observations:  135

Analysis of Variance Table

Response: yield
Df  Sum Sq Mean Sq  F value    Pr(>F)
block                        2   0.732   0.366   0.6578  0.543910
nitrogen                     4  61.641  15.410  27.6953 9.734e-05 ***
Ea                           8   4.451   0.556
management                   2  42.936  21.468  81.9965 2.303e-10 ***
nitrogen:management          8   1.103   0.138   0.5266  0.822648
Eb                          20   5.236   0.262
variety                      2 206.013 103.007 207.8667 < 2.2e-16 ***
variety:nitrogen             8  14.145   1.768   3.5679  0.001916 **
variety:management           4   3.852   0.963   1.9432  0.114899
variety:nitrogen:management 16   3.699   0.231   0.4666  0.953759
Ec                          60  29.732   0.496
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cv(a) = 11.4 %, cv(b) = 7.8 %, cv(c) = 10.7 %, Mean = 6.554415

Study: yield ~ nitrogen

LSD t Test for yield

Mean Square Error:  0.5564188

nitrogen,  means and individual ( 95 %) CI

yield      std  r      LCL      UCL   Min    Max
0   5.384704 1.206963 27 5.053665 5.715743 3.320  8.020
50  6.220333 1.615861 27 5.889294 6.551372 3.188  9.942
80  6.995741 1.371302 27 6.664702 7.326780 4.422  9.320
110 6.937370 1.474547 27 6.606331 7.268409 4.246  9.660
140 7.233926 1.968153 27 6.902887 7.564965 3.132 10.360

Alpha: 0.05 ; DF Error: 8
Critical Value of t: 2.306004

least Significant Difference: 0.4681598

Treatments with the same letter are not significantly different.

yield groups
140 7.233926      a
80  6.995741      a
110 6.937370      a
50  6.220333      b
0   5.384704      c

Study: yield ~ management

LSD t Test for yield

Mean Square Error:  0.2618167

management,  means and individual ( 95 %) CI

yield      std  r      LCL      UCL   Min    Max
m1 5.900378 1.486531 45 5.741267 6.059488 3.132  9.314
m2 6.486156 1.621936 45 6.327045 6.645266 3.625  9.680
m3 7.276711 1.635020 45 7.117601 7.435822 4.225 10.360

Alpha: 0.05 ; DF Error: 20
Critical Value of t: 2.085963

least Significant Difference: 0.2250164

Treatments with the same letter are not significantly different.

yield groups
m3 7.276711      a
m2 6.486156      b
m1 5.900378      c

Study: yield ~ variety

LSD t Test for yield

Mean Square Error:  0.4955415

variety,  means and individual ( 95 %) CI

yield      std  r      LCL      UCL   Min    Max
1 5.126822 0.971530 45 4.916915 5.336730 3.132  7.309
2 6.396133 1.065752 45 6.186226 6.606041 4.166  8.950
3 8.140289 1.314438 45 7.930381 8.350197 5.244 10.360

Alpha: 0.05 ; DF Error: 60
Critical Value of t: 2.000298

least Significant Difference: 0.2968543

Treatments with the same letter are not significantly different.

yield groups
3 8.140289      a
2 6.396133      b
1 5.126822      c

Error: block
Df  Sum Sq Mean Sq
block  1 0.07891 0.07891

Error: block:nitrogen
Df Sum Sq Mean Sq
nitrogen  1  52.13   52.13

Error: block:nitrogen:management
Df Sum Sq Mean Sq
management  2  30.57   15.28

Error: Within
Df Sum Sq Mean Sq F value   Pr(>F)
nitrogen                      1   4.44    4.44   9.124  0.00309 **
management                    2  12.93    6.46  13.292 6.16e-06 ***
variety                       1 204.32  204.32 420.120  < 2e-16 ***
nitrogen:management           2   0.71    0.36   0.731  0.48341
nitrogen:variety              1   9.22    9.22  18.957 2.85e-05 ***
management:variety            2   0.43    0.21   0.440  0.64531
nitrogen:management:variety   2   0.84    0.42   0.867  0.42278
Residuals                   119  57.87    0.49
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

agricolae documentation built on Sept. 13, 2017, 1:03 a.m.