【例3.3.1.2】玉米品种A有4个水平，分别是A1-A4，施肥B有两个水平，分别是B1-B2，重复三次，采用随机区组，数据如下：

数据见附件：

数据录入：

> library(reshape);library(agricolae)

>df<-read.table(file="r3.3.1.2.csv",header=T,sep=",")

> df.2<-melt(df,id=c("A","B"))

> colnames(df.2)[3:4]<-c("Blk","y")

方差分析

> duncan.model<-aov(y~A*B+Blk,data=df.2)

> summary(duncan.model) # show ANOVA table

Df Sum Sq Mean Sq F value Pr(>F)

A 398.79 32.9315.199 0.000111 ***

B 177.04 77.0435.558 3.47e-05 ***

Blk 2 20.33 10.17 4.692 0.027567 *

A:B 3136.46 45.4920.994 1.90e-05 ***

Residuals 1430.33 2.17

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Signif. codes:0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> anova.tab(duncan.model) #方差格式整理

Df Sum Sq Mean Sq F value Pr(>F)

A 3 98.8 32.9315.199 0.000111 ***

B 1 77.0 77.0435.558 3.47e-05 ***

Blk 220.3 10.17 4.692 0.027567 *

A:B 3 136.5 45.4920.994 1.90e-05 ***

Residuals 14 30.3 2.17

Total 23363.0

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Signif. codes:0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

由方差分析表可知A、B、AB互作均达到极显著水平，区组达到显著水平，下面进行多重比较。

多重比较

> duncan.test(duncan.model,"A",alpha=0.05,console=T) #对A因素进行多重比较

Study: duncan.model ~ "A"

Duncan's new multiple range test

for y

Mean Square Error:2.166667

A,means

y std r Min Max

A1 12.00000 1.264911 61013

A2 17.16667 2.926887 61220

A3 13.00000 5.291503 6 719

A4 12.66667 3.829708 6 817

alpha: 0.05 ; Df Error: 14

Critical Range

2 3 4

1.822718 1.909920 1.963738

Means with the same letter are notsignificantly different.

Groups, Treatments and means

a A2 17.17

b A3 13

b A4 12.67

b A1 12

由上表可知，A2水平和其他水平相比差异显著，处理效果最好。

> duncan.test(duncan.model,"B",alpha=0.05,console=T) #对B因素进行多重比较

Study: duncan.model ~ "B"

Duncan's new multiple range test

for y

Mean Square Error:2.166667

B,means

y stdr Min Max

B1 15.50000 2.540580 121219

B2 11.91667 4.420167 12 720

alpha: 0.05 ; Df Error: 14

Critical Range

2

1.288856

Means with the same letter are notsignificantly different.

Groups, Treatments and means

a B1 15.5

b B2 11.92

由上表可知，B1和B2相比较，差异显著。

> with(df.2, duncan.test(y, A:B, DFerror = 14, MSerror =2.17,console=T)) #对AB进行多重比较

Study: y ~ A:B

Duncan's new multiple range test

for y

Mean Square Error:2.17

A:B,means

y std r Min Max

A1:B1 12.666667 0.5773503 312 13

A1:B2 11.333333 1.5275252 310 13

A2:B1 15.666667 3.5118846 312 19

A2:B2 18.666667 1.5275252 317 20

A3:B1 17.666667 1.5275252 316 19

A3:B28.333333 1.5275252 3 7 10

A4:B1 16.000000 1.0000000 315 17

A4:B29.333333 1.5275252 3 8 11

alpha: 0.05 ; Df Error: 14

Critical Range

2 3 4 5 6 7 8

2.579695 2.703112 2.779281 2.8307672.867363 2.894153 2.914097

Means with the same letter are notsignificantly different.

Groups, Treatments and means

a A2:B2 18.67

ab A3:B1 17.67

ab A4:B1 16

b A2:B1 15.67

c A1:B1 12.67

cd A1:B2 11.33

de A4:B2 9.333

e A3:B2 8.333

有互作的多重比较可知，A2:B2互作效果最好，显著高于A2:B1、A1:B1、A1:B2、A4:B2、A3:B2。