随机区组设计又叫完全随机区组设计，通过使用区组的方法较少误差变异，通过区组方法分离出由无关变量引起的变异，使其不出现在处理效应和误差的变异中。

例如：水稻参试品种有A-F五种，重复4次，采用随机区组设计，产量结果录入，数据如下：

数据见附件“one_way_anova_analyses.csv”

数据录入：

> library(reshape);library( agricolae )

> df<- read.table(file='one_way_anova_analyses.txt',header=T,sep='\t')

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

> colnames(df.2)[2:3]<-c("Rep","y") #命名列

方差分析

> lmaov<-aov(y~Variety+Rep,data=df.2) #模型

> summary(lmaov)

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

Variety 552.38 10.47678.764 3.17e-10 ***

Rep 32.68 0.893 6.7170.00431 **

Residuals 15 2.000.133

---

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

> anova.tab(lmaov) #方差格式整理

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

Variety 552.38 10.47678.764 3.17e-10 ***

Rep 32.68 0.893 6.7170.00431 **

Residuals 15 2.000.133

Total 2357.05

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

由方差分析可知，品种间和区组间均达到极显著水平，说明区组设计合理，降低了实验误差，提高了精确度。下面对品种进行多重比较。

多重比较

> LSD.test(lmaov,"Variety",group=F,console=T)

Study: lmaov ~ "Variety"

LSD t Test for y

Mean Square Error:0.133

Variety,means and individual ( 95 %)CI

y std r LCL UCLMin Max

A 15.650 0.6557439 4 15.26134 16.03866 14.916.2

B 18.125 0.4272002 4 17.73634 18.51366 17.618.6

C 17.450 0.5744563 4 17.06134 17.83866 16.617.8

D 17.200 0.5830952 4 16.81134 17.58866 16.417.8

E 13.800 0.1825742 4 13.41134 14.18866 13.614.0

F 17.575 0.4924429 4 17.18634 17.96366 17.018.2

alpha: 0.05 ; Df Error: 15

Critical Value of t: 2.13145

Comparison between treatments means

Difference pvalue sig. LCL UCL

A - B -2.475 8.553878e-08 *** -3.0246495533 -1.9253504

A - C -1.800 4.424801e-06 *** -2.3496495533 -1.2503504

A - D -1.550 2.386356e-05 *** -2.0996495533 -1.0003504

A - E 1.8503.207722e-06***1.30035044672.3996496

A - F -1.925 1.998570e-06 *** -2.4746495533 -1.3753504

B - C 0.6751.940896e-02 *0.12535044671.2246496

B - D 0.9252.696626e-03 **0.37535044671.4746496

B - E 4.3253.975797e-11***3.77535044674.8746496

B - F 0.550 4.987171e-02 *0.00035044671.0996496

C - D 0.2503.476899e-01 -0.29964955330.7996496

C - E 3.6504.392580e-10***3.10035044674.1996496

C - F -0.125 6.348707e-01 -0.67464955330.4246496

D - E 3.4001.181753e-09***2.85035044673.9496496

D - F -0.375 1.664982e-01 -0.92464955330.1746496

E - F -3.775 2.737184e-10 *** -4.3246495533 -3.2253504

多重比较的结果如上表所示，B品种产量最高，显著高于其他品种。A品种和其他品种相比也达到极显著水平。