agridat (version 1.27)

clewer.wheat: Randomized complete block design for wheat

Description

Randomized complete block design (RCBD) comparing three new wheat varieties against a standard variety.

Usage

data("clewer.wheat")

Format

A data frame with 12 observations on the following 5 variables.

row

Row in field, numeric

col

Column in field, numeric

block

Block factor, 3 levels

gen

Variety factor, 4 levels

yield

Yield, t/ha

Details

An experiment to compare three new wheat varieties (V2, V3, V4) with a standard variety (V1). The experimental area was divided into three blocks, each containing four plots of equal size. The blocks were positioned at right angles to a suspected fertility gradient.

This is Example 10.1 from Clewer and Scarisbrick (2001), Chapter 10, demonstrating the analysis of a randomized complete block design.

The book reports:

ANOVA results:

Source	DF	SS	MS	F
Block	2	9.78	4.89	12.22
Variety	3	6.63	2.21	5.52
Error	6	2.40	0.40
Total	11	18.81

Variety means (t/ha):

V1	6.50
V2	7.60
V3	6.60
V4	8.30

Grand mean: 7.25 t/ha.

Block means: B1=8.50, B2=6.85, B3=6.40 t/ha.

Data added by Paul Scmidt.

References

None

Examples

if (FALSE) {

library(agridat)
data(clewer.wheat)
dat <- clewer.wheat

# Field layout
libs(desplot)
desplot(dat, yield ~ col*row,
  out1 = block, text = gen, cex = 1,
  main = "clewer.wheat")

# Verify variety means
aggregate(yield ~ gen, data = dat, FUN = mean)
##   gen yield
## 1  V1  6.50
## 2  V2  7.60
## 3  V3  6.60
## 4  V4  8.30

# RCBD analysis
m1 <- aov(yield ~ block + gen, data = dat)
anova(m1)
## Response: yield
##           Df Sum Sq Mean Sq F value   Pr(>F)
## block      2  9.780  4.8900  12.225 0.007626 **
## gen        3  6.630  2.2100   5.525 0.036692 *
## Residuals  6  2.400  0.4000

# Matches book: Block SS=9.78, Variety SS=6.63, Error SS=2.40, MSE=0.40

# Compare ignoring blocks (CRD analysis)
m0 <- aov(yield ~ gen, data = dat)
anova(m0)
## Response: yield
##           Df  Sum Sq Mean Sq F value Pr(>F)
## gen        3  6.6300  2.2100  1.4517  0.297
## Residuals  8 12.1800  1.5225

# Matches book: Without blocking, VR=1.45, not significant
# Blocking reduced error variance from 1.52 to 0.40

}