Randomized complete block design for wheat

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.

Source

Clewer, Alan G. and Scarisbrick, David H. (2001). Practical Statistics and Experimental Design for Plant and Crop Science. Wiley, New York. Example 10.1, Table 10.1, page 135.

References

None

Examples

if (FALSE) { # \dontrun{

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

} # }