Fractional factorial of rice, 1/2 2^6 = 2x2x2x2x2x2

Fractional factorial of rice, 1/2 2^6 = 2x2x2x2x2x2. Two reps with 2 blocks in each rep.

Format

A data frame with 64 observations on the following 6 variables.

yield

grain yield in tons/ha

rep

replicate, 2 levels

block

block within rep, 2 levels

trt

treatment, levels (1) to abcdef

col

column position in the field

row

row position in the field

a

a treatment, 2 levels

b

b treatment, 2 levels

c

c treatment, 2 levels

d

d treatment, 2 levels

e

e treatment, 2 levels

f

f treatment, 2 levels

Details

Grain yield from a 2^6 fractional factorial experiment in blocks of 16 plots each, with two replications.

Gomez has some inconsistencies. One example:

Page 171: treatment (1) in rep 1, block 2 and rep 2, block 1.

Page 172: treatment (1) in Rep 1, block 1 and rep 2, block 1.

This data uses the layout shown on page 171.

Used with permission of Kwanchai Gomez.

Source

Gomez, K.A. and Gomez, A.A.. 1984, Statistical Procedures for Agricultural Research. Wiley-Interscience. Page 171-172.

Examples

if (FALSE) { # \dontrun{

library(agridat)
data(gomez.fractionalfactorial)
dat <- gomez.fractionalfactorial

# trt abcdef has the highest yield
# Gomez, Figure 4.8
libs(desplot)
desplot(dat, yield~col*row,
        # aspect unknown
        text=trt, shorten="none", show.key=FALSE, cex=1,
        main="gomez.fractionalfactorial - treatment & yield")


  # Ensure factors
  dat <- transform(dat,
                   a=factor(a), b=factor(b), c=factor(c),
                   d=factor(d), e=factor(e), f=factor(f) )
  
# Gomez table 4.24, trt SS totalled together.
# Why didn't Gomez nest block within rep?
m0 <- lm(yield ~ rep * block + trt, dat)
anova(m0)

# Gomez table 4.24, trt SS split apart
m1 <- lm(yield ~ rep * block + (a+b+c+d+e+f)^3, dat)
anova(m1)

libs(FrF2)
aliases(m1)
MEPlot(m1, select=3:8,
       main="gomez.fractionalfactorial - main effects plot")

} # }