Rice fractional factorial experiment 1/2 2^6. — gomez.fractionalfactorial • agridat

Rice fractional factorial experiment 1/2 2^6. 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

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

# \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")


# Split treatment into individual factors
dat <- transform(dat,
                 a = -1 + 2 * grepl('a',trt),
                  b = -1 + 2 * grepl('b',trt),
                 c = -1 + 2 * grepl('c',trt),
                 d = -1 + 2 * grepl('d',trt),
                 e = -1 + 2 * grepl('e',trt),
                 f = -1 + 2 * grepl('f',trt))

# 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)
#> Analysis of Variance Table
#> 
#> Response: yield
#>           Df  Sum Sq Mean Sq F value  Pr(>F)    
#> rep        1  0.0564 0.05641  6.0982 0.01944 *  
#> block      1  0.0039 0.00391  0.4223 0.52073    
#> trt       31 12.0815 0.38973 42.1346 < 2e-16 ***
#> Residuals 30  0.2775 0.00925                    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Gomez table 4.24, trt SS split apart
m1 <- lm(yield ~ rep * block + (a+b+c+d+e+f)^3, dat)
anova(m1)
#> Analysis of Variance Table
#> 
#> Response: yield
#>           Df Sum Sq Mean Sq  F value    Pr(>F)    
#> rep        1 0.0564  0.0564   6.0982 0.0194445 *  
#> block      1 0.0039  0.0039   0.4223 0.5207290    
#> a          1 3.0016  3.0016 324.5072 < 2.2e-16 ***
#> b          1 0.5776  0.5776  62.4461 8.075e-09 ***
#> c          1 2.0022  2.0022 216.4665 2.928e-15 ***
#> d          1 3.2041  3.2041 346.4048 < 2.2e-16 ***
#> e          1 0.5041  0.5041  54.4998 3.175e-08 ***
#> f          1 1.7623  1.7623 190.5228 1.565e-14 ***
#> rep:block  1 0.0039  0.0039   0.4223 0.5207290    
#> a:b        1 0.0342  0.0342   3.7002 0.0639421 .  
#> a:c        1 0.0132  0.0132   1.4298 0.2411643    
#> a:d        1 0.0016  0.0016   0.1730 0.6804364    
#> a:e        1 0.0001  0.0001   0.0108 0.9178793    
#> a:f        1 0.0410  0.0410   4.4333 0.0437219 *  
#> b:c        1 0.0352  0.0352   3.8008 0.0606285 .  
#> b:d        1 0.0410  0.0410   4.4333 0.0437219 *  
#> b:e        1 0.0138  0.0138   1.4926 0.2313218    
#> b:f        1 0.0042  0.0042   0.4568 0.5043110    
#> c:d        1 0.3570  0.3570  38.5970 7.707e-07 ***
#> c:e        1 0.0116  0.0116   1.2494 0.2725423    
#> c:f        1 0.0030  0.0030   0.3270 0.5716668    
#> d:e        1 0.1388  0.1388  15.0014 0.0005404 ***
#> d:f        1 0.0400  0.0400   4.3245 0.0462114 *  
#> e:f        1 0.0529  0.0529   5.7192 0.0232535 *  
#> a:b:d      1 0.0046  0.0046   0.4926 0.4881840    
#> a:b:e      1 0.0039  0.0039   0.4223 0.5207290    
#> a:b:f      1 0.0240  0.0240   2.5974 0.1175108    
#> a:c:d      1 0.0915  0.0915   9.8930 0.0037271 ** 
#> a:c:e      1 0.0176  0.0176   1.8981 0.1784872    
#> a:c:f      1 0.0009  0.0009   0.0973 0.7572498    
#> a:d:e      1 0.0495  0.0495   5.3523 0.0277314 *  
#> a:d:f      1 0.0462  0.0462   4.9975 0.0329765 *  
#> a:e:f      1 0.0000  0.0000   0.0027 0.9588823    
#> Residuals 30 0.2775  0.0092                       
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

libs(FrF2)
aliases(m1)
#>                           
#>  rep:block = a:b:c = d:e:f
#>  a:b:d = c:e:f            
#>  a:b:e = c:d:f            
#>  a:b:f = c:d:e            
#>  a:c:d = b:e:f            
#>  a:c:e = b:d:f            
#>  a:c:f = b:d:e            
#>  a:d:e = b:c:f            
#>  a:d:f = b:c:e            
#>  a:e:f = b:c:d            
MEPlot(m1, select=3:8,
       main="gomez.fractionalfactorial - main effects plot")

# }