gomez.fractionalfactorial.Rd
Rice fractional factorial experiment 1/2 2^6. Two reps with 2 blocks in each rep.
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
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.
Gomez, K.A. and Gomez, A.A.. 1984, Statistical Procedures for Agricultural Research. Wiley-Interscience. Page 171-172.
# \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#> #> 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:dMEPlot(m1, select=3:8, main="gomez.fractionalfactorial - main effects plot")# }