Nothing
### a. The whole plot column space is defined by the
### plots %in% blocks
### dummy variables generated by the
## alternate residuals formula: orthogonal contrasts are critical
data(yatesppl)
yatesppl.resida.aov <- aov(y ~ blocks/plots,
data=yatesppl, x=TRUE,
contrasts=list(blocks=contr.helmert,
plots=contr.helmert))
summary(yatesppl.resida.aov)
t(yatesppl.resida.aov$x)
###
### b. This is the same column space defined by the
### variety + blocks:variety
### dummy variables generated by the
## computational shortcut
yatesppl.short.aov <-
aov(terms(y ~ blocks + variety + blocks*variety +
nitrogen + variety*nitrogen,
keep.order=TRUE), ## try it without keep.order=TRUE
data=yatesppl, x=TRUE)
summary(yatesppl.short.aov)
t(yatesppl.short.aov$x)
###
### c. We illustrate this by regressing the response variable y on
### the variety + blocks:variety dummy variables
## project y onto blocks/plots dummy variables
plots.aov <- lm(y ~ yatesppl.resida.aov$x[,7:18], data=yatesppl)
summary.aov(plots.aov)
y.bp <- predict(plots.aov)
variety.aov <- aov(y.bp ~ blocks*variety, data=yatesppl)
summary(variety.aov)
### and seeing that we reproduce the plots %in% blocks
### stratum of the ANOVA table
### Error: plots %in% blocks
### Df Sum of Sq Mean Sq F Value Pr(F)
### variety 2 1786.361 893.1806 1.48534 0.2723869
### Residuals 10 6013.306 601.3306
### obtained from the complete five-factor specification.
###
## split plot analysis
yatesppl.anova <- aov(y ~ variety*nitrogen +
Error(blocks/plots/subplots),
data=yatesppl)
summary(yatesppl.anova)
###
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