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Growth of Apple Trees from Different Root Stocks

Source: R/datasets.R
RootStock.Rd

In a classic experiment carried out from 1918 to 1934, growth of apple trees of six different rootstocks were compared on four measures of size.

Format

A data frame with 48 observations on the following 5 variables.

rootstock

a factor with levels 1 2 3 4 5 6

girth4

a numeric vector: trunk girth at 4 years (mm x 100)

ext4

a numeric vector: extension growth at 4 years (m)

girth15

a numeric vector: trunk girth at 15 years (mm x 100)

weight15

a numeric vector: weight of tree above ground at 15 years (lb x 1000)

Source

Andrews, D. and Herzberg, A. (1985). Data: A Collection of Problems from Many Fields for the Student and Research Worker Springer-Verlag, pp. 357--360.

Details

This is a balanced, one-way MANOVA design, with n=8 trees for each rootstock.

References

Rencher, A. C. (1995). Methods of Multivariate Analysis. New York: Wiley, Table 6.2

Examples


library(car)
data(RootStock)
## maybe str(RootStock) ; plot(RootStock) ...
root.mod <- lm(cbind(girth4, ext4, girth15, weight15) ~ rootstock, data=RootStock)
car::Anova(root.mod)
#> 
#> Type II MANOVA Tests: Pillai test statistic
#>           Df test stat approx F num Df den Df    Pr(>F)    
#> rootstock  5    1.3055   4.0697     20    168 1.983e-07 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

pairs(root.mod)


# test two orthogonal contrasts among the rootstocks
hyp <- matrix(c(2,-1,-1,-1,-1,2,  1, 0,0,0,0,-1), 2, 6, byrow=TRUE)
car::linearHypothesis(root.mod, hyp)
#> 
#> Sum of squares and products for the hypothesis:
#>            girth4      ext4   girth15 weight15
#> girth4   2.684223  7.573365  7.792122 1.617892
#> ext4     7.573365 22.489458 23.293194 5.760003
#> girth15  7.792122 23.293194 24.145778 6.090615
#> weight15 1.617892  5.760003  6.090615 2.248755
#> 
#> Sum of squares and products for error:
#>             girth4      ext4   girth15 weight15
#> girth4   0.3199875  1.696564 0.5540875 0.217140
#> ext4     1.6965637 12.142790 4.3636125 2.110214
#> girth15  0.5540875  4.363612 4.2908125 2.481656
#> weight15 0.2171400  2.110214 2.4816562 1.722525
#> 
#> Multivariate Tests: 
#>                  Df test stat  approx F num Df den Df     Pr(>F)    
#> Pillai            2  1.426293  24.86102      8     80 < 2.22e-16 ***
#> Wilks             2  0.020401  58.51245      8     78 < 2.22e-16 ***
#> Hotelling-Lawley  2 26.121884 124.07895      8     76 < 2.22e-16 ***
#> Roy               2 25.254884 252.54884      4     40 < 2.22e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
heplot(root.mod, hypotheses=list(Contrasts=hyp, C1=hyp[1,], C2=hyp[2,]))


heplot1d(root.mod, hypotheses=list(Contrasts=hyp, C1=hyp[1,], C2=hyp[2,]))