Yields from Nitrogen nutrition of grass species

The data frame Grass gives the yield (10 * log10 dry-weight (g)) of eight grass Species in five replicates (Block) grown in sand culture at five levels of nitrogen.

Format

A data frame with 40 observations on the following 7 variables.

Species: a factor with levels B.media D.glomerata F.ovina F.rubra H.pubesens K.cristata L.perenne P.bertolonii
Block: a factor with levels 1 2 3 4 5
N1: species yield at 1 ppm Nitrogen
N9: species yield at 9 ppm Nitrogen
N27: species yield at 27 ppm Nitrogen
N81: species yield at 81 ppm Nitrogen
N243: species yield at 243 ppm Nitrogen

Source

Gittins, R. (1985), Canonical Analysis: A Review with Applications in Ecology, Berlin: Springer-Verlag, Table A-5.

Details

Nitrogen (NaNO3) levels were chosen to vary from what was expected to be from critically low to almost toxic. The amount of Nitrogen can be considered on a log3 scale, with levels 0, 2, 3, 4, 5. Gittins (1985, Ch. 11) treats these as equally spaced for the purpose of testing polynomial trends in Nitrogen level.

The data are also not truly multivariate, but rather a split-plot experimental design. For the purpose of exposition, he regards Species as the experimental unit, so that correlations among the responses refer to a composite representative of a species rather than to an individual exemplar.

Examples


str(Grass)
#> 'data.frame':	40 obs. of  7 variables:
#>  $ Species: Factor w/ 8 levels "B.media","D.glomerata",..: 7 7 7 7 7 2 2 2 2 2 ...
#>  $ Block  : Factor w/ 5 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 4 5 ...
#>  $ N1     : num  1.013 0.945 1.045 0.987 0.826 ...
#>  $ N9     : num  1.71 1.58 1.48 1.46 1.34 ...
#>  $ N27    : num  1.64 1.53 1.62 1.55 1.49 ...
#>  $ N81    : num  2.08 2.07 1.73 2.07 1.89 ...
#>  $ N243   : num  1.96 2.12 2.09 2.21 1.95 ...
grass.mod <- lm(cbind(N1,N9,N27,N81,N243) ~ Block + Species, data=Grass)
car::Anova(grass.mod)
#> 
#> Type II MANOVA Tests: Pillai test statistic
#>         Df test stat approx F num Df den Df   Pr(>F)    
#> Block    4   0.90834   1.5865     20    108  0.06902 .  
#> Species  7   2.03696   2.7498     35    140 1.49e-05 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

grass.canL <-candiscList(grass.mod)
names(grass.canL)
#> [1] "Block"   "Species"
names(grass.canL$Species)
#>  [1] "dfh"         "dfe"         "eigenvalues" "canrsq"      "pct"        
#>  [6] "rank"        "ndim"        "means"       "factors"     "term"       
#> [11] "terms"       "coeffs.raw"  "coeffs.std"  "structure"   "scores"