Soil characteristics were measured on samples from three types of contours (Top, Slope, and Depression) and at four depths (0-10cm, 10-30cm, 30-60cm, and 60-90cm). The area was divided into 4 blocks, in a randomized block design. (Suggested by Michael Friendly.)
SoilsA data frame with 48 observations on the following 14 variables. There are 3 factors and 9 response variables.
Groupa factor with 12 levels, corresponding to the combinations of Contour and Depth
Contoura factor with 3 levels: Depression Slope Top
Deptha factor with 4 levels: 0-10 10-30 30-60 60-90
Gpa factor with 12 levels, giving abbreviations for the groups:
D0 D1 D3 D6 S0 S1 S3 S6 T0 T1 T3 T6
Blocka factor with levels 1 2 3 4
pHsoil pH
Ntotal nitrogen in %
Densbulk density in gm/cm$^3$
Ptotal phosphorous in ppm
Cacalcium in me/100 gm.
Mgmagnesium in me/100 gm.
Kphosphorous in me/100 gm.
Nasodium in me/100 gm.
Conducconductivity
These data provide good examples of MANOVA and canonical discriminant analysis in a somewhat
complex multivariate setting. They may be treated as a one-way design (ignoring Block),
by using either Group or Gp as the factor, or a two-way randomized block
design using Block, Contour and Depth (quantitative, so orthogonal
polynomial contrasts are useful).
Khattree, R., and Naik, D. N. (2000) Multivariate Data Reduction and Discrimination with SAS Software. SAS Institute.
Friendly, M. (2006) Data ellipses, HE plots and reduced-rank displays for multivariate linear models: SAS software and examples. Journal of Statistical Software, 17(6), 10.18637/jss.v017.i06.