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.)
A data frame with 48 observations on the following 14 variables. There are 3 factors and 9 response variables.
a factor with 12 levels, corresponding to the combinations of
a factor with 3 levels:
a factor with 4 levels:
a factor with 12 levels, giving abbreviations for the groups:
a factor with levels
total nitrogen in %
bulk density in gm/cm$^3$
total phosphorous in ppm
calcium in me/100 gm.
magnesium in me/100 gm.
phosphorous in me/100 gm.
sodium in me/100 gm.
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
by using either
Gp as the factor, or a two-way randomized block
Depth (quantitative, so orthogonal
polynomial contrasts are useful).
Horton, I. F.,Russell, J. S., and Moore, A. W. (1968) Multivariate-covariance and canonical analysis: A method for selecting the most effective discriminators in a multivariate situation. Biometrics 24, 845–858. Originally from ‘http://www.stat.lsu.edu/faculty/moser/exst7037/soils.sas’ but no longer available there.
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), doi: 10.18637/jss.v017.i06.