A multivariate extension of a univariate procedure for the analysis of experimental designs is presented. A Euclidean-distance permutation procedure is used to evaluate multivariate residuals obtained from a regression algorithm, also based on Euclidean distances. Applications include various completely randomized and randomized block experimental designs such as one-way, Latin square, factorial, nested, and split-plot designs, with and without covariates. Unlike parametric procedures, the only required assumption is the randomization of subjects to treatments.
References
1.
BerryK. J.MielkeP. W.Jr. (1998) Least absolute regression residuals: analyses of block designs. Psychological Reports, 83, 923–929.
2.
BerryK. J.MielkeP. W.Jr. (1999a) Least absolute regression residuals: analyses of randomized designs. Psychological Reports, 84, 947–954.
3.
BerryK. J.MielkeP. W.Jr. (1999b) Least absolute regression residuals: analyses of split-plot designs. Psychological Reports, 85, 445–453.
4.
CadeB. S.RichardsJ. D. (1996) Permutation tests for least absolute deviations regression. Biometrics, 52, 886–902.
5.
FreedmanD.LaneD. (1983) A nonstochastic interpretation of reported significance levels. Journal of Business & Economic Statistics, 1, 292–298.
6.
HarterS. (1985) Manual for the Self-perception Profile for Children.Denver, CO: Univer. of Denver.
7.
KaufmanE. H.TaylorG. D.MielkeP. W.BerryK. J. (2002) An algorithm and Fortran program for multivariate LAD (l1 of l2) regression. Computing, 68, 275–287.
8.
ManlyB. J. F. (1991) Randomization and Monte Carlo methods in biology.London: Chapman & Hall.
9.
MielkeP. W.Jr. (1987) L1, L2 and L3 regression models: is there a difference?Journal of Statistical Planning and Inference, 13, 430
10.
MielkeP. W.Jr.BerryK. J. (1997) Permutation covariate analyses of residuals based on Euclidean distance. Psychological Reports, 81, 795–802.
11.
MielkeP. W.Jr.BerryK. J. (2001) Permutation methods: a distance function approach.New York: Springer-Verlag.
