Programming Univariate and Multivariate Analysis of Variance

Methods and Problems in the Analysis of Multivariate Data

“…In such a case, the SEX effect would be determined as before but the DRUG-within-SEX effect would correspond to a coalescing of what before were the DRUG and SEX × DRUG sources of variation. The term "interaction" has no meaning for exclusively nested designs; general effects for hierarchical factors after the first may always be obtained com putationally by a pooling of what, for factorial designs, would be main effects and certain interactions (see Bock, 1963). Design textbooks like Winer's (1962) should be studied for further details relating to interpreta tions of nested designs.…”

“…However, Bock (1963) presented a more elegant procedure to deal with the case where whole-vectors are missing. His approach can be explained with reference to Equations 4 and 12.…”

“…His approach can be explained with reference to Equations 4 and 12. Given that D s 2 is a × diagonal matrix of "cell" frequencies, Bock (1963) performed an exact analysis based on…”

Probability Estimation of Dichotomous Response Patterns by Logistic Fractional-Factorial Representation

“…e is a vector of random components with mean vector 0 and variance-covariance matrix I. The model matrix W can he specified by an n-fold Kronecker product of a 2 x2 basis matrix (Bock, 1963), for instance, as follows, where the operator "x" indicates Kronecker product, and c is a scalar constant. Since the scale unit c is absorbed in the values of fi, the value of c does not affect the results of the present study.…”

CANCOR: A general least-squares program for univariate and multivariate analysis of variance and covariance

“…There are general least-squares programs capable of reduced-model tests [e.g., SAS's GLM (Barr et al, 1976); Bock, 1965;BMDX63/11V (Dixon, 1973);Finn, 1972;Woodward & Overall, 1974]. These are not labeled as canonical correlation programs, since they work with sums of squares and cross-products (SP) matrices, rather than with correlation matrices; the procedures are nevertheless equivalent.…”