Nonorthogonal analysis of variance has received considerable attention in recent years
resulting in numerous articles advocating a number of nonequivalent approaches. These
approaches are briefly summarized along with the arguments for and against each. It is
suggested that each technique is appropriate for certain situations, but that the
comprehensive strategy presented by Appelbaum and Cramer (1974) is perhaps best for
the majority of nonorthogonal analyses.
Get full access to this article
View all access options for this article.
References
1.
Appelbaum, M.I. and E.M. Cramer (1974). "Some problems in the nonorthogonal analysis of variance." Psych. Bull.81: 335-343.
2.
Bancroft, T.A. (1968) Topics in Intermediate Statistical Methods Volume 1. Ames: Iowa State Univ. Press .
3.
Carlson, J.E. and N.H. Timm (1974) "Analysis of nonorthogonal fixed-effects designs ." Psych. Bull.81: 563-570.
4.
Finn, J.D. (1974) A General Model for Multivariate Analysis. New York: Holt, Rinehart & Winston .
5.
——— (1972) Multivariance. Ann Arbor, MI : National Educational Resources.
6.
Gocka, E.F. (1973) "Regression analysis of proportional cell data ." Psych. Bull.80: 25-27.
7.
Humphreys, L.G. and A. Fleishman (1974) "Pseudo-orthogonal and other analysis of variance designs involving individual-difference variables." J. of Educ. Psychology66: 464-472.
8.
Joe, G.W. (1971) "Comment on Overall and Spiegel's 'Least squares analysis of experimental data.'" Psych. Bull.75: 364-366.
9.
Keren, G. and C. Lewis (1977) "A comment on coding in nonorthogonal designs." Psych. Bull.84: 346-348.
10.
——— (1976) "Nonorthogonal designs: Sample versus population ." Psych. Bull.83: 817-826.
11.
Lewis, C. and G. Keren (1977) "You can't have your cake and eat it too: considerations of the error term." Psych. Bull.84: 1150-1154.
O'Brien, R.G. (1976) "Comment on 'some problems in the nonorthogonal analysis of variance'." Psych. Bull.83: 72-74.
16.
Overall, J.E. and D.K. Spiegel (1973a) "Comment on 'Regression analysis of proportional cell data'." Psych. Bull.80: 28-30.
17.
——— (1973b) "Comments on Rawlings' nonorthogonal analysis of variance." Psych. Bull.79: 164-167.
18.
——— (1969) "Concerning least squares analysis of experimental data." Psych. Bull.72: 311-322.
19.
——— and J. COHEN (1975) "Equivalence of orthogonal and non-orthogonal analysis of variance." Psych. Bull.82: 182-186.
20.
Rawlings, R.R., Jr. (1973) "Comments on the Overall and Spiegel paper ." Psych. Bull.79: 168-169.
21.
——— (1972) "Note on nonorthogonal analysis of variance." Psych. Bull.77: 373-374.
22.
Rock, D.A. (1974) "Appropriate method for the least squares analysis of categorical data." Psych. Bull.81: 1012-1013.
23.
———, C.E. Werts and R.A. Linn (1976) "Structural equations as an aid in the interpretation of the nonorthogonal analysis of variance." Multivariate Behavioral Research11: 443-448.
24.
Smith, I.L. (1973) "Comment on Joe's 'Comment on Overall and Spiegel's "Least squares analysis of experimental data."'" Psych. Bull.79: 170-171.
25.
Steinhorst, R.K. and C.D. Miller (1969) "Disproportionality of cell frequencies in psychological and educational experiments involving multiple classification." Educ. and Psych. Measurement29: 799-811.
26.
Williams, J.D. (1972) "Two way fixed effects analysis of variance with disproportionate cell frequencies." Multivariate Behavioral Research7: 67-83.
27.
Winer, B.J. (1971) Statistical Principles in Experimental Design. New York: McGraw-Hill.
28.
Wolf, G. and B. Cartwright (1974) "Rules for coding dummy variables in multiple regression ." Psych. Bull.81: 173-179.
