Many researchers have pointed out that contrasts should be “tested instead of, rather than as a supplement to, the ordinary ‘omnibus’ F test” (Hays, 1973, p. Because researchers typically have specific hypotheses about which condition means differ from each other, a priori contrasts (i.e., comparisons planned before the sample means are known) be- tween specific conditions or combinations of conditions are the appropriate way to represent such hypotheses in the statistical model. However, for effects with more than one numerator degrees of freedom, e.g., for experi- mental factors with more than two levels, the ANOVA omnibus F-test is not informative about the source of a main effect or interaction. MATLAB is primarily used in Chapter 16, which goes into detail on the use of MATLAB in matrix computations.Factorial experiments in research on memory, language, and in other areas are often analyzed using analysis of variance (ANOVA). Includes plentiful new illustrations depicting the importance of geometry as well as historical interludes.Contains more than 400 examples and exercises to reinforce understanding, along with select solutions.Analyzes multiresponse linear models where several responses can be of interest.Covers the analysis of balanced linear models using direct products of matrices.Contains new coverage on vector spaces and linear transformations and discusses computational aspects of matrices.The book is also appropriate as a reference for independent readers who use statistics and wish to improve their knowledge of matrix algebra. This is a textbook for advanced undergraduate and first-year graduate level courses in statistics and other related disciplines. Khuri, who has extensive research and teaching experience in the field, joins this edition as co-author. Featuring numerous applied illustrations, numerical examples, and exercises, the book has been updated to include the use of MATLAB for the execution of matrix computations. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained. Matrix Algebra Useful for Statistics addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole.
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