By Richard Heiberger
Addresses the statistical, mathematical, and computational elements of the development of applications and research of variance (ANOVA) courses. encompasses a disk behind the publication that comprises all application codes in 4 languages, APL, simple, C, and FORTRAN. provides illustrations of the twin house geometry for all designs, together with confounded designs
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The additional research question to be answered is: Are the differences among Units of the same Brand large enough that we should compare differences among Brands to differences among Units within Brands and not just to differences of replications on one Unit representing its Brand? In this experiment only Brands are to be considered a fixed factor; that is, each represents a distinct manufacturer and model. 4. Tables of means for the crossed design. 92 the Brand made as a result of the experiment would be expected to hold for any Unit similarly manufactured.
In addition, we have gained some information on the behavior of the different Brands for the different Paragraphs. In the nested design example, we were able to compare the variability among Brands to the variability among Units within Brands instead of to the variability of multiple measurements of a single Unit. In this example, there are only 8 degrees of freedom in the Unit(Brand) residual. However, by taking two measurements on each Unit, it can be shown that we have increased both the precision with which the Brand means have been estimated and the power for the test of Brand differences over what they would have been with only one observation per Unit(Brand).
The usual interpretation of the p-value as a probability is not appropriate. Such an interpretation is based on an assumption of a null hypothesis about Typist speeds (that all Typists type equally fast), an assumption that contradicts the assumption of known differences that led us to block on Typists. 5 An Alternative Design Specification A different design specification that produces the same sums of squares in the ANOVA table is (in P-STAT notation) MODEL SPEED = TYPIST + BRAND ; BRAND ; or in SAS notation, MODEL SPEED = TYPIST This model specification statement is also a shorthand notation for an algebraic statement Speed, j = [k + Typist, + Brand, + e, v The difference between this statement and the one initially presented is that, here, both factors have been specified equivalently and the distinction in the role of the two factors has been suppressed.