By Richard Heiberger
Addresses the statistical, mathematical, and computational points of the development of programs and research of variance (ANOVA) courses. incorporates a disk in the back of the ebook that comprises all application codes in 4 languages, APL, simple, C, and FORTRAN. provides illustrations of the twin area geometry for all designs, together with confounded designs
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Extra info for Computation For The Analysis of Designed Experiments
4. 92 36 2 SIMPLE DESIGNED EXPERIMENTS or, equivalently, with the nesting operator / expanded: MODEL SPEED = BRAND + UNIT(BRAND) ; or in SAS (without the repeated measure statement): MODEL SPEED = BRAND UNIT(BRAND) ; In the alternative model, no distinction in role is made between the two effects BRAND a n d UNIT(BRAND). This model specification statement is a shorthand notation for the algebraic statement Speed i j j k = /i + Brand, + (Unit(Brand)), 4- e y i J t k Note that the specification of both the main effect term, Brand,, and the nesting term, (Unit(Brand)), , , in the algebraic statement is implied by the nesting operator / in the design specification.
1 says that the observation is to be made on the third Brand and this will be the first observation made on that Brand. The assignment of order to the observations on a specific Brand is in this case arbitrary. We assume there is no learning effect. 1. Field plan for one-way design. Table entry is observation number indexed by Brand and Replication within Brand. 2. Speeds (in wpm) of an experienced typist for typing a sample paragraph (simulated data for one-way design). 92 unrelated to observation 1 on any other Brand.
In the first analysis, we do a one-way ANOVA for Typist. 2 THE ONE-WAY DESIGN same speed we would have a small MS for Typist compared to the residual MS. If some are fast and others slow, we would have a large MS for Typist and hence a large value for the F-ratio of Typist MS against residual MS. This large F-ratio would reflect the known differences among the Typists. It would not, in any sense, be a test; there is no null hypothesis of equality of Typists. In the second analysis of the same null experiment we do a one-way ANOVA for Brand.
Computation For The Analysis of Designed Experiments by Richard Heiberger