By Richard Heiberger
Addresses the statistical, mathematical, and computational points of the development of applications and research of variance (ANOVA) courses. features a disk behind the publication that includes all software 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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There are three natural extensions of the one-way design to incorporate a second factor: the blocked design, the crossed design, and the nested design. 3, the second factor, the blocking factor, is assumed to have an effect on the level of the response variable. There is consequently no need to test for such an effect. The blocking factor is included in the design and the analysis because its use improves the sensitivity of the design to the effect of the treatment factor. 4, the two factors are to be investigated symmetrically for their effect on the level of the response variable.
Together these four define a complete replication of a one-factor experiment within a single Typist, although with one replication per Typist instead of six replications per Typist. The second four observations are the same with a prefix 2. for the second Typist. The entire experiment consists of six copies of the one-way experiment. The randomization, the decision as to which Brand is used first, is made independently for each Typist. This blocked design is the natural generalization to 4 Brands of the pairedcomparison i-test for two Brands.
The variability of the estimates of the effects for both factors is compared to the same underlying variability. 5, the second or nested factor participates in the measurement of the underlying variability, but it is assumed not to have an effect on the level of the response variable. 2 THE ONE-WAY DESIGN The simplest experimental design is the one-way design. One factor, with k levels, is to be studied. For example, let us consider computer keyboard Brands as the factor and let the levels be k = 4 different Brands.
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