Computation For The Analysis of Designed Experiments by Richard Heiberger

By Richard Heiberger

Addresses the statistical, mathematical, and computational points of the development of applications and research of variance (ANOVA) courses. contains a disk behind the booklet that comprises all software codes in 4 languages, APL, easy, C, and FORTRAN. offers illustrations of the twin house geometry for all designs, together with confounded designs

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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 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. 1 and by not calling it observation 1. 4 on blocked and crossed designs. 2. For ease of presentation, the table has been made more compact than the field plan.

2 Suppression of Redundant Notation Why suppress redundant notation? There are two important reasons. First, the redundant notation provides visual clutter, but provides no information. The symbol "Brand" never appears without the subscript i. This becomes clearer as the design become more complex. 18) the algebraic statement Y I J F K = B + VJ + (BV)JJ T + D + (VD) K m + e j i t t k must be scanned by the human reader at least twice, once to see which terms are in it and once to identify the associated subscripts.

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