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Chapter 7 Blocking and Confounding in the 2 k Factorial Design. 7.2 Blocking a Replicated 2 k Factorial Design. Blocking is a technique for dealing with controllable nuisance variables A 2 k factorial design with n replicates.
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Chapter 7 Blocking and Confounding in the 2k Factorial Design
7.2 Blocking a Replicated 2k Factorial Design • Blocking is a technique for dealing with controllable nuisance variables • A 2k factorial design with n replicates. • This is the same scenario discussed previously (Chapter 5, Section 5-6) • If there are n replicates of the design, then each replicate is a block • Each replicate is run in one of the blocks (time periods, batches of raw material, etc.) • Runs within the block are randomized
Consider the example from Section 6-2; k = 2 factors, n = 3 replicates This is the “usual” method for calculating a block sum of squares • Example 7.1
7.3 Confounding in the 2k Factorial Design • Confounding is a design technique for arranging a complete factorial experiment in blocks, where block size is smaller than the number of treatment combinations in one replicate. • Cause information about certain treatment effects to be indistinguishable from (confounded with) blocks. • Consider the construction and analysis of the 2k factorial design in 2p incomplete blocks with p < k
7.4 Confounding the 2k Factorial Design in Two Blocks • For example: Consider a 22 factorial design in 2 blocks. • Block 1: (1) and ab • Block 2: a and b • AB is confounded with blocks! • See Page 289 • How to construct such designs??
Defining contrast: • xi is the level of the ith factor appearing in a particular treatment combination • i is the exponent appearing on the ith factor in the effect to be confounded • Treatment combinations that produce the same value of L (mod 2) will be placed in the same block. • See Page 290 • Group: • Principal block
