HW7_sol - 4.18 4.18 B1B2=1234*2345=15 So the interaction 15...

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Unformatted text preview: 4.18 4.18 B1B2=1234*2345=15. So the interaction 15 is confounded with the block effect The main effect 5 will not be B1B2 and the ability to estimate 15 is sacrificed. affected. 4.19. (a) b1 : B1 = 123, B2 = 456, B3 = 167 B1 B2 = 123456, B1 B3 = 2367, B2 B3 = 1457, B1 B2 B3 = 23457 g (b1 ) = (0,0,3,2,1,1,0) . Order of estimability=2. (b) From Table 4A.1, g (b2 ) = (0,0,0,7,0,0,0) . Order of estimability=3. (c) In the second scheme all the 3 factor interactions are estimable, whereas in the first scheme the interactions 123, 456, and 167 are confounded with block effects. 4.21. (a) Code the blocking variable as (-1,-1,1,1,-1,1,-1,1). The correlations of the blocking variable with the 7 columns are, 1 0 2 0.5 3 0.5 12 -0.5 13 0.5 23 0 123 0 Because the correlation coefficients are neither 1 nor –1, the blocking variable is not identical to any of the columns and therefore is not confounded with any of the factorial effects. (b) From the correlations we see that, the blocking variable is not orthogonal to the columns 2,3,12, and 13. These effects are therefore partially aliased with the blocking variable. In this blocking scheme two of the main effects are partially aliased with the blocking variable, which is undesirable. (c) No. They should be orthogonal to the effects of interest. 5.14. (a) The defining words are 134, 235, and 1245. The resolution is III. (b) The two factor interactions 23, 12 and 24 can be estimated. ...
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This note was uploaded on 04/26/2011 for the course STATS 424 taught by Professor Peterqian during the Spring '11 term at University of Wisconsin.

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