26 SPSS UPDATE /-9 The first DESIGN specification reguests an analysis of variance for this experiment (Figure 1.26b). | Figure 1.26b TESTS OF SIGNIFICANCE FOR DEP USING SEOUENTIAL SUMS OF SOUARES SOURCE OF VARIATION . SUM OF SOUARES DF MEAN SOUARE F SIG. OF F RESIDUAL 8909.36190 43 207. 19446 CONSTANT 461120.05556 l 461120.05556 2225 .54237 0.0 REPLICS 3836.61111 3 1278.87037 6.17232 -001 BLOCKS WITHIN REPLICS 2836 .33333 8 354.54167 1.71115 123 A 1116.02778 2 558.01389 2.69319 079 B 253.69444 2 126.84722 61221 B47 boj 868 .05556 l 868.05556 4. 18957 047 A BY B ž 1129.34921 4 282.33730 1.36267 265 A BY C 2995.02778 2 1497.51389 7.22758 -002 B BY C 423.52778 2 2l1.76389 i1.02205 - 36B A BY B BY C 1015.95556 4 253. 98889 1.22585 -314 The second and third analyses give the AB and AC two-way means adjusted for the block effects (Figure 1.26c). For more information about the use of CONSPLUS to obtain marginal means and summary tables, see Section 1.50. Figure 1.26c O a o O NOE IONE CONSPLUS A AND B PARAMETER COEFF. STD. ERR. T-VALVE SIG. OF T LOWER .95 CL UPPER .95 CL l2 72.1964285714 6.02764 11.97757 0.0 60.10109 B4..29176 13 713.2261904762 6.02764 12.14841 0.0 61.13086 . 85.32152 l4 79.7023809524 6.02764 13.22283 0.0 67.60705 91.79771 15 86 ..7738095238 6.02764 14.39600 0.0 74 .6784B 98.86914 16 87.8035714286 6.02764 14.56684 0.0 75 .70824 99.89891 17 79.4226190476 6.02764 13.17641 0.0 67 .32729 91.51795 18 89.0297619048 6.02764 14.77026 0.0 716.93445 101.12510 19 T4.3452380952 6.02764 12.33406 0.0 62.24990 86 .44057 20 77.7500000000 6.02764 12.89892 0.0 65 .65467 89. 84533 CONSPLUS A AND C PARAMETER COEFF. STD. ERR. T-VALJE SIG. OF T LOWER .95 CL UPPER .95 CL 12 62.5833333333 4.2161l 14.84385 0.0 54. 13406 71.03261 13 87.5000000000 4.2161l 20.75372 0.0 79.05073 95 .94927 la 84.3333333333 4.21611 20.00264 0.0 75..88406 92.7826l 15 85..0000000000 4.21611 20.16076 0.0 716.55073 93 .44927 l6 82.7500000000 4.2161l 19.62709 0.0 7T4.30073 91.19927 17 78.0000000000 4.21611l 18,50046 0.0 69.55073 B6 . 44927 OM AE AA ČE a O NE EN RA | 1.27 Split-plot Designs In many factorial designs, it may not be possible to completely randomize the assignment of treatments to the experimental unit. Consider, for example, an experiment to compare three varieties of wheat (factor A) and two different types of fertilizer (factor B). Three locations are selected as blocks. Three levels of A are randomly assigned to plots of egual area within each block. After A is assigned, each plot is "split" into halves (called subplots) to receive the random assignment of B. What is the difference between a complete 3 x 2 factorial and the 3 x 2 split-plot design? In a 3 x 2 factorial, each block is divided into six subplots to receive the random assignment of treatment combinations of A and B. In the split-plot design, two treatment combinations that have the same level of A are always in the same plot. If the subplot is considered the experimental unit, the plot is a "small" block of size 2. The differences among these "small" blocks are the differences between levels of A, since the main effects of A are confounded. A split-plot design is a design in which certain main effects are confounded. Intuitively, the variation of plots within A should be used as the error term to test for the main effects of A. The effects of plot within A can be partitioned into two parts. One is the block effects and another is the block and A interaction. Thus the model for a split-plot design is Yječ uta; t Be t (aB)a vj t (yi €je where a, is the A effect, B, is the block effect, (aB). is the interaction of A and block and is the error term for testing A, »; is the B effect, (ay);; is the AB interaction, and e;;, is the residual used as the error term for testing B and AB. Another model is Via 5 poto t Be t (aB)a t yi t (ami t (Brje bt (aBy)ije t ega