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# Kuehl+-+Chapter+14+Notes+-+Overheads+(06) - Split-Plot in a...

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1 Split-Plot in a RCBD Section 14.1-14.3 pp 469-477 Block 1 Block 2 N1 N2 N4 N3 N4 N1 N3 N2 N1T3 N2T2 N4T2 N3T1 N4T2 N1T2 N3T3 N2T1 N1T2 N2T3 N4T1 N3T2 N4T3 N1T1 N3T1 N2T3 N1T1 N2T1 N4T3 T3T3 T4T1 N1T3 N3T2 N2T2 Whole Plot Factor is N and Subplot Factor is T Experimental unit size differs for N and T so errors will differ. We assume: 1) a correlation ñ between on any two subplots in the same whole plot. 2) no correlation between observations from different whole plots.

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3 Very conservative approach Source df R F F EMS 2 4 3 i j k C i B 1 1 4 3 j N 3 2 0 3 (ij) BN 3 1 1 3 k T 2 2 4 0 ik BT 2 1 4 1 jk NT 6 2 0 0 (ijk) BTN 6 1 1 1 total 23

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4 The more common approach Source df R F F EMS 2 4 3 i j k C i B 1 1 4 3 j N 3 2 0 3 1(ij) e 3 1 1 3 k T 2 2 4 0 jk NT 6 2 0 0 2(ijk) e 8 1 1 1 total 23
5 df MS EMS Blocks r-1 MSB ----- N n-1 MSN Error 1 (b-1)(n-1) MSE(1) T t-1 MST NT (n-1)(t-1) MSNT Error 2 n(b-1)(t-1) MSE(2)

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6 This is the Penncross Creeping Bent Grass problem of Chapter 14. This is a split-plot in an RCBD with two reps. data a; do N = "Urea", "NH4SO4", "IBDU", "Urea_SC"; do B = 1,2; do T = 2,5,8; input Chlrphyl @@; output; end; end; end; cards; 3.8 5.3 5.9 3.9 5.4 4.3 5.2 5.6 5.4 6.0 6.1 6.2 6.0 5.6 7.8 7.0 6.4 7.8 6.8 8.6 8.5 7.9 8.6 8.4 ;;;;
7 Proc sort data=a; by N T; run; Proc means data=a mean noprint; var Chlrphyl; output out=junk mean=meanchl; by N T; run; Proc plot data=junk hpercent=20 vpercent=50; plot meanchl*T / vaxis=2 to 10 by 2; by N; run; Nitrogen=IBDU meanchl*Thatch. A=1, B=2, etc. meanchl ‚ 10 ˆ 8 ˆ A ‚A 6 ˆ A 4 ˆ 2 ˆ Šˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆ 2 5 8 Thatch Nitrogen=NH4SO4 meanchl*Thatch. A=1, B=2, etc. meanchl ‚ 10 ˆ 8 ˆ 6 ˆA A A 4 ˆ 2 ˆ Šˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆ 2 5 8 Thatch Nitrogen=Urea meanchl*Thatch. A=1, B=2, etc. meanchl ‚ 10 ˆ 8 ˆ 6 ˆ A A 4 ˆA 2 ˆ Šˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆ 2 5 8 Thatch Nitrogen=Urea_SC meanchl*Thatch. A=1, B=2, etc. meanchl ‚ 10 ˆ A 8 ˆ A ‚A 6 ˆ 4 ˆ 2 ˆ Šˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆ 2 5 8 Thatch

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8 Proc Mixed data=a; Class B N T; Model Chlrphyl = N T N*T / ddfm=sattterth; Random B B*N; run; Covariance Parameter Estimates Cov Parm Estimate B 0.007593 B*N 0.06824 Residual 0.2146 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F N 3 3 29.67 0.0099 T 2 8 8.89 0.0093 N*T 6 8 3.23 0.0646 So is this interaction significant?
9 If the interaction is ignored then we might do something like the following where we investigate the two main effects of Nitrogen and Thatch and ignore that interaction because it didn’t hit the sacred p<=.05 level. Proc Mixed data=a; Class B N T; Model Chlrphyl = N T N*T / ddfm=sattterth ; Random B B*N; contrast "T linear" T -1 0 1; contrast "T quad" T 1 -2 1; lsmeans N / pdiff adj=tukey; run;

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10 Contrasts Num Den Label DF DF F Value Pr > F T linear 1 8 17.27 0.0032 T quad 1 8 0.51 0.4940 Least Squares Means Standard Effect N Estimate Error DF t Value Pr > |t| N IBDU 6.7667 0.2714 3.97 24.93 <.0001 N NH4SO4 5.7500 0.2714 3.97 21.18 <.0001 N Urea 4.7667 0.2714 3.97 17.56 <.0001 N Urea_SC 8.1333 0.2714 3.97 29.96 <.0001 Differences of Least Squares Means Standard Effect N _N Estimate Error DF t Value Pr > |t| Adjustment
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• Spring '08
• Bullock,D
• Errors and residuals in statistics, Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bonferroni Bo, N*T N*T N*T

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