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### rcbd

Course: STAT 850, Fall 2009
School: Wisconsin
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Word Count: 443

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Statistics 850 Clayton February 19, 2004 &lt;a href=&quot;/keyword/randomized-complete-block-design/&quot; &gt;&lt;a href=&quot;/keyword/randomized-complete-block/&quot; &gt;randomized complete block&lt;/a&gt; design&lt;/a&gt; Model Yij = + i + j + where i = 1, . . . , k j = 1, . . . , b eij N (0, 2 ) ij indexes treatment indexes block corresponds to plot error...

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Statistics 850 Clayton February 19, 2004 <a href="/keyword/randomized-complete-block-design/" ><a href="/keyword/randomized-complete-block/" >randomized complete block</a> design</a> Model Yij = + i + j + where i = 1, . . . , k j = 1, . . . , b eij N (0, 2 ) ij indexes treatment indexes block corresponds to plot error ANOVA Table Source Blocks Treatment Error Total df b-1 k-1 (k - 1)(b - 1) kb - 1 SS k j (Y j - Y )2 i - Y )2 b i (Y 2 j (Yij - Yi - Y j + Y ) 2 (Yij - Y ) i j i MS MSBlk MSTrt MSErr E(MS) 2 + k 2 + b 2 2 j /(b - 1) 2 i i /(k - 1) j Notes: The word &quot;complete&quot; in the name &quot;<a href="/keyword/randomized-complete-block-design/" ><a href="/keyword/randomized-complete-block/" >randomized complete block</a> design</a> &quot; means that every treatment appears at least once in each block. This is different from the meaning in &quot;completely randomized design&quot; where the word &quot;completely&quot; refers to the fact that the design is randomized as much as possible, subject to the constraint that each treatment must show up a prescribed number of times. In proc glm we fit this model with a term like model y = trt blk; . RCB with Subsampling Model Yijl = + i + j + where i = 1, . . . , k j = 1, . . . , b l = 1, . . . , s 2 ij N (0, ) 2 ijl N (0, ) ij + ijl indexes treatment indexes block indexes subsample (within each plot) corresponds to plot error corresponds to subsample error ANOVA Table Source Blocks Treatment Plot Error Subsampling Error Total df b-1 k-1 (k - 1)(b - 1) kb(s - 1) kbs - 1 SS ks j (Y j - Y )2 i - Y )2 bs i (Y 2 j (Yij - Yi - Y j + Y ) ij - Yijl )2 i j l (Y SSTot MS MSBlk MSTrt MSPE MSSSE E(MS) 2 + s 2 + ks 2 + s 2 + bs 2 + s 2 2 2 j /(b - 1) 2 i i /(k - 1) j s i 1 Statistics 850 Clayton February 19, 2004 A Comment on SAS for This Design The correct error term for testing treatments is the &quot;interaction&quot; blk*trt, which correctly captures the variability from plot to plot. Typical SAS commands for this model might look like: proc glm; classes trt blk; model y=blk trt blk*trt; test h=trt e=blk*trt; Lati...

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Wisconsin - STAT - 850
Statistics 850ClaytonMarch 11, 2004Analyzing One-Way Unbalanced Designs in SAS and RSAS Codeoptions ls=78 ps=54; data a; input a y ; datalines; 1 2 1 3 2 9 2 7 2 8 3 6 ; proc glmmod; class a; model y = a; proc glm; class a; model y = a/soluti
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Mich Tech - CS - 4811
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Temperature (*C) 2/13/03 12:39 2/13/03 12:54 2/13/03 13:09 2/13/03 13:24 2/13/03 13:39 2/13/03 13:54 2/13/03 14:09 2/13/03 14:24 2/13/03 14:39 2/13/03 14:54 2/13/03 15:09 2/13/03 15:24 2/13/03 15:39 2/13/03 15:54 2/13/03 16:09 2/13/03 16:24 2/13/03 1
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Idaho - SOIL - 205
1
Idaho - SOIL - 205
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Idaho - SOIL - 205
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Idaho - SOIL - 205
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Idaho - SOIL - 205
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Idaho - SOIL - 205
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Idaho - SOIL - 205
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East Los Angeles College - PAS - 402
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East Los Angeles College - PAS - 402
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East Los Angeles College - PAS - 402
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University of Illinois, Urbana Champaign - IB - 109
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