EXST7015 Fall2011 Appendix 13

EXST7015 Fall2011 Appendix 13 - Statistical Techniques II...

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Unformatted text preview: Statistical Techniques II Design Layouts Appendix 13 Supplement Page 252 Schematic layouts of some CRD experiments. 1) CRD: Treatment levels are t=5 where each treatment occurs in 3 cells (experimental units : n=3) and each cell is sampled once. CRD with experimental error. Model Source Treatments Error Yij = iij Expected Mean Squares 2 n 2 2) CRD: Treatment levels are t=5 where each A B D E B Yijk = iijijk Expected Mean Squares 2 nnd 2 n 2 treatment occurs in 3 cells (experimental units : d=3) and each cell is sampled twice (sampling units : n=2). CRD with both experimental error and sampling error. Model Source Treatment Experimental Error Sampling Error A B D E B A B D E B A C A D E A C A D E 3) CRD?: Treatment levels=5; each treatment occurs in one cell (experimental unit) and each cell is sampled three times. CRD with no experimental error, this experiment has sampling error only (Pseudo-replication). Model Source Treatments Sampling Error A C A D E C A D E B D B E C C D B E C C C A D E B D B E C C C A D E B Yijk = iijk Expected Mean Squares 2 nn 2 James P. Geaghan - Copyright 2011 Statistical Techniques II Design Layouts Appendix 13 Supplement Page 253 Schematic layouts of some RBD experiments. 4) RBD: Three blocks (b=3) and five treatment levels (t=5) where each block has 5 cells (experimental units) and each treatment occurs once in each block and each is sampled once. RBD with experimental error only Block 1 C A D E B Block 2 B C A D E Block 3 D B E A C Block 1 C C A A D D E E B B Yijk = ijijijk Expected Mean Squares 2 nnb 2 nnt 2 n 2 Block 2 B B C C A A D D E E Block 3 D D B B E E A A C C Model Yij = ijij Source Expected Mean Squares Treatment 2b 2 Block t 2 Error 5) RBD: Three blocks (b=3) and five treatment levels (t=5) where each block has 5 cells, and each treatment occurs once in each block and each cell is sampled twice (n=2). In this case the residual error term measures only within cell variation. Model Source Treatment Block Block*Treatment Error 6) RBD: Blocks=3, Treatment levels=5; each block has 10 cells and each treatment occurs twice in each block. Each cell (treatment by block and within block replicate combination) is sampled once. In this case the residual error term measures between cell variation. Model Source Treatment Block Block*Treatment Error Block 1 D C A E A E B C D B Yijk = ijijijk Expected Mean Squares 2 nnb 2 nnt 2 n 2 Block 2 A E B A E C C D B D Block 3 C A D B A E D B E C James P. Geaghan - Copyright 2011 Statistical Techniques II Design Layouts Appendix 13 Supplement Page 254 Layouts of some other experiments. E2 | E1 7) CRD Split-plot : Main plot treatment levels are A2 | A1 t1=5, sub-plot treatment levels t2=2 where each D1 | D2 main plot treatment occurs in d=3 cells E2 | E1 (experimental units) and each cell is subdivided into A1 | A2 two parts (d=2) for one application of each level of the sub-plot treatment. Model Yijk = + 1i ij2k12ikijk Source Expected Mean Squares 2 2 2 2 Treatment nd n ndt2 2 B2 C1 B1 D2 E2 | | | | | B1 C2 B2 D1 E1 D1 B1 C2 A1 C1 | | | | | D2 B2 C1 A2 C2 2 Error a t2 SubPlot Treatment Interaction n nt1 2 2 n Error b 2 2 2 2 8) RBD: Blocks=3, Treatment Levels=5; each block has 10 cells and each treatment occurs twice in each block. Each cell (treatment by block combination) is sampled twice. Block D D A A A A B B D D C E E C B C E E C B Block A A B B E E C C B B E A C D D E A C D D Block C C D D A A D D E E A B E B C A B E B C Yijk = ijijijijl Expected Mean Squares 2 2 2 2 n ns nsb 2 2 2 2 n ns nst Model Source Treatment Block Treatment*Block Rep(Treatment*Block) Error 2 2 2 n ns 2 2 n 2 9) Latin Square Design (LSD): Three rows (r=3) C B A and three columns (c=3) for three treatment levels B A C (t=3) where each treatment occurs in each row and B A C column. Experimental units are row by column combination cells. There could also be several separate squares (blocks) and several sampling units within cells for Latin Square Designs. Model Yijk = ijkijk Source Row Expected Mean Squares Column Treatment Error 2 r 2 r 2 r 2 James P. Geaghan - Copyright 2011 ...
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This note was uploaded on 12/29/2011 for the course EXST 7015 taught by Professor Wang,j during the Fall '08 term at LSU.

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