42 OMIS 1000 C - Lecture 9 - Randomized Blocking &amp; Two-Way ANOVA

# 42 OMIS 1000 C- - Blocking&TwoWayANOVA Sections112and113 BlockDesign Terminology (Textsterminology (Excelsterminology Other Blockdesign 3

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Block Design
3 Terminology Randomized Complete Block ANOVA  (Text’s terminology)  Two-way ANOVA without replication  (Excel’s terminology) Other: Randomized Block Design Block design

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4 The Logic of  Blocking Remember the matched pairs test: We removed any variability introduced  by the subjects by keeping them  constant for both treatments E.g. the  same person  got their blood  pressure measured by the physician and  then by the machine
5 The Logic of  Blocking  (cont’d) We do exactly the same thing in  ANOVA but with more than 2 treatments The matched pairs test can be viewed  as a randomized block design with only  two treatments

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6 Example Three fertilizers are applied to 20 plots  of land to test the impact on crop yields We want to test for variation between  fertilizers,  but We could have variation between the  plots
Treatment 2 Treatment 1 Example (cont’d) Plot Fertilizer A Fertilizer B Fertilizer C 1 563 588 575 2 593 624 593 3 542 576 564 4 649 672 653 5 565 583 556 6 587 612 590 7 595 617 607 8 429 446 423 9 500 515 483 10 610 641 626 11 524 547 523 12 559 586 568 13 546 582 551 14 503 530 502 15 550 573 567 16 492 518 495 17 497 529 513 18 619 643 626 19 473 497 479 20 533 556 540 Block 1 Treatment 3 Block 2 Block 3 Etc…

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8 Example (cont’d) Since we want to control for differences  that may exist between plots of land (i.e.  blocks), we carry out a block design  ANOVA Thus the first row (block) is represents the  three different fertilizers in plot #1, the  second, plot #2, etc. Notice the similarity to Matched Pairs  Design
9 The Logic of Blocking (cont’d) Block design ANOVA consists of  two tests: 1. Testing the  blocks (or rows) : H O : All block means are equal  H A : At least two block means differ 1. Testing the  treatments (or columns) : H O : All treatment means are equal  H A At least two treatment means are not  equal

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10 Back to Our Example  1. Blocks or Rows (Plots): H O :   μ BL1 = μ BL2 = μ BL3 =…= μ BL18 = μ BL29 = μ BL20 H A At least two block means are not equal Rejection region: F .01,19,38  = 2.42 (Excel) 2. Columns (Fertilizers): H O :   μ 1 = μ 2 = μ 3 H A At least one is not equal Rejection region: F .01,2,38  = 5.21 (Excel) Assume  α  = 0.01
11 The Logic of Blocking (cont’d) The calculations for the block means  test are  exactly the same  as the  calculations for treatment means Only, they are done  horizontally  and  not

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## This note was uploaded on 09/25/2010 for the course OMIS OMIS 1000 taught by Professor Alexandershoumarov during the Fall '09 term at York University.

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42 OMIS 1000 C- - Blocking&TwoWayANOVA Sections112and113 BlockDesign Terminology (Textsterminology (Excelsterminology Other Blockdesign 3

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