Confounding In Two Blocks and How to Assign.pptx

Confounding In Two Blocks and How to Assign.pptx

• 1.
  CONFOUNDING IN TWO BLOCKSAND HOW TO ASSIGN TREATMENTS IN TWO BLOCKS SYEDA IQRAAHMAD 2023-phD-1029 Physiology
• 2.
  CONFOUNDING IN BLOCKS Confounding is a design technique for arranging a complete factorial experiment in blocks, where the block size is smaller than the number of treatment combinations in one replicate.  When block effect and the treatment interaction are identical. That is, confounded with blocks.
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  IMPORTANCE  This approachcan be used to confound any effect A, B, or AB interaction with blocks.  When a block effect is completely confounded with a main effect or an interaction effect, calculation of the two effects, as well as the sum of squares, are identical.
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  The common blockingmethod for 2k designs is to confound blocks with certain high order interactions. 2, 4, 8, . . . blocks from an non replicated 2k design.
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   If thereare replicates of the design, then each replicate is a block  Within each block, all treatments (level combinations) are conducted.  Run order in each block must be randomized. Analysis follows general block factorial design  Confounding makes the effect Inestimable
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  2 2 FACTORIALDESIGN WITH TWO BLOCKS Treatment A B AB Block (1) -1 -1 1 1 a 1 -1 -1 2 b -1 1 -1 2 ab 1 1 1 1 AB Effect =1/2 [ ab + (1) - a - b] Effect of A= ½ [ab + a – b – 1 ] Effect of B = 1/2[ab + b - a - 1]
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   In ourexample each block is be composed of two treatments. In this case it is the AB effect that we will use to determine our blocks. As you can see in the table above we have used the high level of AB to denote Block 1, and the low-level of AB to denote Block 2. This determines our design.
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  Block 1 2 AB+ - (1) a ab b This design confounds blocks with the AB interaction. You can see this by these contrasts - the comparison between block 1 and Block 2 is the same comparison as the AB contrast. Note that the A effect and the B effect are orthogonal to the AB effect.
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   Suppose thereare two factors (A, B) each with 2 levels, and two blocks (b1, b2) each containing two runs (treatments). Since b1 and b2 are interchangeable, there are three possible blocking scheme.
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  BLOCKING A B RESPONSE (Y) 12 - - - - b1 b1 b1 - + - + b1 b2 b2 + + + + b2 b2 b1 + - + - b2 b1 b2 B A + - - +
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  COMPARING BLOCKING SCHEMES: Scheme;1 Block Effect: b = y1 – y2 = ½ [( -y- - ) - (y+-) +(y-+) -(y+ +)] Main effect of B= ½ (- y-- - y+- + y-+ - y++) B and b are not distinguishable, or, confounded. Scheme; 2 Main effect of A= ½ (-y-- + y+- - y-+ + y ++) A and b are not distinguishable, or, confounded.
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  Scheme; 3 Interaction AB=1/2(y-- -y+- -y-+ + y++) 1/2[ab + (1) - a - b] AB and b become indistinguishable, or confounded.