FACTORIAL DESIGNS Two Factor Factorial Designs

4 FACTORIAL Factor FACTORIAL DESIGNS Atwo- Factor factorialdesign is an experimental design in which data is collected for all possiblecombinations of the levels of the two factors of interest. If equal sample sizes are taken for each of the possible Factor combinations then the design is abalanced two- Factor factorialdesign. A balanceda bfactorial design is a FACTORIAL design for which there arealevels of factorA,blevelsof factorB, andnindependent replications taken at each of thea btreatment combinations. Thedesign size isN=abn. The effect of a Factor is defined to be the average change in the response associated with a change inthe level of the Factor . This is usually called amain effect. If the average change in response across the levels of one Factor are not the same at all levels of theother Factor , then we say there is aninteractionbetween the (ifnij=n)Cell(i,j)yij = nijk=1yijkyij =yij /nij=yij /nithlevel ofAyi = bj=1 nijk=1yijkyi =yi / bj=1nij=yi /bnjthlevel ofBy j = ai=1 nijk=1yijky j =y j / ai=1nij=y j /anOverally = ai=1 bj=1 nijk=1yijky =y / ai=1 bj=1nij=y /abnwherenijis the number of observations in cell (i,j).

4 FACTORIAL DESIGNS 4.1 Two Factor Factorial Designs A two-factor factorial design is an experimental design in which data is collected for all possible combinations of the levels of the two factors of interest.

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  Design, Factors, Factorial designs two factor factorial designs, Factorial, Factorial designs, Two factor factorial designs, Factor factorial

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