25anova_Factorial

# 25anova_Factorial - Statistical Techniques I EXST7005...

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Statistical Techniques I EXST7005 Factorial Treatments & Interactions

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Also known as "two-way" ANOVA This analysis has two (or more) Treatments, for example treatment A with two levels (a1 and a2) and treatment B with two levels (b1 and b2). Each level of one treatment occurs with each leve of the other treatment (cross-classified) e.g. a1b1, a1b2, a2b1, a2b2 Each treatment may be fixed or random (independently) The Factorial Treatment Arrangement
The Factorial Treatment Arrangement (continued) Combinations of treatments are assigned at random to experimental units, so the design is still a CRD (there are 4 combinations in the example given (a1b1, a1b2, a2b1, a2b2) The treatment arrangement is called a "factoria and the dimensions are usually given as 2 by 2 (above), 2 by 3, 3 by 3, etc.

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Schematic of a 3 by 3 factorial Treatments A1 A2 A3 B1 a1b1 a2b1 a3b1 B2 a1b2 a2b2 a3b2 B3 a1b3 a2b3
Marginal sums or means Treatments A1 A2 A3 Sum B1 a1b1 a2b1 a3b1 b1 sum B2 a1b2 a2b2 a3b2 b2 sum B3 a1b3 a2b3 a3b3 b3 sum Sum a1 sum a2 sum a3 sum

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The principle treatments (A and B in the previou examples) are called main effects. The main effect for treatment A will be calculate from the marginal of that treatment, averaged across the B treatment. Likewise, the main effect of treatment B will be
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## This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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25anova_Factorial - Statistical Techniques I EXST7005...

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