Monday, November 26 Factorial Design Two-Way ANOVA.

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Monday, November 26 Factorial Design Two-Way ANOVA

The factorial design is used to study the relationship of two or more independent variables (called factors) to a dependent variable, where each factor has two or more levels. - p. 244

In this design, you can evaluate the main effects of each factor independently (essentially equivalent to doing one- way ANOVA’s for each of the factors independently), but you are also able to evaluate how the two (or more factors) interact.

TOTAL VARIATION Variation within groups (error) Variation between groups Variation from Factor 1 Variation from Factor 2 Variation from Factor 1 x 2 interaction Partitioning variation in a 2x2 factorial design.

1.ACompute SS T B. Compute SS B C.Subtract SS B from SS T to obtain SS W (error) D.Compute SS 1 E.Compute SS 2 F.Compute SS 1x2 by subtracting SS 1 and SS 2 from SS B 2.Convert SS to MS by dividing SS by the appropriate d.f. 3.Test MS 1,MS 2 and MS 1x2 using F ratio.