Question

# The calculations for a factorial experiment involving four levels of factor A, three levels of factor...

The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST= 248, SSA= 22, SSB= 21, SSAB= 155.

Set up the ANOVA table and test for significance using alpha= .05 . Show entries to 2 decimals, if necessary. If the answer is zero enter “0”.

 Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Factor A Factor B Interaction Error Total

Level of factor A, a = 4

Level of factor B,b = 3

Replications, r = 3

 Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Factor A 22 a-1 = 3 22/3 = 7.3333 7.333/2.0833 = 3.52 F.DIST.RT(3.52, 3, 24) = 0.0303 Factor B 21 b-1 = 2 21/2 = 10.5 10.5/2.0833 = 5.04 F.DIST.RT(5.04, 2, 24) = 0.0149 Interaction 155 (a-1)*(b-1) = 6 155/6 = 25.8333 25.8333/2.0833 = 12.4 F.DIST.RT(12.4, 6, 24) = 0.0000 Error 248 -22-21-155 = 50 ab(r-1) = 24 50/24 = 2.0833 Total 248 abr -1 = 35

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