The partially complete ANOVA table given here is for a two-factor factorial expe

Question

The partially complete ANOVA table given here is for a two-factor factorial experiment Source Df MS factor A 3 2.25 0.75 Factor B 0.95 Interaction 3 0.30 2.40 0.15 error total 23 6.50 The number of degrees of freedom for the error term is equal to The Sum of Squares for the interaction is equal to The Sum of Squares for the treatments is equal to The number of degrees of freedom for the treatments is equal to The Mean of Squares for factor B is equal to The F-test for interaction effect is equal to The rejection region at alpha 0.01 for the test of significance of the interaction is equal to

Explanation / Answer

a) As the total degrees of freedom is 23, therefore the degrees of freedom for error term would be computed as:

= 23 - (3 +1 + 3) = 16

Therefore the degrees of freedom for the error term here are 16

b) The sum of square for the interaction term would be computed as:

= 6.5 - 2.25 - 0.95 - 2.4

= 0.9

Therefore the sum of the square of the interaction term here would be 0.9

c) The sum of squares for the treatment is equal to

= 0.9 + 2.25 + 0.95

= 4.1

Therefore the sum of squares for the treatment is equal to 4.1 here.

d) The number of degrees of freedom for treatments is equal to

= 3 + 1 + 3

= 7

Therefore the degrees of freedom for the treatment terms here is 7

e) The mean square error term for factor B is computed as:

SSB / DFB

= 0.95 / 1

= 0.95

Therefore 0.95 is the required value here.

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