Question

13.7 (9e) Describing a two-way ANOVA model. A 3 x 3 ANOVA was run with four observations per cell.

a) Give the degrees of freedom for the F statistic that is used to test for interaction in this analysis and the entries from Table E (F- distribution table that was provided earlier) that correspond to this distribution.

b) Sketch a picture of this distribution with the information from the table included.

c. ) The calculated value of this F statistic is 3.03.  Report the P-value and state your conclusion.

d.) Based on your answer to part (c), would you expect an interaction plot to have mean profiles that look parallel? Explain your answer.

Answer 1

a)

degree of freedom of numerator =(levels for factor A-1)*(levels for factor B-1)=(3-1)*(3-1)=4

degree of freedom of denominator =(levels for factor A)*(levels for factor B)*(replication-1)

=3*3*(4-1)=27

b)

from excel: p value =fdist(3.03,4,27)= 0.0347

since p value is less than 0.05 ,we reject null hypothesis

d) since interaction is signficant ( p value <0.05) , we do not expect n interaction plot to have mean profiles that look parallel