Question

Consider a​ two-way ANOVA with two levels for factor​ A, four levels for factor​ B, and four replicates in each of the 88 ​cells, with SSA=25, SSB=30, SSE=120, and SST=280. Complete parts​ (a) through​ (d).

a) Form the ANOVA summary table and fill in all values in the body of the table.

b) At the 0.01 level of​ significance, is there an effect due to factor​ A?

c) At the 0.01 level of​ significance, is there an effect due to factor​ B?

d) At the 0.01 level of​ significance, is there an interaction​ effect?

Answer 1

a)

Source	SS	df	MS	F	p vlaue
Factor A	25	1	25.00	5.71	0.0250
Factor B	30	3	10.00	2.29	0.1044
Interaction	120	3	40.00	9.14	0.0003
error	105	24	4.38
total	280	31

b)

as p value for factor A is higher than 0.01 ; effect due to factor​ A is not significant.

c)

as p value for factor B is higher than 0.01 ; effect due to factor​ B is not significant.

d)

as p value for interaction is lower than 0.01 ; effect due to interaction is significant.