Question

onsider the following partially completed two-way ANOVA table. Suppose there are 2 levels of Factor A and 3 levels of Factor B. The number of replications per cell is 3. Use the 0.01 significance level. (Hint: estimate the values from the F table.)

1. Complete an ANOVA table. (Round MS and F to 2 decimal places.)

SS df MS F

Factor A 100(SS)

Factor B 30(SS)

interaction 250(SS)

Error 200(SS)

Total 580(SS)

1. Find the critical values to test for equal means. (Round your answers to 2 decimal places.)
2. Determine if there is a significant difference in Factor A means, Factor B means.

4. Determine if there is a significant difference in interaction means.

Answer 1

1.

Source	SS	df	MS	F
Factor A	100	2-1=1	100	100/(200/12)=6.00
Factor B	30	3-1=2	30/2=15	15/(200/12)=0.90
Interaction	250	(2-1)(3-1)=2	250/2=125	125/(200/12)=7.50
Error	200	17-5=12	200/12=16.67
Total	580	2*3*3-1=17

2. Critical value for Factor A=F_0.01,1,12=9.33, Critical value for Factor B=F_0.01,2,12=6.93, Critical value for Interaction=F_0.01,2,12=6.93.

3. Since Value of F corresponding to factor A<Critical value for Factor A hence effect of Factor A is insignificant.

Since Value of F corresponding to factor B<Critical value for Factor B hence effect of Factor B is insignificant.

4. Since Value of F corresponding to interaction>Critical value for interaction hence interaction effect is significant.

Note that since interaction effect is significantly present so it is irrelevant that whether the main effects A and B are present or absent.