Question

A researcher conducts a two-way ANOVA test with interaction and provides the following ANOVA table.

a.	Find the missing values in the ANOVA table. (Round your answers to 2 decimal places.)

ANOVA
Source of Variation	SS	df	MS	F	p-value	F crit
Sample	766.98	2	MSB =	Ffactor B =	0.0109	3.885
Columns	12,122.69	1	MSA =	Ffactor A =	0	4.747
Interaction	57.60	2	MSAB =	FInteraction =	0.6148	3.885
Within	682.14	12	MSE =
Total	13,629.41	17

b.

At the 5% significance level, can you conclude that there is an interaction effect?

	Yes, since the value of the F statistic for interaction is less than the critical value.
	Yes, since the value of the F statistic for interaction is greater than the critical value.
	No, since the value of the F statistic for interaction is less than the critical value.
	No, since the value of the F statistic for interaction is greater than the critical value.

c.

At the 5% significance level, can you conclude that the column means differ?

	Yes, since the value of the F statistic for Factor A is less than the critical value.
	Yes, since the value of the F statistic for Factor A is greater than the critical value.
	No, since the value of the F statistic for Factor A is less than the critical value.
	No, since the value of the F statistic for Factor A is greater than the critical value.

d.

At the 5% significance level, can you conclude that the row (sample) means differ?

	Yes, since the value of the F statistic for Factor B is less than the critical value.
	Yes, since the value of the F statistic for Factor B is greater than the critical value.
	No, since the value of the F statistic for Factor B is less than the critical value.
	No, since the value of the F statistic for Factor B is greater than the critical value.

Answer 1

as MS (Factor) =SS(fctor)/df(factor)

F(factor)=MS(factor)/MS(error)

Source of Variation	SS	df	MS	F	p-value	F crit
Sample	766.98	2	383.49	6.75	0.0109	3.885
Columns	12,122.69	1	12122.69	213.26	0	4.747
Interaction	57.6	2	28.80	0.51	0.6148	3.885
Within	682.14	12	56.85
Total	13,629.41	17

b)

No, since the value of the F statistic for interaction is less than the critical value

c)

Yes, since the value of the F statistic for Factor A is greater than the critical value

d)

Yes, since the value of the F statistic for Factor B is greater than the critical value