Question

1. A researcher conducts a 2 way ANOVA test with interaction and provides the following ANOVA table.
2. Find the missing values in the ANOVA table.

Source	SS	Df	MS	F	p-value	F crit
Sample	700.21	2			.014
Columns	12,199.15	1			5.02E-09
Interaction	56.34	2			0.62
Within	680.38	12
Total	13,636.08	17

1. At the 5% significance level, can you conclude that there is an interaction effect?
2. At the 5% significance level, can you conclude that the column means differ?
3. At the 5% significance level, can you conclude that the row (sample) means differ?

Answer 1

Ans:

Source	SS	Df	MS	F	p-value	F crit
Sample	700.21	2	350.105	6.17	0.014	3.89
Columns	12,199.15	1	12199.15	215.16	5.02E-09	4.75
Interaction	56.34	2	28.17	0.50	0.62	3.89
Within	680.38	12	56.69833
Total	13,636.08	17

critical F value=FINV(0.05,2,12)=3.89

critical F value=FINV(0.05,1,12)=4.75

As,p-value for interaction effect is greater than 0.05,so we do not reject null hypothesis and conclude that there is no significant interaction effect.

As,p-value for interaction effect is less than 0.05,so we reject null hypothesis and conclude that column means differ.

As,p-value for interaction effect is less than 0.05,so we reject null hypothesis and conclude that sample or row means differ.