Question

Using the data below, perform a two-way ANOVA. Test the hypothesis of interaction at the 1% level of significance. Also, use a 1% level of significance to test the null hypotheses of equal column and equal row means.

Factor	Level 1			Level 2
Level A	14	16	18	12	16	16
Level B	10	12	16	12	12	14

Answer 1

Step 1: Set the null and alternative hypothesis

Row effect:   H₀: All the row means are equal

H₁: All the row means are not equal

Column effect:   H₀: All the column means are equal

H₁: All the column means are not equal

Interaction effect: H₀: Interaction effects are zero

H₁: Interaction effect is not zero

Step2:  Determine the appropriate statistical test

F-test statistics in two-way ANOVA

Step3:  Set the level of significance

Let  

Step4:  Collect the sample data

Factor	Level 1			Level 2
Level A	14	16	18	12	16	16
Level B	10	12	16	12	12	14
	14.33			13.67

Step5:  Analyse the data

Let c be the number of column treatments, r be the number of row treatments, n the number of observations in each cell, N be total number of observations.

The ANOVA summary table is

Source	SS	df	MS	F	P
Rows	21.33	1	21.33	4.27	0.0726
Columns	1.33	1	1.33	0.27	0.6174
Interaction	1.34	1	1.34	0.27	0.6174
Error	40	8	5
Total	64	11

Step6: Arrive at a statistical conclusion

As the p-value is greater than 0.01 for all rows, columns, interaction. Thus, reject all null hypothesis.