Question

Download data.self.csv. The accompanying data table lists measures of self- esteem from a student project. The objective of the project was to study how levels of self-esteem in subjects relate to their perceptions of self-esteem in other target people who were described in writing. The test here works well even though the data are at the ordinal level of measurement. Use a 0.03 significance level and apply the methods of two-way analysis of variance. What is your conclusion?

Responses	Row Factor	Column Factor
5	Target Low	Subject Low
4	Target Low	Subject Low
3	Target Low	Subject Low
5	Target Low	Subject Low
4	Target Low	Subject Low
3	Target Low	Subject Low
5	Target Low	Subject Low
4	Target Low	Subject Low
2	Target Low	Subject Low
4	Target Low	Subject Low
3	Target Low	Subject Low
5	Target Low	Subject Low
3	Target Low	Subject Medium
3	Target Low	Subject Medium
3	Target Low	Subject Medium
3	Target Low	Subject Medium
3	Target Low	Subject Medium
2	Target Low	Subject Medium
4	Target Low	Subject Medium
3	Target Low	Subject Medium
1	Target Low	Subject Medium
3	Target Low	Subject Medium
2	Target Low	Subject Medium
4	Target Low	Subject Medium
3	Target Low	Subject High
1	Target Low	Subject High
2	Target Low	Subject High
2	Target Low	Subject High
2	Target Low	Subject High
5	Target Low	Subject High
2	Target Low	Subject High
3	Target Low	Subject High
2	Target Low	Subject High
2	Target Low	Subject High
4	Target Low	Subject High
2	Target Low	Subject High
2	Target High	Subject Low
2	Target High	Subject Low
4	Target High	Subject Low
2	Target High	Subject Low
2	Target High	Subject Low
3	Target High	Subject Low
2	Target High	Subject Low
4	Target High	Subject Low
2	Target High	Subject Low
2	Target High	Subject Low
2	Target High	Subject Low
3	Target High	Subject Low
4	Target High	Subject Medium
3	Target High	Subject Medium
1	Target High	Subject Medium
2	Target High	Subject Medium
1	Target High	Subject Medium
3	Target High	Subject Medium
2	Target High	Subject Medium
4	Target High	Subject Medium
3	Target High	Subject Medium
1	Target High	Subject Medium
1	Target High	Subject Medium
4	Target High	Subject Medium
3	Target High	Subject High
2	Target High	Subject High
3	Target High	Subject High
2	Target High	Subject High
3	Target High	Subject High
4	Target High	Subject High
3	Target High	Subject High
4	Target High	Subject High
4	Target High	Subject High
3	Target High	Subject High
3	Target High	Subject High
4	Target High	Subject High

Answer 1

Two-way ANOVA: Responses versus Row Factor, Column Factor

Source DF SS MS F P
Row Factor (Target) 1 2.7222 2.72222 2.94 0.091
Column Factor (Subject) 2 4.1944 2.09722 2.26 0.112
Interaction (TargetxSubject) 2 13.0278 6.51389 7.03 0.002
Error 66 61.1667 0.92677
Total 71 81.1111

From the ANOVA table it is observed that the interaction effect between target and subject is significantly present since p-value=0.002<0.03. So it is meaningless to test separately the levels of taget and levels of Subject whether they are equal or not.