For Exercises 15.1 to 15.3, see pages 15-6 to 15-7; for 15.4 to 15.6, see page 15-10; for 15.7, see pages 15-12 to 15-13; for 15.8 to 15.10, see page 15-15; for 15.11, see page 15-16; for 15.12 and 15.13, see page 15-18; and for 15.14 to 15.16, see pages 15-20 to 15-21.
15.7 Is there an interaction?
Each of the following tables gives means for a two-way ANOVA. Make a plot of the means with the levels of Factor A on the x axis. State whether or not there is an interaction, and if there is, describe it.
Factor A | |||
Factor B | 1 | 2 | 3 |
1 | 12 | 18 | 24 |
2 | 5 | 8 | 11 |
15-13
Factor A | |||
Factor B | 1 | 2 | 3 |
1 | 10 | 15 | 20 |
2 | 30 | 35 | 40 |
Factor A | |||
Factor B | 1 | 2 | 3 |
1 | 10 | 5 | 15 |
2 | 20 | 25 | 15 |
Factor A | |||
Factor B | 1 | 2 | 3 |
1 | 20 | 5 | 20 |
2 | 10 | 25 | 10 |
15.7
(a) There is a slight interaction. Factor B level 1 is higher than Factor B level 2, but this difference increases as the level of Factor A increases, hence the interaction. (b) There is no interaction, Factor B level 2 is consistently higher than level 1 regardless of Factor A. Additionally, the means increase as Factor A level increases. (c) There is an interaction. For Factor A level 1, Factor B level 2 is higher than level 1; this difference increases for Factor A level 2. Finally there is no difference between level 2 and 1 for Factor B when Factor A is level 3. (d) There is an interaction, for Factor A levels 1 and 3, Factor B level 1 is higher than level 2; however, this reverses for Factor A level 2, where Factor B level 1 is now much higher than level 2.