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.

Question 15.7

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.

  1. Factor A
    Factor B 1 2 3
    1 12 18 24
    2 5 8 11

    15-13

  2. Factor A
    Factor B 1 2 3
    1 10 15 20
    2 30 35 40
  3. Factor A
    Factor B 1 2 3
    1 10 5 15
    2 20 25 15
  4. 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.