Chapter 13 - Section 13.4 - Assess Your Understanding - Vocabulary and Skill Building - Page 666: 10

(a) The factor A main effect is calculated by taking difference of average of the dependent variable when factor A is at high level and low level. It is computed as follows: \[\begin{align} & =\frac{84+55+76+43}{4}-\frac{104+96+143+121}{4} \\ & =\frac{258}{4}-\frac{464}{4} \\ & =-51.5 \\ \end{align}\] If factor A increases from low to high level, the dependent variable decreases by 51.5 units. The factor B main effect is calculated by taking difference of average of the dependent variable when factor B is high and low. It is computed as follows: \[\begin{align} & =\frac{104+96+84+76}{4}-\frac{143+121+55+43}{4} \\ & =\frac{360}{4}-\frac{362}{4} \\ & =-0.5 \\ \end{align}\] If factor B increases from low to high level, the dependent variable decreases by 0.5 units. The effect of one factor on other can be checked by using the interaction effect. Considering lower level of B, it can be seen that effect of factor A from low to high is \[\begin{align} & \frac{\text{high level of factor A}}{2}-\frac{\text{low level of factor A}}{2} \\ & =\frac{84+76}{2}-\frac{104+96}{2} \\ & =-20 \\ \end{align}\] So, at lower level of factor B, dependent variable decreases by 20 units when A changes from low to high. Considering higher level of factor B, it can be seen that effect of factor A from low to high is \[\begin{align} & \frac{\text{high level of factor A}}{2}-\frac{\text{low level of factor A}}{2} \\ & =\frac{55+43}{2}-\frac{143+121}{2} \\ & =49-132 \\ & =-83 \\ \end{align}\] So, at higher level of factor B, dependent variable decreases by 83 units when A changes from low to high. Considering lower level of factor A, it can be seen that effect of factor B from low to high is \[\begin{align} & \frac{\text{high level of factor B}}{2}-\frac{\text{low level of factor B}}{2} \\ & =\frac{143+121}{2}-\frac{104+96}{2} \\ & =132-100 \\ & =32 \\ \end{align}\] At lower level of factor A, dependent variable changes by 32 units when factor B changes from low to high. Considering higher level of factor A, it can be seen that effect of B from low to high is \[\begin{align} & \frac{\text{high level of factor B}}{2}-\frac{\text{low level of factor B}}{2} \\ & =\frac{55+43}{2}-\frac{84+76}{2} \\ & =49-80 \\ & =-31 \\ \end{align}\] At higher level of A, dependent variable decreases by 31 units when factor B changes from low to high. It is seen that changes in dependent variable for factor A do not depend on level of factor A. So, there is no interaction effect among both factors. (b) The interaction plot is shown below:

The interaction plot also shows that there is no interaction between factors.