# How to calculate the interaction effects?

The calculation of the interaction effects from a factorial design of experiment is provided in Video 3.

In contrast to the main effects (the independent effect of a factor), in real world, factors (variables) may interact between each other to affect the responses. For an example, the temperature and the humidity may interact with each other to affect the human comfort.

At the low humidity level (0%), the comfort increases by 5 (=5-0) if the temperature increases from 0- to 75-degree Fahrenheit. However, at the high humidity level (35%), the comfort increases by 7 (=9-2) if the temperature increases form 0- to 75-degree Fahrenheit (Figure 4). Therefore, at different levels of the humidity factor, the changes in comfort are not the same even if the temperature change is same (from 0 to 75 degree). The effect of temperature (factor A) is different across the level of the factor B (humidity). This phenomenon is called the Interaction Effect, which is expressed by AB.

The average difference or change in comfort can be calculated as AB= (7-5)/2= 2/2=1.

= the change in comfort level increases by 1 more at the high level as compared to the low level of humidity (factor B) if the temperature (factor A) increase from the low level (0-degree) to the high level (75-degree).

Similarly, the interaction effect can be calculated for the humidity factor across the level of temperature factor as follows.

At the low level of A, effect of B = 2-0 = 2; at the high level of A, the effect of B = 9-5 = 4 (Figure 5). Therefore, the average difference or change in comfort can be calculated as AB= (4-2)/2= 2/2=1.

= the change in comfort level increases by 1 more at the high level as compared to the low level of temperature (factor A) if the humidity (factor B) increase from the low level (0 %) to the high level (35%).

The interaction effect is same whether it is calculated across the level of factor A or factor B. Figure 4. Interaction effects of the temperature (factor A) and the humidity (factor B). Figure 5. Interaction effects of the temperature (factor A) and the humidity (factor B).

# What is a Strong or No/Absence of Interaction?

As the interaction effect is comparatively low or small in this example, the figure shows a slight or small interaction (Figure 4 & Figure 5). A strong interaction is depicted in Figure 6. No interaction effect would produce parallel lines shown in Figure 7. Figure 6. Visualization of a strong interaction effect. Figure 7. Visualization of no interaction effect.