# Practice Problem in 22 Design

Assume that four replications were made for the human comfort study provided in Table 3.

Table 3. Practice Problem for a 22 Factorial Design of Experiment

### Questions

1. Calculate the main and the interaction effects

2. Calculate the estimates for A, B, and AB

3. Write down the estimated regression equation

4. Calculate the Sum of Squares

5. Develop the ANOVA Table

6. Interpret the effects in the context of the problem

7. Which effects are likely to be significant based on the effect calculation? Why?

### Solution

1. Effect of A = 7.5, B = 1.75, & AB = 1

2. Estimate of A = 3.75, B = 0.875, & AB = 0.5

3. Estimated regression Equation:

4. Sum of Square of A = 225, B = 12.25, & AB = 4

5. ANOVA table

6. The comfort level increases by 7.5 if the temperature increases from 0 to 75-degree Fahrenheit. The comfort level increases by 1.75 if the humidity increases from 0 to 35 percent. As compared to the low level, at the high level of the temperature, the comfort increases by 1 if the humidity increases from 0 to 35 %.

7. The effect is very large for the temperature factor as compare to the main effect of humidity and the interaction effect. Therefore, the temperature factor is likely to be significant. As the experimental error is small as compare to the main and the interaction effects, results in high f-value. Therefore, both the main effects of A and B and the interaction could be significant too.