Ratio effects can provide a measure of the practical significance of a factor's effect. The ratio effect indicates the proportional increase or decrease in the standard deviation of the response when the factor is changed from the low to high level. The closer the ratio effect is to one, the smaller the effect of the factor.
The ratio effect estimates the ratio of the standard deviation of responses at the high level of the factor to the standard deviation of responses at the low level of the factor. The ratio effect is easily calculated by exponentiating the effect of a factor.
In this example:
- For material, the ratio effect is 0.3830. This means that when the insulation uses formula 2 the standard deviation is 38% of the value when the insulation is formula 1. Because the material by injection pressure interaction is significant, the main effect for material cannot be interpreted without considering the interaction effect.
- For the material by injection pressure interaction, the ratio effect is 0.3709.
To predict the result of changing material from formula 1 to formula 2 while keeping injection pressure the same, multiply or divide the ratio effect for material by the ratio effect for the interaction. If injection pressure is at its low level, then divide the ratio effect for material by the ratio effect for the interaction to get 0.3830/0.3709 = 1.0326, is a small increase in the standard deviation of about 3%. If injection pressure is at the high level, multiply the two ratio effects to get 0.3830 * 0.3709 = 0.1421, a reduction in the standard deviation of over 85% (1 – 0.1421 = 0.8579).
When both factors are set at their low levels (or at their high levels) then the interaction term is at its high level (−1 * −1 = 1; 1 * 1 = 1). Remember, −1 is the low level and 1 is the high level. When one factor is set at the high level and the other set at the low level, then the interaction term is at the low level (−1 * 1 = −1). Changing material from low to high while keeping injection pressure low changes the interaction term from high to low. The two ratios work in opposite directions, and you divide them to determine the effect. If injection pressure is high, then changing material from low to high also changes the interaction term from low to high. The ratios work in the same direction, and you multiply them to determine the effect.
Coded Coefficients for Ln(Std)
Term Effect Effect Coef SE Coef T-Value P-Value VIF
Constant 0.3424 0.0481 7.12 0.001
Material -0.9598 0.3830 -0.4799 0.0481 -9.99 0.000 1.00
InjPress -0.1845 0.8315 -0.0922 0.0481 -1.92 0.113 1.00
InjTemp 0.0555 1.0571 0.0278 0.0481 0.58 0.589 1.00
CoolTemp -0.1259 0.8817 -0.0629 0.0481 -1.31 0.247 1.00
Material*InjPress -0.9918 0.3709 -0.4959 0.0481 -10.32 0.000 1.00
Material*InjTemp 0.1875 1.2062 0.0937 0.0481 1.95 0.109 1.00
Material*CoolTemp 0.0056 1.0056 0.0028 0.0481 0.06 0.956 1.00
InjPress*InjTemp -0.0792 0.9239 -0.0396 0.0481 -0.82 0.448 1.00
InjPress*CoolTemp -0.0900 0.9139 -0.0450 0.0481 -0.94 0.392 1.00
InjTemp*CoolTemp 0.0066 1.0066 0.0033 0.0481 0.07 0.948 1.00