Analyze Variability

Coefficients Table - Ratio Effects

  

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.

Example Output

 

Coded Coefficients for Ln(Std)

 

                             Ratio

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

Interpretation

For the insulation data, the ratio effects indicate that:

·    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 its 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).

Why does it work this way? When both factors are set at their low levels (or at their high levels) then the interaction term will be 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 its low level (-1 * 1 = -1). Changing material from low to high while keeping injection pressure low changes the interaction term from high to low, which means 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, so the ratio work in the same direction, and you multiply them to determine the effect.