Analyze Factorial Design

Two-Level Factorial Designs
Coded Coefficients  - Coefficients

  

For each main effect term and each interaction term, there is a coefficient and an effect. The effect is two times the coefficient.

Look at the effects and coefficients to determine the relative strength of the factors. The value and the sign are both important in the determination:

·    The absolute values determine the relative strengths of the factors. The higher the value, the greater the effect on the response.

·    In the absence of interactions, the sign determines which factor setting results in a higher response measurement:

-    A positive sign indicates that the high factor setting results in a higher response than the low setting.

-    A negative sign indicates that the low factor setting results in a higher response than the high setting.

Because these coefficients are estimated using coded units, putting the uncoded factor values into an equation with these coefficients yields incorrect predictions about strength. If the model is hierarchical, then the regression equation displays the uncoded coefficients.

In theory, any variance inflation factor (VIF) value greater than 1 can inflate the variance of the coefficients so much that statistical significance is a less useful way to identify candidate models. In practice, values greater than 5–10 can produce unstable coefficients that are difficult to interpret and, thereby, prompt corrective measures

Example Output

Coded Coefficients

 

Term               Effect    Coef  SE Coef  T-Value  P-Value   VIF

Constant                     56.0     21.0     2.66    0.056

MeasTemp                   -1.229    0.979    -1.25    0.278  5.87

Material            5.316   2.658    0.678     3.92    0.017  3.23

InjPress            5.645   2.822    0.401     7.04    0.002  1.13

InjTemp             4.355   2.177    0.378     5.76    0.005  1.00

CoolTemp           -3.457  -1.729    0.420    -4.12    0.015  1.24

Material*InjPress  -0.723  -0.361    0.415    -0.87    0.433  1.21

Material*InjTemp   -1.025  -0.512    0.443    -1.16    0.312  1.38

Material*CoolTemp  -0.208  -0.104    0.510    -0.20    0.848  1.82

InjPress*InjTemp   -0.837  -0.419    0.510    -0.82    0.458  1.82

InjPress*CoolTemp  -0.055  -0.027    0.382    -0.07    0.947  1.03

InjTemp*CoolTemp    1.933   0.966    0.381     2.54    0.064  1.02

Interpretation

For the insulation data, the effects suggest the following interpretations:

·    InjPress has the greatest effect (5.645) on insulation strength. The standard error of the coefficient (0.401) clarifies that the effect of injection pressure is not statistically greater than the effect of material. Also, a high injection pressure produced stronger insulation than a low injection pressure strength.

·    Material has the second greatest effect (5.316) on insulation strength. Also, using Formula 2 produced stronger insulation than Formula 1.

·    InjTemp has the third greatest effect (4.355) on insulation strength. Also, a high injection temperature produced a stronger insulation than a low injection temperature.

·    CoolTemp has the smallest effect (-3.457) on insulation strength. Also, a high cooling temperature produced a weaker insulation than a low cooling temperature.

The VIF for the covariate is 5.87. The temperature at the time of measurement is moderately correlated with the material and more weakly correlated with the other factors and interactions. The temperature could have an effect that the multicollinearity hides. The coefficient could also change dramatically as the model changes.