Analyze Variability

Analysis of Variance Table - P-Values

  

Use the p-values (P) in the analysis of variance table to determine which of the effects in the model are statistically significant. Typically, you look at the interaction effects in the model first because a significant interaction will influence how you interpret the main effects. To use the p-value, you need to:

·    Identify the p-value for the effect you want to evaluate.

·    Compare this p-value to your a-level. A commonly used a-level is 0.05.

-    If the p-value is less than or equal to a, you can conclude that the effect is significant.

-    If the p-value is greater than a, you can conclude that the effect is not significant.

Example Output

 

Analysis of Variance for Ln(Std)

 

Source                 DF   Adj SS   Adj MS  F-Value  P-Value

Model                  10  65.4970   6.5497    21.73    0.002

  Linear                4  31.7838   7.9459    26.36    0.001

    Material            1  30.0559  30.0559    99.71    0.000

    InjPress            1   1.1104   1.1104     3.68    0.113

    InjTemp             1   0.1005   0.1005     0.33    0.589

    CoolTemp            1   0.5170   0.5170     1.71    0.247

  2-Way Interactions    6  33.7132   5.6189    18.64    0.003

    Material*InjPress   1  32.0953  32.0953   106.47    0.000

    Material*InjTemp    1   1.1466   1.1466     3.80    0.109

    Material*CoolTemp   1   0.0010   0.0010     0.00    0.956

    InjPress*InjTemp    1   0.2046   0.2046     0.68    0.448

    InjPress*CoolTemp   1   0.2642   0.2642     0.88    0.392

    InjTemp*CoolTemp    1   0.0014   0.0014     0.00    0.948

Error                   5   1.5072   0.3014

Total                  15  67.0043

Interpretation

For the insulation data, the analysis of variance table shows the following:

·    Interaction effects - the model contains six 2-way interaction effects that you must evaluate first.

The p-value for the set of 2-way interactions (0.003) is less than 0.05. Therefore, there is significant evidence that at least one factor depends on the level of another factor. The individual interaction results indicate that the interaction between material and injection pressure interaction is significant (p-value = 0.000).

·    Main effects - the model contains four main effects, which you should evaluate after significant interactions are examined.

The p-value for the set of main effects (0.001) is less than 0.05. Therefore, there is significant evidence that at least one coefficient is not equal to zero. The individual results indicate that Material is the only significant main effect (p-value = 0.000).