Analyze Factorial Design

Two-Level Split-Plot  Designs
Analysis of Variance Table - P-Value

  

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, conclude that the effect is significant.

-    if the p-value is greater than a, conclude that the effect is not significant.

Example Output

Analysis of Variance

 

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

Pretreatment[HTC]         1  194.407  194.407    24.61    0.008

WP Error                  4   31.600    7.900     1.21    0.430

Stain                     1    0.007    0.007     0.00    0.975

Pretreatment[HTC]*Stain   1   60.301   60.301     9.21    0.039

SP Error                  4   26.187    6.547

Total                    11

Interpretation

For the water resistance data, the analysis of variance table shows the following:

·    Interaction effects: the model contains one two-way interaction that must be evaluated first.

The interaction between Pretreatment and Stain is statistically significant (P = 0.039). The effect of Stain depends on the type of Pretreatment used.

·    Main effects: the model contains two main effects, Pretreatment and Stain.

Because the interaction between Pretreatment and Stain is significant, do not interpret the main effects separately.