Analyze Factorial Design

General Full Factorial Designs - Analysis of Variance Table

  

Use the p-values (P) in the analysis of variance table to determine which of the effects in the model are statistically significant. If you have any interaction effects in the model, you need to interpret them 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

Model                  9  1.11278  0.123642     6.59    0.007

  Blocks               1  0.00500  0.005000     0.27    0.620

  Linear               4  1.00556  0.251389    13.41    0.001

    ExCoat             2  0.65778  0.328889    17.54    0.001

    Alloy              2  0.34778  0.173889     9.27    0.008

  2-Way Interactions   4  0.10222  0.025556     1.36    0.328

    ExCoat*Alloy       4  0.10222  0.025556     1.36    0.328

Error                  8  0.15000  0.018750

Total                 17  1.26278

Interpretation

For the metal parts data, the analysis of variance table shows the following:

·    Interaction effects: the model contains one interaction effect (ExCoat*Alloy) which must be evaluated first.

The p-value of 0.328 for the exterior coating by alloy type interaction is not less 0.05. Therefore, there is no significant interaction effect. That is, there is no evidence that effect of exterior coating on corrosion resistance depends on the type of alloy.

·    Main effects: the model contains two main effects (ExCoat and Alloy) that can be evaluated in the absence of a significant interaction.

-    ExCoat: the p-value of 0.001 for the effect of exterior coating on corrosion resistance is less than 0.05. Therefore, you conclude that there is a significant effect. That is, there is a difference in the mean corrosion resistance among the three different coatings. Use the table of means to look at this difference.

-    Alloy: the p-value of 0.008 for the effect of alloy on corrosion resistance is less than 0.05. Therefore, you conclude that there is a significant effect. That is, there is a difference in the mean corrosion resistance among the three alloy types. Use the table of means to look at this difference.

·    Block effects: the data was collected on two consecutive days, each of which serves as a block.

The p-value of 0.620 for blocks is not less than 0.05. Therefore, there is no evidence of a significant block effect. That fact that the data was collected in two blocks (each block represents a different day) does not have a significant effect on the corrosion resistance of the metal part.

You may want to refit the model excluding the non-significant interaction and block terms.