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ANOVA - Two Factors

ANOVA - Two Factors

Example: We consider a data set with two factors (Reduction Gear and Axis) and several levels, as in the following table.

Axis
 Reduction Gear Noise
Rolled Imported 39.6
Rolled National 42.1
Imported National 40.9
Cut National 38.2
Rolled National 42
Cut Imported 41.3
Imported Imported 39.6
Rolled National 40.3
Imported National 40.7
Imported Imported 36.9
Rolled Imported 40.2
Cut Imported 46.8
Cut Imported 40.3
Cut National 37.4
Cut National 37
Rolled Imported 48.4
Imported Imported 39.9
Imported National 39.4
Rolled Imported 40.9
Rolled National 38.9
Cut Imported 40.5
Cut National 42.3
Imported Imported 38.1
 Imported Imported 38
Imported Imported 36.2
Rolled Imported 41
Cut Imported 39.9
Rolled Imported 41
Cut National 41.3
Imported National 42
Cut Imported 39.3
Cut National 42.1
Imported Imported 36.7
Cut National 40.5
Rolled National 38.9
Imported Imported 37.2
Rolled Imported 39.9
Rolled National 43.7
Imported National 41.4
Rolled National 41
Cut Imported 41.3
Imported National 41.3
Imported Imported 36.7
Rolled National 40.1
Cut National 41.3
Rolled Imported 41
Imported National 40.6
Cut National 40.4
Rolled National 40.3
Imported National 41.3
Cut Imported 40.1
Rolled Imported 42.7
Cut Imported 41.6
Imported National 41.6

click here to download the data

To use the tool ANOVA, the user must follow these steps: 

1. Access the menu:

Action $ \blacktriangleright $ ANOVA $ \blacktriangleright $ ANOVA

 

2. The following screen will be shown;

3. With the cursor in the field Data Set select the columns that contain the data that will be analyzed;

4. The titles of the columns can also be selected. If you only select the data, disable the option Columns With Name. Then click the button Read;

5. Select the Response Variable, in the appropriate item;

6. Create the Formula: use double click in the process variable to add it in the box Formula, and click in the buttons with arithmetical sign to add them;

7. In Show Resuls, choos one of the options. We suggest the option New Sheet, because Action does not have the undo command;

8. To finish, click Ok.

 

REMARK: The names of the columsn can not contain symbols, space or tab.

 

Results and Interpretation

Once the process is finished, the following results will be shown:

As the associated p-value between the axis and the reduction gear is too small (0,00096) we conclude that the interaction between these factors is significant. This way, we must to be careful  in interpreting the factors