# Multilevel Categoric (pt 2)¶

## Part 2 - Making Factors Numeric¶

## Continued – A Case Study on Battery Life¶

In the preceding, General Factorial Tutorial – Part 1, you treated all factors categorically. The main purpose of Part 2 of this tutorial is to illustrate some of the functions built into Design-Expert that can be used to make effects graphs better fit the type of data we’re dealing with, in addition to making the results easier to interpret and understand. We’ve already said that Montgomery’s classic battery experiment could have been handled by using the Response Surface tab in Design-Expert software and constructing a one-factor design on temperature, with the addition of one categorical factor at three levels for the material type. Never fear, we’ll cover response surface methods like this from the ground up in the Response Surface Tutorials. But to demonstrate the flexibility of Design-Expert, let’s explore how you can make the shift from categoric to numeric after-the-fact, even within the context of a general factorial design.

To get started, re-open the file named **Battery.dxpx** saved earlier. If the
file is already open, then click the **Design** node.

## Changing a Factor from Categoric to Numeric¶

Right-click on the **B:Temperature** factor column heading, and select **Make
Numeric** then **Continuous Numeric**. (The “discrete” option could also work in
this case. It works well for numeric factors that for convenience-sake must be
set at specific levels. For example, imagine that the testing chamber for the
batteries has only three settings – 15, 70 and 125.)

The software pops up a warning not to do this if the factor really is
categorical. To acknowledge it and move on, click the **OK** button below the
message.

## Re-Analyzing the Results¶

To re-analyze your data, click the analysis node labeled **Life**. Then click the
**Model** tab. When you designated a factor being numeric, Design-Expert
automatically shifted to fitting a polynomial, such as those used for response
surface methods. To model non-linear response to temperature (factor B),
double-click the **AB**^{2} term, or via a right click add it to the
**Model** as shown below. (Squared terms capture curvature.)

Click the **ANOVA** tab. You will get a warning about hierarchy.

This warning arises because you chose a higher order term without support by
parent terms, in this case: AB and B^{2}. Click **Yes** and move on.

Note

**Statistical reasons for maintaining model hierarchy**: For
details, search out the topic on “Model Hierarchy Check” in the Help System.

The ANOVA report now displays in the view (annotated or not) that you used last.
By comparing this output with the ANOVA done in Part One, observe that the lines
for the model and residual come out the same, but the terms involving B differ.
In Part One we treated factor B (temperature) categorically, although in an
ordinal manner. Now that this factor is recognized explicitly as numeric, what
was the effect of B is now broken down to two model terms – B and B^{2},
and AB becomes AB plus AB^{2}.

The whole purpose of this exercise is to make a better looking effects graph.
Let’s see what this looks like by clicking the **Model Graphs** tab. Go to the
Factors Tool on the right, right-click the box next to **B:Temperature** and
change it to the **X1 Axis**.

You now have a plot characterizing the data from Part One of this case study,
except that the above lines are now continuous with temperature, whereas in Part
One they were displayed as discrete (categorical) segments. Notice that the curves
by temperature (modeled by B) depend on the type of material (A). This provides
graphical verification of the significance of the AB^{2} term in the model.

The dotted lines are the confidence bands, which in this case cause more trouble
than they’re worth for conveying the uncertainty in fitting, so let’s change
Graph Preferences to take these off. First, right-click the graph and select
**Graph Preferences**. Now move to the XY Graphs section and find **Polynomial: L
SD bars or bands**, then select the **None** option as shown below.

Press **OK**. That cleans up the picture, but perhaps too much! Let’s put the
points back on for perspective. Again, right-click over the graph and select
**Graph Preferences**. Now, under the **All Graphs** section, turn on (check) the
**Show design points** option.

Your plot should now look like that copied out below. (Note: if you don’t have the A1, A2, and A3 labels, remove the legend from your graph by going to View->Show legend).

The conclusions remain the same as before: Material A3 will maximize battery life with minimum variation in ambient temperature. However, by treating temperature numerically, predictions can be made at values between those tested. Of course, these findings are subject to confirmation tests.

## Postscript: Demo of “Pop out” View¶

Before exiting Design-Expert, give this a try: Go to **View** and select
**Pop-Out View**.

This pushes the current graph out of its fixed Windows pane into a ‘clone’ that
floats around on your screen. Now on the original **Factors Tool** right click
the box next to **A:Material** and return it to the **X1 Axis**. Then do an
Alt-Tab to bring back the clone of the previous view back on your current window.

You can present Design-Expert outputs both ways for your audience:

- Curves for each material as a function of temperature on the X1 axis, or
- Two temperature lines connected to the three discrete materials as X1.

Another way to capture alternative graphs is to copy and paste them into a word processor, spreadsheet, or presentation program. Then you can add annotations and explanations for reporting purposes.