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Analysis of Variance |

Consider the two-way analysis of variance model Kutner (1974) proposed for these data:

where is the overall mean effect,
is the effect
of the *i*th level of **DRUG**,
is the effect
of the *j*th level of **DISEASE**,
is
the joint effect of the *i*th level of **DRUG**
with the *j*th level of **DISEASE**,
and is the
random error term for the *k*th
observation in the *i*th level of **DRUG**
and *j*th level of **DISEASE**.
The 's are assumed to be
normally distributed and uncorrelated and to have mean 0
and common variance .

The effects for **DRUG** and **DISEASE** are often
referred to as the *main effects* in the model and
the **DRUG*DISEASE** effect as an *interaction effect*.
The interaction effect enables you to determine whether the
level of **DRUG** affects the change in blood pressure
differently for different levels of **DISEASE**.
To begin the analysis of variance, follow these steps.

Choose Analyze:Fit (Y X). |

Select CHANG_BP in the variables list on the left, then click the Y button. |

**CHANG_BP** appears in the **Y** variables list
and is now defined as the response variable.

Select DRUG and DISEASE, then click the Expand button. |

Your variables dialog should now appear, as shown
in Figure 15.5.

The **Expand** button provides a convenient
way to specify interactions of any order.
The degree of expansion is controlled by
the value below the **Expand** button.
The order **2** is the default, so clicking **Expand**
constructs all possible effects from the selected
variables up to second-order effects.
This adds **DRUG**, **DISEASE**, and **DRUG*DISEASE**
to the effects list.

Note | You could have added the same effects by using the X and Cross buttons, but the
Expand button is faster.
There is also a Nest button for specifying nested effects.
For more information on the effects buttons, see Chapter 39, "Fit Analyses." |

Click the OK button. |

A fit window appears, as shown in Figure 15.6.

You can control which tables and graphs the fit window contains
by clicking the **Output** button in the fit variables dialog
or by choosing from the **Tables** and **Graphs** menus.
By default, the fit window contains tables for model
specification, **Nominal Variable Information**,
**Parameter Information**, **Model Equation**,
**Summary of Fit**, **Analysis of Variance**,
**Type III Tests**, and **Parameter Estimates**,
as well as a residual-by-predicted plot.

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