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.

**Figure 15.5:** Fit Variables Dialog with Variable Roles Assigned

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.

**Figure 15.6:** Fit Window - Model Information

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