To conduct a Factorial ANOVA one only need extend the logic of the oneway design. Table 13.2 presents the data for a 2 by 5 factorial ANOVA. The first factor, AGE, has two levels, and the second factor, CONDITION, has five levels. So, once again each observation can be uniquely coded.

AGE | CONDITION |

Old = 1 | Counting = 1 |

Young = 2 | Rhyming = 2 |

Adjective = 3 | |

Imagery = 4 | |

Intentional = 5 |

For each pairing of AGE and CONDITION, there are 10 observations. That is, 2*5 conditions by 10 observations per condition results in 100 observations, that can be coded as follows. [Note, that the names for the factors are meaniful.]

AGE | CONDITIO | Scores |

1 | 1 | 9 |

1 | 1 | 8 |

1 | 1 | 6 |

1 | ... | ... |

1 | 1 | 7 |

1 | 2 | 7 |

1 | 2 | 9 |

1 | 2 | 6 |

1 | ... | ... |

1 | ... | ... |

1 | ... | ... |

1 | 5 | 10 |

1 | 5 | 19 |

1 | ... | ... |

1 | 5 | 11 |

2 | 1 | 8 |

2 | 1 | 6 |

2 | 1 | 4 |

2 | ... | ... |

2 | 1 | 7 |

2 | 2 | 10 |

2 | 2 | 7 |

2 | 2 | 8 |

2 | ... | ... |

2 | ... | ... |

2 | ... | ... |

2 | 5 | 21 |

2 | 5 | 19 |

2 | ... | ... |

2 | 5 | 21 |

Examine the table carefully, until you understand how the
coding has been implemented. Note: one
can enhance the readability of the output by using **
Value Labels** for the two factors.

To compute the relevant statistics - a simple approach,

- Select
**[Statistics => General Linear Model => Simple Factorial...]** - Select and move "Scores" into the
**Dependent:**box - Select and move "Age" into the
**Factor(s):**box. - Click on
**[Define Range...]**to specify the range of coding for the Age factor. Recall that**1**is used for Old and**2**is used for Young. So, the**Minimum:**value is <1>, and the**Maximum:**value is**2**. Click on**[Continue]**. - Select and move "Conditio" into the
**Dependent:**box - Click on
**[Define Range...]**to specify the range of the Condition factor. In this case the**Minimum:**value is**1**and the**Maximum:**value is**5**.By clicking on the

**[Options...]**button one has the opportunity to select the**Method**used. According to the online help,-
"

**Method:**Allows you to choose an alternate method for decomposing sums of squares. Method selection controls how the effects are assessed."For the our purposes, selecting the

**Hierarchical**, or the**Experimental**method will make available the option to output**Means and counts**. --- Note: I don't know the details of these methods, however, they are probably documented. - Under
**[Options...]**activate**Hierarchical**, or**Experimental**, then activate**Means and counts**- Click**[Continue]** - Click on
**[OK]**to generate the output.

As you can see the use of the

**Means and count**option produces a nice summary table, with all the**Variable Labels**and**Value Labels**that were incorporated into the datasheet. Again, the use of those options makes the output a great deal more readable.

The output is a complete source table with the factors identified with

**Variable Labels**

- By selecting
**[Model...]**, one can specify a**Custom**model. The default is for a**Fully Factorial**model, however, with the**Custom**option one can explicitly determine the effects to look at. - The
**Contasts**option allows one "test the differences among the levels of a factor" (see the manual for greater detail). - Various graphs can be specified with the
**[Plots...]**option. For example, one can plot "Conditio" on the**Horizontal Axis:**, and "Age" on**Separate Lines:**, to generate a simple "conditio*age" plot (see the dialog box for**[Plots...]**,

- The standard post-hoc tests for each factor can be calculated
by selecting the desired options under
**[Post Hoc...]**. All one has to do is select the factors to analyze and the appropriate post-hoc(s). - The
**[Options...]**dialog box provides a number of diagnostic and descriptive features. One can generate descriptive statistics, estimates of effect size, and tests for homogeneity of variance - among others. An example source table using some of these options would look like the following,

Higher order factorial designs are carried in the same manner as the two factor analysis presented above. One need only code the factors appropriately, and enter the corresponding observations.

Repeated measures designs will be discussed in the next section.