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Analysis of Variance |

The One-Way ANOVA task enables you to perform an analysis of variance when you have a continuous dependent variable and a single classification variable.

For example, consider the data set on air quality (Air), described in the preceding section. Suppose you want to compare the ozone level corresponding to each of the three factory workshift periods.

- Select
**Statistics****ANOVA****One-Way ANOVA**... - Select o3 as the dependent variable.
- Select shift as the independent variable.

Figure 10.4 defines the one-way ANOVA model.

- Click on the
**Means**button in the main dialog. The resulting window displays the**Comparisons**tab. - Click on the arrow adjacent to the
**Comparison method**list. - Select
**Tukey's HSD**. - Highlight the variable shift in the
**Main Effects:**box. - Click on the
**Add**button.

You can click on the arrow next to **Significance level:** to select a
significance level, or you can type in the desired value.

- Click
**OK**.

Figure 10.5 specifies Tukey's studentized range (HSD) means comparison test at the 0.05 significance level.

- Click on the
**Plots**button in the main dialog. - Select
**Box-&-whisker plot**. - Click
**OK**.

Figure 10.6 displays the Plots dialog with the
**Box-&-whisker plot** selected.

Click **OK** in the One-Way ANOVA dialog
to perform the analysis.

The R-square value, which follows the ANOVA table in Figure 10.7, represents the proportion of variability accounted for by the independent variable. Approximately 28% of the variability in the ozone level can be accounted for by differences between shifts.

Information detailing which particular means are different is available in the multiple comparison test, as displayed in Figure 10.8. The means comparison output provides the alpha value, error degrees of freedom, and error mean square.

In the "Tukey Grouping" table, means with the same letter are not significantly different. The analysis shows that the daytime shift is associated with ozone levels that are significantly different from the other two shifts. The early and late shifts cannot be statistically distinguished on the basis of mean ozone level.

The box-and-whisker plot displayed in Figure 10.9 provides a graphical view of the multiple comparison results. The variance among the ozone levels may be unequal: subsequent analyses may include a test for homogeneity of variance or a transformation of the response variable, o3.

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