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[Salinan]Disalin!
ratio of how good the model is compared to how bad it is (its error).
I have just explained how ANOVA can be represented as a regression equation, and this
should help you to understand what the F-ratio tells you about your data. Figure 10.2 shows
the Viagra data in graphical form (including the group means, the overall mean and the difference
between each case and the group mean). In this example, there were three groups;
therefore, we want to test the hypothesis that the means of three groups are different (so, the
null hypothesis is that the group means are the same). If the group means were all the same,
then we would not expect the placebo group to differ from the low-dose group or the highdose
group, and we would not expect the low-dose group to differ from the high-dose group.
Therefore, on the diagram, the three coloured lines would be in the same vertical position
(the exact position would be the grand mean – the dashed line in the figure). We can see from
the diagram that the group means are actually different because the coloured lines (the group
means) are in different vertical positions. We have just found out that in the regression model,
b2 represents the difference between the means of the placebo and the high-dose group, and
b1 represents the difference in means between the low-dose and placebo groups. These two
distances are represented in Figure 10.2 by the vertical arrows. If the null hypothesis is true
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