1. Practical Solutions Analysis of Variance
© Scott Harris University of Southampton
Practical Solutions Analysis of Variance
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Analysis of Variance

2. © Scott Harris University of Southampton
Practical Solutions
The ANOVA table shows that at least one of the groups is significantly different from the others (p=0.010).
Analysis of Variance

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Practical Solutions
Looking at the individual LSD and Bonferroni corrected pair-wise comparisons it can be seen that there is only one contrast that shows a significant difference at the 5% level and that is Active A vs. Placebo, with the Placebo levels higher.
Analysis of Variance

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Practical Solutions
For the non-parametric test, again, there is only a p value to report from the test (although the group medians could be reported from elsewhere, the pair-wise comparisons need to be done as separate Mann-Whitney U tests as shown in Analysing Continuous data and CI’s for these differences could be calculated from CIA).
The Kruskal-Wallis test shows that at least one of the groups is significantly different from the others (p=0.013)
Analysis of Variance

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Practical Solutions
3) i.
By adding HBA1C_2 as the dependent variable and GROUP as a Fixed factor we can replicate the one-way ANOVA
Analysis of Variance

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Practical Solutions
The same multiple comparisons:
Analysis of Variance

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3) ii.
By adding HBA1C_1 to the model GROUP has become more significant. We are explaining an additional amount of variability, hence increasing the precision.
Analysis of Variance

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Practical Solutions
We need to use the contrasts option when a continuous covariate is added to the model.
To see the remaining contrast we need to re-run with a different reference category.
Analysis of Variance

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Practical Solutions
3) iii.
Adding in another categorical covariate means we need to go into the model options or we will get interaction terms fitted as default.
Analysis of Variance

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Practical Solutions
The size of the effects alters slightly but the conclusion remains the same.
Although Gender is not statistically significant it may still be important in the model. We can include terms if they are significant in our sample, they are key variables that have shown to be important in the literature or we want to test them for differences.
Analysis of Variance

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Practical Solutions
Analysis of Variance