Comparing treatments for continuous data

Our main interest is still simply to compare the treatments, but we must recognise that it would not be unusual to see centre differences in an overall sense different standards of ancillary care, cultural and environmental differences are just some of the things that could contribute to this. 

Statistical analysis proceeds through two-way analysis of variance (ANOVA). The focus in this methodology is to compare the treatment groups while recognising potential centre differences. To enable this to happen we allow the treatment means and gig to be different in the different centres as seen in Table 5.2. 

This null hypothesis is saying that the treatment means are the same within each centre, but not necessarily across centres we are allowing the centres to be different. Two-way ANOVA gives us a p-value relating to this null hypothesis. If that p-value is significant (p 0.05) then we reject the null hypothesis and there is evidence that the treatments are different. 

Initially you may think that this approach to comparing the treatments is over elaborate why not just compare the overall means (which happened to be 11.8 and 4.9) in an unpaired t-test Well in one sense you could, but it would not be the most efficient thing to do. Simply comparing the overall means loses the fact that the means in centre 1,12.4 and 5.8, are linked, as are those in each of the other centres. The two-way ANOVA procedure maintains that link, it simultaneously compares 

This analysis assumes that the treatment effect is consistent across the centres. For the above data this seems a reasonable assumption, but we will return to a more formal evaluation of this assumption in the next section. The weighted average of the treatment differences that is the basis of the signal provides the best estimate of the overall treatment effect. In the above example this was 6.74 mmHg and we can construct confidence intervals around this value to allow an interpretation of the size of the (assumed common) true treatment effect. 

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