Omnibus F test

Bonferroni s test is the most straightforward of several statistical methodologies that can appropriately be used in the context of multiple comparisons. That is, Bonferroni s test can appropriately be used to compare pairs of means after rejection of the null hypothesis following a significant omnibus F test. Imagine that we have c groups in total. Bonferroni s method makes use of the following inequality ... 

The significant result of the omnibus F test led to the rejection of the null hypothesis of no significant differences, thereby revealing the presence of a significant difference between at least one pair of means. It is now of interest to determine precisely which pair or pairs of means are significantly different. 

The first step in our analytical strategy was to conduct an ANOVA. This ANOVA tested the null hypothesis that there were no differences among the three means. The null hypothesis was tested at an a level of O.OS, and was rejected on the basis of the significant omnibus f test. 

If the omnibus F test is significant, what are the pairwise comparisons that would be of interest ... 

In Chapter 11 we discussed the issue of multiple comparisons and multiplicity in the context of pairwise treatment comparisons following a significant omnibus F test. When we adopt the 5% significance level (a = 0.05), by definition it is likely that a type 1 error will occur when 20 separate comparisons are made. That is, a statistically significant result will be "found" by chance alone. The greater the number of objectives presented in a study protocol, the greater the number of comparisons that will be... 

Alternatively, instead of using the EBE of the parameter of interest as the dependent variable, an estimate of the random effect (t ) can be used as the dependent variable, similar to how partial residuals are used in stepwise linear regression. Early population pharmacokinetic methodology advocated multiple linear regression using either forward, backwards, or stepwise models. A modification of this is to use multiple simple linear models, one for each covariate. For categorical covariates, analysis of variance is used instead. If the p-value for the omnibus F-test or p-value for the T-test is less than some cut-off value, usually 0.05, the covariate is moved forward for further examination. Many reports in the literature use this approach. 

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