7.
Product and Process Comparisons
7.4. Comparisons based on data from more than two processes


What to do after equality of means is rejected  When processes are compared and the null hypothesis of equality (or homogeneity) is rejected, all we know at that point is that there is no equality amongst them. But we do not know the form of the inequality.  
Typical questions 
Questions concerning the reason for the rejection of the null
hypothesis arise in the form of:


Multiple Comparison test procedures are needed 
One popular way to investigate the cause of rejection of the null
hypothesis is a Multiple Comparison Procedure. These are
methods which examine or compare more than one pair of means or
proportions at the same time.
Note: Doing pairwise comparison procedures over and over again for all possible pairs will not, in general, work. This is because the overall significance level is not as specified for a single pair comparison. 

ANOVA F test is a preliminary test 
The ANOVA uses the F test to determine whether there exists a
significant difference among treatment means or interactions. In
this sense it is a preliminary test that informs us if we should
continue the investigation of the data at hand.
If the null hypothesis (no difference among treatments or interactions) is accepted, there is an implication that no relation exists between the factor levels and the response. There is not much we can learn, and we are finished with the analysis. When the F test rejects the null hypothesis, we usually want to undertake a thorough analysis of the nature of the factorlevel effects. 

Procedures for examining factorlevel effects  Previously, we discussed several procedures for examining particular factorlevel effects. These were  
Determine contrasts in advance of observing the experimental results 
These types of investigations should be done on combinations of
factors that were determined in advance of observing the
experimental results, or else the confidence levels are not as
specified by the procedure. Also, doing several comparisons might
change the overall confidence level (see note
above). This can be avoided by carefully selecting contrasts to
investigate in advance and making sure that:


Tests on Means after Experimentation  
Procedures for performing multiple comparisons 
If the decision on what comparisons to make is withheld until after
the data are examined, the following procedures can be used:


Multiple Comparisons Between Proportions  
Procedure for proportion defective data  When we are dealing with population proportion defective data, the Marascuilo procedure can be used to simultaneously examine comparisons between all groups after the data have been collected. 