For finalizing the change-point
determination, for testing the homogeneity of the means of the sequences separating
change-points, these sequences are re-arranged in increasing order of rank averages.
Groups of sequences having homogeneous rank means are then selected with a trend analysis
similar to the preceding one.
After verification of
independence and identity of the distribution for each determined new group, if the normal
assumption is found to be valid for the original data inside each selected group
(Shapiro-Wilk test for normality, 1965), homogeneity of variances and of means may be
tested for each group of data with parametric tests. For testing homogeneity of variances
and of means, likelihood-ratio tests have then to be used (Mood,
1950). If the underlying
distribution of data remains unspecified, rank tests have to be applied (Siegel
1956).
Final groupings are then accepted
only if differences between close mean values are found to be significant at the size of
the complete series (Sneyers 1975).
