Informative simultaneous confidence intervals for graphical test procedures

Area of Science:

• Statistics
• Statistical inference
• Multiple hypothesis testing

Background:

• Traditional simultaneous confidence intervals (SCIs) compatible with closed test procedures can be uninformative.
• The bounds of these SCIs may remain at the null hypothesis boundary, regardless of the point estimate's deviation.
• This limitation has been observed for Bonferroni-Holm and fall-back procedures.

Purpose of the Study:

• To extend the concept of informative simultaneous confidence intervals to graphical test procedures.
• To develop SCIs that are more informative than traditional ones while maintaining strong family-wise error rate control.
• To offer a practical alternative to existing multiple testing methods.

Main Methods:

• Definition of SCIs using a family of dual graphs.
• Application of the projection method for interval construction.
• Development of a simple iterative algorithm for computing the proposed SCIs.

Main Results:

• The newly suggested SCIs are free from the deficiency of traditional SCIs.
• Information gained from these SCIs increases with evidence against the null hypothesis.
• A simulation study demonstrated the effectiveness for a complex graphical test procedure.

Conclusions:

• The proposed informative SCIs offer a valuable compromise between information gain and power in multiple hypothesis testing.
• These intervals can serve as a replacement for initial multiple tests, providing strong family-wise error rate control.
• The method is applicable to graphical test procedures, enhancing their interpretability and utility.