Background: Eight doctors each rated the same 54 patients on a persuasiveness measure (1-7 Likert scale). The mean score on the persuasiveness measure will eventually be the outcome measure of my experiment. 

Inter-rater reliability was quantified as the intraclass correlation coefficient (ICC), using the two-way random effects model with consistency. Unfortunately, the inter-rater reliability of the eight doctors was low (ICC = .350, single measures). Should I still run further planned analyses with these unreliable data? Or can it possibly be justified that I only include the doctors (i.e., raters) with the highest inter-rater reliability? I found out there are two doctors with a more acceptable inter-rater reliability (ICC = .718, N = 2), but I don't think this is enough reason to exclude the other doctors from analyses. I would really appreciate any references to literature that deals with this problem.


Question: Idolatry in churches allowed?
Answer: You're operating under a misconception that these are idols. Most Christians don't worship these images, statues, etc. Instead, they are considered art, something that we  create because we love the subject, not the work of art.

Asking your question is like asking if looking at a painting of my wife means that I am allowed to cheat on her by devoting my affection to an image of her. I love her, not the painting of her. Christians love Jesus, not the statues of Him.

So, the answer id no, idolatry isn't allowed in Churches.  

Addressing the updates to the question, the things that people are "venerating" are likely "Sacrementals".


  Sacramentals are material objects, things or actions (sacramentalia) set apart or blessed by the Roman and Eastern Catholic
  Churches, the Eastern and Oriental Orthodox Churches, the Church of
  the East, the Anglican Churches, the Independent and Old Catholic
  Churches, and the Lutheran Churches to manifest the respect due to the
  sacraments, and so to excite good thoughts and to increase devotion,
  and through these movements of the heart to remit venial sin,
  according to the Council of Trent (Session XXII, 15).
  
  In Roman Catholicism, sacramentals such as Holy water, the crucifix or
  the Saint Benedict Medal are recommended as a means of protection
  against evil.


Again, the devotion is not to these things, but to the God they represent. There are, those that do worship them like idols, and many view the idea that these could protect us from evil as superstitious, the point remains that officially, these aren't idols. They aren't to be worshiped. They are reminders of the one we should be worshiping.