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Table 1 Examples of association parameters and distinguishability patterns between adjacent categories from NUA models in a 5 × 5 contingency table

From: Power estimation of tests in log-linear non-uniform association models for ordinal agreement

Hypothesis Association parameters Distinguishability patterns
H 0 All association parameters are equal  
  β 1,2 = β 2,3 = β 3,4 = β 4,5 = log(3) 1 ---- 2 ---- 3 ---- 4 ---- 5
1 association parameter is different  
β 1,2β 2,3 = β 3,4 = β 4,5 = log(3) 1 - 2 ---- 3 ---- 4 ---- 5
1-------- 2 - 3 - 4 ---- 5
β 2,3β 1,2 = β 3,4 = β 4,5 = log(3) 1 ---- 2 - 3 ---- 4 ---- 5
1 -- 2-------- 3 - 4 -- 5
Β 3,4β 1,2 = β 2,3 = β 4,5 = log(3) 1------ 2 -- 3 - 4 -- 5
1 -- 2 - 3 ------ 4 - 5
Β 4,5β 1,2 = β 2,3 = β 3,4 = log(3) 1 ---- 2 ---- 3 ---- 4 - 5
1 - 2 -- 3 - 4 ---------- 5
2 association parameters are different  
β 1,2 = β 2,3β 3,4 = β 4,5 = log(3) 1-2 - 3------4------5
1------2------ 3-4-5
β 1,2 = β 4,3β 2,3 = β 3,4 = log(3) 1--2---- 3---- 4--5
1 ---- 2 - 3 - 4 ---- 5
  All association parameters are different  
β 1,2β 2,3β 3,4β 4,5 1 - 2 ---- 3 -- 4 ------ 5
  1. *Distinguishabilities values between two categories are proportionnal to number of dashed-lines between these two categories
  2. Symmetric hypotheses in association parameters: and , and