Question 3: Why is weighted kappa larger than simple kappa?
Simple kappa gives equal weight to all disagreements. When categories are ordered, we usually see more disagreements where the observations record categories close together, often adjacent, than we see disagreements where the observations record categories which are far apart. Hence we expect most disagreements to have low weight and relatively few to have high weight. Hence weighted kappa tends to indicate better agreement than does simple kappa and so to have a larger value.
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