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There are 3 subjective methods to measure the severity of a condition. Each method measures it on an ordinal scale, but the scales are different:

method 1 scale is 1-3

method 2 scale is 1-4

method 3 scale is 1-5

Evaluation of a condition according to each method is performed by 3 raters.

Krippendorff's alpha seems like an optimal approach to calculate the agreement between those 3 rates.

How could I compare the 3 resulting Krippendorff's alphas for each method and estimate if one method gives significantly better agreement than the other 2?

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Assuming zero bias among the raters, the "1-4" and "1-5" will have the best agreement. This is actually a simple math problem. When you round a number to fit in a scale of "1-3," you lose more information than you lose with bigger scales.

The bias issue may be a problem. If you ask person A to rate using both scales: (disagree, agree, strongly agree) and (strongly disagree, disagree, agree, strongly agree), would person B do it the same way? People have different intuitive thresholds for "strongly." And then there's the standard bias issue. Seeing things differently.

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  • $\begingroup$ I would expect the opposite: the bigger the number of categories is, the less is the chance for raters to agree. However, it does answer the question: how can I compare if one method gives significantly better agreement than the other 2. Can I test it or shall I bootstrap and look at CIs? $\endgroup$
    – Gregory
    Commented Jul 20, 2020 at 11:17
  • $\begingroup$ How are you measuring bias if you reduce the available scale, hoping for more consistency? You may not actually get that. -- If you are just looking for absolute agreement percent between the two methods, run two tests on two different groups. Group A gets 3 choice answers. Group B gets 5 choice answers. Then count the number of exact matches in both groups. $\endgroup$
    – user255758
    Commented Jul 21, 2020 at 2:32

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