Question 4: Why is the limits of agreement approach inappropriate for the comparison of two observers? What would be better?
The limits of agreement approach was designed to measure the agreement between two different methods of measurement of the same thing. Although we can treat two observers, or a first and second observation by the same observer, in the same way, the estimate which we get is not useful. Other researchers or clinicians are not going to be using these particular observers, so a method which involves estimating the direction of the a method which involves estimating the direction of the bias between them has no relevance.
We can find similar statistics, repeatability coefficients, which do not do this and estimate instead how far apart measurements by two different observers or two measurements by the same observer are likely to be.
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