I am using SPSS and my model is: 3 raters, two-way mixed effects, absolute agreement. Data are far from normality, I do not know a non parametric procedure and I do prefer not to categorize the continuous data and so use kappa.
Hello Sourangshu,
Normality isn't essential in order to compute a correlation. It is true that, if two score vectors have different marginal distributions, then the maximum correlation cannot reach +/- 1.
For your specific instance, which statistic (ICC or kappa) would better answer your research question? Let that be your guide.
Good luck with your work.
You might consider Lin's concordance coefficient. This is based on the squared difference between the measurements – you can think of it as measuring the squared distance between each measurement pair and the 45º line of perfect agreement. It works with small sample sizes, and makes fewer assumptions about distribution than the ICC.
That said, I would check a Bland and Altman plot to make sure that disagreement is not correlated with absolute value, or concentrated in some part of the range of the variable. This will not be captured by a one-size-fits-all measure, whether ICC or Lin's C.
Note that weighted kappa (with quadratic weights) is equivalent to one common form of the ICC. (See attached.)
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