Kruskal-Wallis multcompare comparison intervals

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currently I am analysing results of my study and I found that a good multcomparison for it would be using the kruskalwallis with dunn-sidak.
My question is now, how to interpret the comparison intervals, which are not confidence intervals. I know, that if they do not overlap, the data comes from different distributions. But how are these comparison intervals generated?
Through researching and playing with the data and multcompare graphs I found that the width of the comparison intervals equals to 4 x the standard error (obtained through [m] = multcompare(stats)). Why is that the case?
However, I cannot find a reference of how these standard errors are calculated. And I cannot find anything on the MATLAB documentation.
Can you help me?
Another question is how do I label the x-axis of the multcompare graph for a publication? In principal, 'ranks' should be correct, right?
Thank you and kind regards
Michael Werthmann
Michael Werthmann on 11 Jul 2021
Edited: Michael Werthmann on 11 Jul 2021
Okay, then I'll explain it.
I applied 4 different image registration to 30 image pairs and want to test if the algorithms could improve certain metrics.
For example, I tested if they significantly increased the Jaccard coefficient (segmentation overlap metric) compared to the initial value
In the top row, it is the initial comparison interval, followed by the intervals of the algorithms.
The boxplots for the data are also displayed. The initial Jaccard has the median around ~0.75. As you can see, the medians of the results from the algorithms are higher.
I used kruskal wallis and dunn sidak to create the multcompare.
All mean ranks of the algorithms are different compared to the initial, thus they are significantly different.
Does that help you in suggesting a x-label?
Scott MacKenzie
Scott MacKenzie on 11 Jul 2021
I'm not sure about the 2nd plot, but for the box plot, let's start first with the y-axis.
I doubt "Jaccard" is the correct label. The label should be whatever the values represent. For the first box, the value is about 0.77. What is that? Perhaps "Coefficient Increase" or "Segmentation Overlap", or whatever the measure represents.
For the x-axis label, an appropriate label is probably something like "Image Registration Technique". For the x-axis tick labels, the first one should probably be "Jaccard". The other four tick labels should be names associated with the algorithms. Probably, "Algorithm 1", "Algorithm 2", etc., is a bit bland. I'm sure you have better names for these. Hope this helps. Good luck.

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