High correlation but different median scores. How can this be possible?

#1
I am writing a research paper. We asked the same patients to fill out a form at two different times. Data is non-normal.

I used Spearman's correlation, which gave me a moderate correlation between the two scores. I also used weighted kappa and this too gave me a moderate agreement between both scores. But when I used the Wilcoxon signed-rank test, it told me the medians were statistically different.

How can I explain this result if all the other questionnaires had low agreement, low correlation and same median scores?
 

Karabiner

TS Contributor
#2
But when I used the Wilcoxon signed-rank test, it told me the medians were statistically different.
The Wilcoxon is not a test for medians, but anyway - it is important to note that there is no
connection between the size of a correlation and degree of (dis)similarity of central
tendencies. E.g. look at these 5 pairs:
1 11
2 12
3 13
4 14
5 15
There is a perfect correlation between the first and second column, but the means are
largely apart. They march in step, but on different levels.

With kind regards

Karabiner