I am running the Jonckheere-Terpstra in place of Kruskal-Wallis test, as my factor is in ordinal scale (i.e. groups can be ordered).
The Asymptotic significance (2-tailed) is 0.000, so it seems there is a trend in the response variable, according to the trend of the factor.
However, if I look at the medians, this trend is not clear; in fact I have 4 levels in my factor and, in ascending order, their medians are: 0.1387, 0.2814, 0.5882, 0.3492.
So, I ran a Mann Withney test with Bonferroni correction to check if the difference between last two pairs is significant and it is NOT.
Two questions: 1) Am I doing it right? 2) I ran the J-T test for another response variable, which is ordered conversely with respect to the factor (i.e. if I increase the factor, the response variable decreases). If the J-T statistic is NEGATIVE and the p-value is 0.000, can I conclude that the response variable is DECREASING (instead of increasing) according to a factor increase?