I am looking to perform a nonparametric test for trend on a continuous outcome across three groups, preferably in Python. For example height (pretend height is not normal) in 4th, 5th and 6th graders.
I would like to implement something like the Cuzick method. Scipy has Wilcoxon rank sum and other nonparametric methods but only for two groups. Similarly, Scipy has a Kruskal-Wallis method for three groups but it does not indicate direction or trends. Does anything like this exist for exploring a directional trend across three groups?
To clarify I am trying to determining whether there is a significant shift in a continuous trait measured across three groups. The groups will be of very different size: group 1 has 1000's of samples and likely to be normally distributed, group 2 100's os samples, group 3 ~10 or less. Group 1 serves as the "control" group, and my hypothesis is that the mean value of group 1 will be shifted in either direction relative to group 0, and group 2 will be shifted further in the same direction as group 1. Because group 3 will always be very small compared to the other group, my instinct was to use nonparametric methods, but I am open to other suggestions.
Can anyone suggest a method to explore this type of directional trend?