# Nonparametric test for trend using Python

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?

• Welcome to the site, @alexhli. If this question were only searching for a function or library to do this in Python, it would be off-topic for CV (see our help page). However, it's not clear to me whether that's what you are asking (eg, "preferably in Python"). If you have a substantive statistical question about these methods beyond looking for a function, would you edit to clarify it? – gung - Reinstate Monica Oct 17 '13 at 19:15
• If you were to modify the question to something like "What is a way or ways to what I want, and is there a python implementation?" the first part should be sufficiently on topic. But then your question would require clarification (you end by asking about exploring, not testing -- those are very different exercises) – Glen_b -Reinstate Monica Oct 17 '13 at 20:24
• There appear to be implementations of that Cuzick method in R. (e.g. Here, or here). I haven't tried these, but I'm wondering if a rank-based correlation like Spearman or Kendall would accomplish essentially the same thing. – Sal Mangiafico Aug 30 '18 at 0:59
• Just for fun, I ran some comparisons on simulated data between the Cuzick test and Spearman correlation. (Not publication quality). Just looking at p-values: The p-values for the tests follow each other, but there's some scatter. For example when the p <= 0.05 for Cuzick test, 85% - 90% of p values from Spearman are <=0.05. If you look only at cases where Cuzick p <= 0.04 and Spearman p <= 0.05 this becomes about 95%. If you look only at cases where Cuzick p <= 0.03 and Spearman p <= 0.05 this becomes about 97%. There was no clear bias in power favoring either test. – Sal Mangiafico Aug 30 '18 at 14:16

Also, it is implemented in R in the clinfun package.