Non-parametric repeated-measure ANOVA for multifactorial design?

by exin   Last Updated September 11, 2019 13:24 PM

I'm searching for an appropriate statistical test, briefly as described in the title.

Expt design:

10 larvae are allowed to swim in an experiment chamber virtually divided into 4 brightness quartiles (Q1 to Q4, Q1 being closest to a lamp source).
They are recorded for 1 minute. Every 5 seconds I score the number of larvae that's in each quartile (score out of 10 for t0, t5, t10, t15 etc.).
This assay is run 3 times for each treatment (T1, T2)(different drugs being added to the water).

Hence I have:
y - score (not normally distributed)
x1 - T1, T2 (what I really care about)
x2 - t0, t5, t10... (13 time points)
x3 - Q1 to Q4 (4 quartiles)

1. Simply do a Wilcoxon rank sum test to compare Scores between T1 and T2, across the timepoints (treat as 2 series of data, paired). Do this for each quartile separately. 2. non-parametric version of repeated measures ANOVA (Friedman test), but this doesn't cater for a multifactorial design.

1 is probably over-simplifying it. I can't seem to find the solution to 2.
Ordinal logistic regression seems to be an option too...?

Advice would be greatly appreciated!

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