Does ordinal logistic regression substitute for "multifactorial Friedman test"?

by exin   Last Updated September 12, 2019 01:19 AM

I'm searching for an appropriate statistical test, more or less a multifactorial version of Friedman test. But I'm also wondering if Wilcoxons rank sum test can do the job.

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. H0: scores in T1 = T2)
x2 - t0, t5, t10... (13 time points)
x3 - Q1 to Q4 (4 quartiles)

Choices:
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, I've never used this before and wonder if it fits my purpose at all.

Advice would be greatly appreciated!



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