I've got a dataset where I want to compare statistical differences in data between two different experiments. The data has been collected from 5 participants who each took part in the same two experiments. However, rather than each participant contributing just 1 data point per experiment, each participant contributes thousands of data points (it's sensor data collected over each experiment.)

If each participant contributed just one data point per experiment, I'd just do a simple Wilcoxon rank test to find if there's a difference. However, because each participant contributes thousands of repeated measures, I am unsure of what to do.

The situation that I don't want to end up in is incorrectly running a Wilcoxon which 'thinks' the participant sample size is many thousands of individuals, not just 5. To sanity check this, when I run a Wilcoxon this way, I get a p << 0.001 and Z > -100 which seems ridiculous. However, equally, I think that if I summed up the repeated measures with just one mean or median value for each participant and then ran a Wilcoxon, I'd miss the scale of the data per participant.

This makes me think that I either need to run a mysterious special type of Wilcoxon or Wilcoxon is not the correct test- in which case how should I handle this data?

  • $\begingroup$ Is there any particular reason, why you need a nonparametric test? Else a mixed effects regression (ANOVA) with a fixed effect on the experiments and random effect on the participant seems to fit. $\endgroup$ – Bernhard Feb 7 '18 at 15:25

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