Test for non-parametric repeated measures for replicated block data

Question

I asked 133 students to rate 12 audio-samples (on a hedonic scale from 1 to 9):

• 4 of those samples were generated by myself (human),
• 4 of those by an algorithm (machine),
• 4 of those are random generated.

I used a 9-point hedonic scale (extremely dislike ... extremely like). The data is not normally distributed (and, given that it is an ordinal scale, going for a non-parametric test should be standard, as far as I know).

Therefore I concluded:

• we need a non-parametric test
• we compare ratings for 3 groups (human-composed, machine-composed, random-generated) and have one population of users, who are rating
• we therefore have connected samples (each user rates each audio-sample)
• we test 133 users and each of them rates 3x4=12 audio-samples

I ended up trying to use Friedman's test, as it is non-parametric and allows for testing 3 groups - but I always get the error:

not an unreplicated complete block design

... which makes sense, as the Friedman's test (as far as I now know) expects only 1 rating per user/group combination (and in my test scenario, each user gets to rate 4 samples per group).

Eg:

| Rating | ComposedBy | Person |
| -- | --- | --- |
| 7 | HUMAN | 1 |
| 8 | HUMAN | 1 |
| 6 | HUMAN | 1 |
| 8 | HUMAN | 1 |
| 5 | MACHINE | 1 |
| 6 | MACHINE | 1 |
| 2 | MACHINE | 1 |
| 7 | MACHINE | 1 |
| 2 | RANDOM | 1 |
| 1 | RANDOM | 1 |
| 2 | RANDOM | 1 |
| 5 | RANDOM | 1 |
| 6 | HUMAN | 2 |
| 7 | HUMAN | 2 |
| ... | ... | ... |

I'm a bit lost now:

• should I simply calculate the mean per user/group to reduce the dataset, so that I have only one value per ComposedBy/Person combination?
• Are there any replicated complete block design, non-parametric tests for more than 2 groups?

Can you help me out / give me input so I get back on track to do my research?

best regards david