I suggest using a beta-model or a quasi-binomial model (after normalizing the values (so that min=0, max=1). This would model the odds of correct answers, what seems a sensible thing to do.

Since this is not such a standard procedure and you said you are "new to statistics", I also strongly suggest to get help from a statistician from your university.

I would not recommend non-parametric analyses because they will be hard to interpret in a practically meaningful way.

Hello Kristina,

Do I understand correctly that you exposed all participants to all 12 conditions (4 levels of occupancy crossed with 3 levels of room condition); in other words, that both IVs are within-subjects factors?

If your sample histogram is showing that most participants obtain the maximum possible score then, as Jochen Wilhelm suggests, perhaps an alternative analytic framework would be better suited (and the associated question changing to whether participants do or don't obtain perfect or near-perfect scores in a given condition combination). If this were a between-subjects design, I could see a case for a log-linear model (with the frequency of fully correct responses being the observation, though sample size would be an important consideration).

If you're completely sold on just comparing means, you could use bootstrap estimation for the significance tests (this is available in spss which you appear to be using, based on the figure you gave).

You could use the Friedman procedure (with all 12 combinations as levels), but there would be a _lot_ of tied ranks in your data set.

Good luck with your work.

What is/are the outcome variable/s? You said errors, so are they presented with a number of trials in each of the 12 conditions where they can either make an error or not?

Jochen Wilhelm Thank you very much for your suggestion! It indeed sounds like a good idea to seek help from a statistician of the university. David Morse they are indeed within-subject factors. Daniel Wright the subjects are presented to a spoken sentence in the 12 different sound environments (15 sentences per sound environment) and get to choose from 6 sentences which one they heard (in the answers the verb, adjective or object of the sentences were changed).

Kristina Mues wrote: "... and get to choose from 6 sentences which one they heard".

How many of the 6 test sentences per cell match one of the 15 sentences that were presented previously? You said "which one", which suggests that only 1 of the 6 matched a previously presented sentence. But that would suggest a maximum "score" of 12, and your histogram shows a maximum score of 15. So I'm still a bit confused! Thanks for clarifying.

Bruce Weaver After each sentence a subject heard they got to choose between 6 sentences( where only one word differed). So they got to choose 15 times per sound environment from a different set of 6 sentences. I hope this clarifies the situation.

Thanks for clarifying, Kristina. So for each subject, there are 4 * 3 * 15 (occupancy * room * sentence) "trials" of choosing from among 6 sentences the one that was heard just previously.

What is your sample size? That histogram you uploaded looks like it was produced with SPSS. Do you use (or have access to) any other statistical software?

Were the sentences randomly allocated to the different conditions so that sentence does not confound condition?

If so, I think the commentators are moving towards a generalized multilevel (or mixed) model, since the individual trial will be the sentence. There can be discussion about which distribution to assume, but I am in Las Vegas so I'll wait five days to answer.

Bruce Weaver correct. my sample size at the time was 40, by now I have a sample size of 52 and I am hoping to get to a sample size around 60. Furthermore I indeed use SPSS and I am not aware of any other statistical software that I can use trough my university.

Daniel Wright Yes the sentences were randomly allocated to the different conditions.

Thanks for clarifying, Kristina. If you are able to get your hands on it, I think you will find this book helpful:

https://www.routledge.com/Multilevel-Modeling-of-Categorical-Outcomes-Using-IBM-SPSS/Heck-Thomas-Tabata/p/book/9781848729568

It should have an example or two of using GENLINMIXED to estimate multilevel logistic regression models with repeated measures. It might also show how to use GENLIN with generalized estimating equations (GEE), which is another way to account for the correlated nature of repeated measures.

Here are some other resources you might find helpful.

• https://www.bristol.ac.uk/cmm/
• https://www.pilesofvariance.com/

HTH.

Pay attention to one important point.

In ANOVA or RM analysis, the question is not that:

Assume Gaussian (Normal) Distribution of Data?

But this is the right question:

Assume Gaussian (Normal) Distribution of Residuals?

So check the normality of the Residuals of the GLM model (like the RM or ANOVA).

The best software for this study is not SPSS but GraphPad Prism v9.