This sounds interesting but so far I cam't follow what you are doing. Can you give a more specific example, a show us what the data looks like, please

Many thanks for your reply! Here's how it looks like with more precision and examples from the data (if more information is helpful I will be happy to provide it): participants (N= 600, which is enough according to a predictive power analysis) read an utterance for instance 'some of the five apples are red'. Next, participants had to bet by dividing the sum of 100 between six options: 0 objects out of 5 have a property vs. 1 object out of 5 has a property vs. 2 objects out of 5 have a property vs. 3 objects out of five have a property vs. 4 objects out of five have a property vs. 5 objects out of 5 have a property. For instance, one person bet 0, 10, 40, 40, 10, 0. I took the mean bets for all answers.

Here's an example graph, it presents the mean bets on each of the options, I compared with a paired samples t-test the mean bets on 4 and 5, but the Reviewer pointed out that this is not the right test for this sort of compositional data. Thus my question: which test is appropriate then?