ok, then I understand.

Power is a fundamental value to contextualize the conclusions, right?

Yes, I think then that I should carry out the 2x2 analysis because I do not have enough power to analyze 2x2x4x4 with this sample, which could lead to erroneous conclusions.

I am using the glimmpse calculator to calculate the sample size, but the sample offered for the 2x2x4x4 interaction is unattainable on a practical level. However if I choose the 2x2 interaction it would be achievable. Would this be a justification for choosing only 2x2? The study must be carried out in a complete 2x2x4x4 manner because the 4x4 interaction will be analyzed from the perspective of reliability.

I add a little extra complexity. The Glimmpse sample size calculator for LLM with the full 2x2x4x4 model if I choose the 2x2x4x4 hypothesis, does not offer me enough power with my sample size, however with the full model if I choose the 2x2 hypothesis it does. Could this be a justification for reporting only the result for the 2x2 interaction? On the other hand, it is curious, if in this calculator I enter the 2x2 model instead of the complete 2x2x4x4 model, when before it had enough power, now I don't have it. I understand that it could be another topic...

The objective is to simplify the analysis and, above all, the writing of the results. This is a complex analysis with many interactions. Furthermore, these data will be analyzed from a reliability perspective later.

LMM requires more "guesswork" for estimating the sample size, to the point of requiring specific data on the group means as well as their relationship coefficients. Assuming this is the first study on the topic, to what extent can it be ethical to make conjectures about the required data? And then, once the study is completed, what happens if your initial guesses do not match the results obtained in the study? For this reason, could doing a retrospective analysis be considered a better option? That is, carry out a study with a specific sample, and report the power obtained.

What I wanted to say is that the justification of a sample size similar to that of another study that, although it did not analyze the same, analyzed similar things, is sufficient. By this it means that for example, to calculate the sample size of an LMM, using the GLIMMPSE calculator, it asks for really specific data, such as the average of the groups, the correlation between them, etc..., and all of these data I understand that should be justified in the writing of the article. If we do not have studies that have analyzed this, how can I justify the choice of specific values?

Finally I think I will choose to try to carry out a mixed model. I will also include more subjects in the study, I think I will be able to increase the sample by 3 or 4 more subjects. In this case, what assumptions should the variables follow? I suppose that, as happens in an anova, the assumptions of normality must be met, as well as equality of variances. Or would it be something different for mixed models? In your case, could they be carried out in software such as JASP or Jamovi?

Yes sure, I can share the data

I want to verify if the changes measured in speed by the instrument are real, that is, if the error is smaller than the changes between shoes. This will be the main objective of the study. For this I am going to calculate the reliability in the form of standard error of measurement (SEM). In SEM I will contextualize it, and see if it is smaller, than the difference in speed between the different shoes and I will visualize it in a dot graph with the SEM in horizontal bars. If the error bars overlap, it means that the difference is not real. Can this be achieved with an LMM system? 2/2

I understood the reason for not using paired samples t-test. Interaction of factors or fatigue could mask data. Could I then do a repeated measures ANOVA? I also understood that the sample size would be 10, even though there were more than 10 measurements in each group. The truth is that LMM is very far from my knowledge right now, but if it is the best option I could try to learn it. Another note, we know that significance testing is not always related to practical or real importance. In this sense, what I am looking to do is the following. 1/2

My only interest is know if there are differences between indoor and outdoor. After this I want to analyze reliability, and after this using standard error of measurement, contextualize results.

Why is not correct to analyze all data together for indoor and outdoor and do a T-Test?