# What type of statistical analysis to perform?

I have an experiment with 10 subjects.

Each of them has to exert force and real-time feedback is received. Each subject experiences all 3 types of feedback (within-subject factor).

Moreover, each type of feedback may be filtered either at 2 or 5 Hz. Again, each subject experiences both filtering frequencies (within-subject factor).

Finally, for each feedback type and filtering frequency, the participant must follow a trace with one of two mean force levels. Once more, both mean force levels are presented to every subject for every feedback type and frequency combination (within-subject factor).

Should I implement a 3-way ANOVA or a Linear Mixel Model (e.g. outcome ~ feedback * frequency * force + (1|subject))? Or something else?

• Do the subjects all receive the same combinations of feedback, frequency and force, and each subject only once for each combination? Dec 6, 2019 at 17:53
• @RobertLong Do the subjects all receive the same combinations of fedback, frequency and force? -> Yes. All of them (3 feedbacks * 2 frequencies * 2 forces = 12 combinations for each subject). BUT each subject receives 2 times each combinations, so there are in total 24 trials per subject. Dec 6, 2019 at 18:04
• OK, and are you interested in any change between measurement occasions ? Dec 6, 2019 at 18:47
• @RobertLong No. Different trials are just meant as a mean to increase statistical power. Dec 6, 2019 at 19:15

• If error is your outcome variable then yes. These are no nested random effects since you have only 1 grouping variable, but you have clustered data because of the repeated measures. Dec 7, 2019 at 3:54
• I fitted the LME model as recommended by you. When checking for model soundness, I found the residuals to be really large and also their variance depends linearly on the x values. Because error is the outcome variable and is a RMSE, it follows a Chi-squared distribution. Is that affecting my residuals? Thanks for any help Dec 9, 2019 at 17:40