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?

  • $\begingroup$ Do the subjects all receive the same combinations of feedback, frequency and force, and each subject only once for each combination? $\endgroup$ Dec 6, 2019 at 17:53
  • $\begingroup$ @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. $\endgroup$
    – Luisda
    Dec 6, 2019 at 18:04
  • $\begingroup$ OK, and are you interested in any change between measurement occasions ? $\endgroup$ Dec 6, 2019 at 18:47
  • 1
    $\begingroup$ @RobertLong No. Different trials are just meant as a mean to increase statistical power. $\endgroup$
    – Luisda
    Dec 6, 2019 at 19:15

1 Answer 1


Since the measurements are repeated for each subject, there is likely to be correlation within subjects because the measurements are not independent. A mixed effect model with random intercepts for subjects is a good way to model these data, whereas a 3-way ANOVA would lead to biased results.

  • $\begingroup$ The model you described would be coded as error ~ feedback * frequency * force + (1|subject)? I say this because of the doubt about the variables being nested $\endgroup$
    – Luisda
    Dec 6, 2019 at 23:04
  • $\begingroup$ 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. $\endgroup$ Dec 7, 2019 at 3:54
  • $\begingroup$ 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 $\endgroup$
    – Luisda
    Dec 9, 2019 at 17:40
  • $\begingroup$ That's a completely different question to do with model fit, so please describe the experimental setup explaining how all the variables including the response arise, in a new question. $\endgroup$ Dec 9, 2019 at 18:26
  • $\begingroup$ I posted a new question treating the topic here $\endgroup$
    – Luisda
    Dec 10, 2019 at 2:51

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