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I am trying to figure out the statistics of a study where I have 60 participants with varying amounts of observations per participant. I am measuring facial muscle activity after a button press over a 45-minute period. Now some participants have 1 or 2 button presses while others have 13.

I am interested in whether positively rated button presses go with more muscle activation than negatively rated button presses. Participants first press a button and later rate the valence (pos or neg) connected to this button press. When I take a t-test comparing the muscle activity of negatively rated button presses with positive ones I think I am not taking into account the variation within participants / paired data.

I have considered doing a multilevel approach but then I would have to use regression which would mean assuming a causal direction, which I do not have.

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    $\begingroup$ Regression doesn't require "assuming a causal direction." In fact, your t-test can be thought of as a very simple form of regression, with a single binary "predictor" (positive vs negative button press) and a continuous outcome (muscle activity). Correcting for within-participant correlations is critical, as you otherwise overweight those with more observations. $\endgroup$
    – EdM
    Commented Apr 19, 2022 at 16:48
  • $\begingroup$ Ah okay. I took that information from websites that say that in regression we test how x influences y and that changing the order of the variables leads to different results. I think that the order is not clear in my case. Does the subjective judgment of valence come first or does the physiological reaction of valence come first (James-Lange theory). I feel like I would need to make a decision (assume one theory but not the other) when using regression, whereas a t-test would just test if there is a significant difference. $\endgroup$
    – Leon
    Commented Apr 20, 2022 at 10:01
  • $\begingroup$ Please edit the question to say more about what you mean by "negatively rated button press." Is the "negative rating" something that's known at the time of the button press, or is that "negative rating" of the button press determined by the participant at some time during or after the measurement of facial muscle activity? Please do that by editing the question, as comments are easy to overlook and can be deleted. $\endgroup$
    – EdM
    Commented Apr 21, 2022 at 15:32
  • $\begingroup$ Adjusted! It is indeed a rating that follows after the button press and therefore also after the measurement of facial muscle activity. $\endgroup$
    – Leon
    Commented Apr 22, 2022 at 19:24
  • $\begingroup$ If you found this answer helpful, then please consider upvoting and/or accepting it. $\endgroup$
    – kjetil b halvorsen ♦
    Commented May 21, 2022 at 15:04

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A standard t-test is handled exactly like a regression, just a very simple form of regression. So you didn't really avoid "a regression approach" at all.

A t-test no more avoids assuming a causal direction than a regression needs to choose one. With your design you don't seem to be able to distinguish which is the cause and which is effect, so any analysis will just show associations.

The most direct extension of your t-test would be a regression model that takes the different numbers of cases among individuals and the likely correlation of results within individuals into account. Your measure of facial muscle activity would be the dependent/outcome variable and the negative/positive assessment would be the independent/predictor variable.

A mixed linear regression model, treating the individuals as random effects, is a common way to take the individuals into account. That's implemented, for example, in the lmer() function of the R lme4 package. This question seems similar to yours in this respect. A generalized least squares model might also work. Both approaches can be implemented via the R nlme package.

You might want to consider whether you should include the trial number as a predictor in some way, to allow for a "learning effect" that might change the association between muscle activity and the negative/positive assessment as the individual becomes more used to the testing procedure.

It might be interesting to turn the model around and use the facial muscle activity as the "independent" variable and the negative/positive assessment as the "dependent" variable. That could be done with a mixed-model logistic regression, e.g. via the glmer() function in lme4. Then you could say that you evaluated the associations in both directions. You also could model the muscle activity flexibly with a regression spline, which might uncover some more subtle associations than you would find by just modeling the mean muscle activity as a function of the negative/positive assessment.

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  • $\begingroup$ If you found this answer helpful, then please consider upvoting and/or accepting it. $\endgroup$
    – kjetil b halvorsen ♦
    Commented May 21, 2022 at 15:04
  • $\begingroup$ Thanks a lot for the extensive answer! The emotion assessment is actually also continuous (0-10, where 0 is most negative and 10 most positive) so a logistic regression is not needed. If I do two mixed linear regressions to test both directions, I will have doubled my chances to find a significant effect so I need to correct for multiple comparisons correct? $\endgroup$
    – Leon
    Commented May 23, 2022 at 9:56
  • $\begingroup$ I also want to test whether facial muscle activity is stronger during the experiment trials when compared to baseline. I have measured two muscles. Is it correct that in this case, I would do a mixed-model logistic regression where I predict the time period (baseline vs. experiment) from the activity of muscle one and activity of muscle 2. $\endgroup$
    – Leon
    Commented May 23, 2022 at 13:22

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