I would really appreciate any advice here on if there are any special parameters I need to use for this example. I am looking at the effect of an analgesic on pain level after ocular surgery. Both eyes receive surgery, but one receives the analgesic and the other doesn't and acts as the control. Would a paired t test be appropriate to compare the differences (pain level postop in eye with analgesic vs eye without)? Thanks so much!
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1$\begingroup$ How is pain level measured? How frequently? Some type of paired analysis is called for, but a t-test might not be appropriate depending on those details. $\endgroup$– EdMCommented Jun 29, 2022 at 17:44
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$\begingroup$ Thank you for responding! The pain level is from a 0-5 scale and was recorded over a period of 5 days daily. However, the greatest reduction in pain is on day 0 as that is when the anesthetic is at the greatest concentration (it is an extended release type of mechanism). $\endgroup$– Emily YCommented Jun 30, 2022 at 3:49
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With a 0-5 scale (often called a Likert item), a t-test isn't a good choice. You only have a small number of possible values or paired differences between values, so the underlying assumption of normally distributed error terms in t-tests won't hold.
Your outcome values are nevertheless ordinal, in that each higher value on the scale represents a higher level of pain, although the levels might not be evenly spaced. There are well established ways for analyzing such ordinal outcomes, with ordinal logistic regression a frequent choice.
Furthermore, as you note, you have paired results on the two eyes from each participant in the study, one eye the control and the other treated. One way to account for this pairing is to treat the participants as "random effects" in a mixed model. In your situation, you would include as "fixed effects" the eye (control versus treated), the day (to account for changes over time) and an interaction between eye and day (to allow for different effects of treatment over time).
Sal Mangiafico's R Companion has a web page illustrating such a model with Student as the random effect, a Likert outcome similar to yours, Time as one fixed effect, Speaker as a second fixed effect, and an interaction between those two fixed effects. That should provide a direct template for your study. I would recommend that you find local statistical consultation for this analysis, particularly if there are other variables that your study needs to take into account.
