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I'm conducting an experimental study. For each group (treatment/control) I have measured the biometrics of both eyeballs (left/right) of each participant.

Can I make a comparison between values of both eyeballs from the control group versus the values of both eyeballs from the experimental group? It seems that inside each group the values are paired, but between the groups, the values are not.

Should I use regular independent tests? Or I should use the mean of both eyeballs? I'd highly appreciate any help.

Example data:

Group   name     eyeball   measurement  
------- -------- --------- -------------
CTL     John     L         0.1          
CTL     John     R         0.2          
CTL     Tom      L         0.1          
CTL     Tom      R         0.1          
CTL     George   L         0.3          
CTL     George   R         0.2          
CTL     Paul     L         0.2          
CTL     Paul     R         0.1          
TRT     Luke     L         0.2          
TRT     Luke     R         0.2          
TRT     Jim      L         0.3          
TRT     Jim      R         0.1          
TRT     Chris    L         0.3          
TRT     Chris    R         0.4          
TRT     Ryan     L         0.3          
TRT     Ryan     R         0.1  
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    $\begingroup$ You may benefit from reading this article. $\endgroup$ Mar 31, 2020 at 10:21
  • $\begingroup$ Thank you. I am aware of it, nevertheless I am hesitant can we treat two eyeballs as repeated measures? I think that it is not the same entity as repeated measures need time points as well. Here we measure two eyeballs at the same time. $\endgroup$
    – Tom
    Mar 31, 2020 at 10:24
  • $\begingroup$ From where I stand, it really looks like a repeated measures design. What makes you doubt? Is your biometric measurement impacted by e.g. eye dominance? $\endgroup$ Mar 31, 2020 at 10:35
  • $\begingroup$ I added data to have a preview on it. I do not repeat measures for eyeballs I just measure both of them at the same time, so I obtain a measurement for each eyeball which belong to one person. I would like to perform a difference comparison within two groups (treatment/control), for example: mean comparision. Can I treat each eyeball as separated entity/value and just use independent test or should I calculate mean from both eyeballs and assign mean to each person and then run a test or maybe mixed models or I should go for more appropiate tools that are not so trivial? $\endgroup$
    – Tom
    Mar 31, 2020 at 11:12

1 Answer 1

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As you are not interested in the differences between the left and right eyeballs, you should calculate the mean of both eyeballs for each person, and then use an independent samples t-test to see whether the control and treatment groups differ.

The design is not a repeated measures design. Firstly, nothing has been measured more than once (Ryan's right eyeball was only measured once, for example).

Secondly, the two groups contain different people. A repeated measures design would involve measuring Ryan's eyeball (the control group), doing something to Ryan (some experimental treatment) and then measuring Ryan's eyeball again (the treatment group).

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  • $\begingroup$ But aren't eyeballs independent entities? Can we just take a mean of both eyes? It does not seem really plausible for me. My intuition says that we should use all eyeballs and use them as a individual values. Big concern is the impact on statistical methods as we define those as mean or as individual values. $\endgroup$
    – Tom
    Mar 31, 2020 at 13:09
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    $\begingroup$ The problem with using all the eyeball measurements is that our statistical test becomes too liberal because we are doubling up on the degrees of freedom. The right and left eyeballs in Ryan's head are NOT independent, they belong to Ryan. Technically we have a nested design, with eyeballs nested within each person. You could use an ANOVA that uses a nested random component (left and right eyeball) but it's much simpler to calculate the mean of both eyeballs. $\endgroup$ Mar 31, 2020 at 13:25
  • $\begingroup$ If you found the answer useful, please help other users by accepting the answer. Thank you. $\endgroup$ Apr 1, 2020 at 12:25

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