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Background: I have 2x8 conditions. I can visualise the 8 different cases on a continuous line (x-axis) and now want to plot the mean and confidence intervals for the 2 different treatments. The CIs shall visualize whether the treatments outcomes are different with 95% confidence.

Question: What are the right confidence intervals to plot when (a) the samples are independent (all different individuals between treatment) and (b) the samples are dependent (the same individuals do both treatments).

Thoughts: Assume, that we plot the 95% CIs for both treatments. I assume one can only be certain at the 90.25% (=0.95*0.95) level since both CIs need to hold for this to be true? If this is the case, the right CIs would be sqrt(0.95). Can one also visualize meaningful CIs, if the observations are dependent?

Thanks a lot!

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  • $\begingroup$ +1 The thought processes at stats.stackexchange.com/a/18259/919 look relevant. The idea behind notched boxplots is also useful. $\endgroup$
    – whuber ♦
    Commented Feb 27, 2022 at 15:38
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    $\begingroup$ Thank you, this was exactly what I was looking for! $\endgroup$
    – Chris
    Commented Feb 28, 2022 at 12:12

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