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Let's say there was an experiment with two groups that I'd like to compare, both with three biological* (n = 3) and three technical* (N = 3) replicates each. For statistical analysis, I'd average the technical replicates in advance (meaning that three values for each group remain) and then only compare the means. (I know it's a small sample size but let's please ignore that aspect here.)

Now I was wondering if it's legitimate to display individual measurements from technical replicates in figures or if it's rather misleading? Below you will find an example (data is made up) including all individual measurements (left side) and averaged technical replicates (right side). On the one hand, I believe that including all individual measurements will give the reader additional information about the obtained data. On the other hand, I think that illustration might be misleading as I'm using the averages for statistical analyses. Is there one "right" way to display the data? Is there an alternative that shows the variation both among technical replicates and among biological replicates?

*biological replicates: measurements of distinct biological samples, e.g. three different animals to assess biological variation

technical replicates: repeated measurements of the same sample to assess variation in the method (e.g. acquiring data from the same animal three times)

enter image description here

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    $\begingroup$ The distinction between biological replicates and technical replicates may be utterly standard in your field, but I imagine it's not familiar to many readers and not just me. That aside, I can see many advantages and few disadvantages to showing raw measurements in situations like this. Doubtless your readers will want to be told which is which. $\endgroup$
    – Nick Cox
    Commented May 25, 2021 at 18:23
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    $\begingroup$ You can just make it obvious through the text and visual cues what the data being represented is e.g. you can color the technical/biological replicates with the same color and clarify in figure description what the plot is showing. Its only misleading if you are not transparent about what you are showing $\endgroup$
    – bdeonovic
    Commented May 25, 2021 at 18:41
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    $\begingroup$ You have plenty of graphical options (lightness, shape, size, pattern, perhaps even color) to distinguish animals from each other as well as geometrical options (position) and artistic options (adding graphical grouping elements like boxes or brackets). Why not utilize them? $\endgroup$
    – whuber
    Commented May 25, 2021 at 18:41
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    $\begingroup$ Also note in this particular example where you are basing inference off of the average of the averages, if the number of technical replicates is the same for each biological replicate then the average of the average is the same as the overall average. $\endgroup$
    – bdeonovic
    Commented May 25, 2021 at 19:01
  • $\begingroup$ Thank you guys for your valuable comments! I guess I didn't think this question through too well. I was mostly concerned about conventions in the scientific community as for me it is often unclear (e.g. from box- and barplots) whether technical replicates were included in the representation of data or not. I will make sure to be transparent about what I'm showing. $\endgroup$
    – mri
    Commented May 25, 2021 at 19:13

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Putting together some comments:

A simple approach is to use color coding for the biological replicates, with the same color used for all the technical replicates performed on an animal or sample. (Use colors that can be distinguished by color-blind individuals.) That way, the reader can see all the raw data while easily distinguishing technical variability (dispersion of same-color values) from biological variability (dispersion among colors). If color coding isn't feasible, use other visual cues like shapes.

One warning:

For statistical analysis, I'd average the technical replicates in advance (meaning that three values for each group remain) and then only compare the means.

It's generally better to include all of your technical replicates rather than taking the mean first. If you code each data point with both the animal and the group it belonged to, statistical software can do the within-animal averaging of technical replicates and then provide estimates not only of differences between groups but also of the magnitude of the technical variability. That can end up being very useful information.

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