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What is the minimum "recommended" sample size to generate boxplots?

If I'm comparing different methods and each method has a different sample size, is it fine to use boxplots for this comparison? If not, what is the best way to compare methods with different sample sizes?

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[I thought I had written an answer to the first question but I can't locate one.]

With 5 or fewer observations, you might as well just plot the actual points.

It doesn't matter when comparing across samples that the samples aren't the same size, but if you have much larger samples in some groups you should see more points outside the ends of the whiskers on those.

what is the best way to compare between methods with different sample size

You might compare quantile plots, perhaps, or (as Nick Cox has suggested on at least one of his answers, but which I also can't locate right now -- edit: see here) you might combine such a plot with a boxplot by plotting the quantile plot under the boxplot.

Nick shows an example of a quantile plot here

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    $\begingroup$ Other examples at stats.stackexchange.com/questions/114744/… stats.stackexchange.com/questions/181501/… $\endgroup$ – Nick Cox Feb 10 '16 at 9:17
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    $\begingroup$ This issue usually comes up only when generating side-by-side boxplots and one or more of the groups is small. In such cases, for visual comparison, it may be advisable to draw boxplots even for groups of one! Also, have you considered including a visual representation of the group size, such as (a) making box widths proportional to the size or (b) including a notch or other device to indicate the standard error of the median? $\endgroup$ – whuber Feb 10 '16 at 14:25

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