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I have a distribution of values for each of 12 months. When I draw the boxplots (one boxplot for each month) the median gradually increases, but the boxes overlap.

Which test do I have to use in order to tell whether this seeming increase is significant or not? Also, how would I quantify the increase? e.g. if between January and Feb the median increased by 1, but the box plots for these two months largely overlap, is that even meaningful?

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  • $\begingroup$ You would likely get a better answer if you told us more about your data - for example, are these the same units observed each month, or a new set of units each month? Are you interested primarily in whether the median is different, or the mean, or something else? $\endgroup$ Feb 15 at 15:28
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You could use time series regression, and test whether the slope/trend has a significant coefficient after accounting for months. This page might be a good place for more details.

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