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I have this specific boxplot that I would like to interpret in my conclusion for my master thesis. I noticed that the most right box does not have any outliers, but a very broad Q2 and Q3 range. Also the most left box seems to have lower outliers. Can I make a conclusions about this? Can anyone give me a push in the right direction?

Some context behind the graph: per category, there are 190 samples of which an error metric (eucledian distance expressed in pixels) per sample is plotted.

enter image description here

Edit. I have added Violin plots:

Original data: enter image description here Natural-log transformed: enter image description here Log-transformed: enter image description here

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  • $\begingroup$ Have you considered looking at a log scale on the axis? $\endgroup$
    – Glen_b
    Commented Nov 10, 2019 at 15:50
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    $\begingroup$ Natural log-transformed and log-transformed (some other base) should produce the same plots! Something else is wrong, e.g. use of a default setting that is a different number on each scale. $\endgroup$
    – Nick Cox
    Commented Nov 11, 2019 at 18:08
  • $\begingroup$ Have to agree with @nickcox. For me it looks like some weird rounding happened after log transformation, so all the values became integers. I would double check it. $\endgroup$ Commented Nov 11, 2019 at 18:21
  • $\begingroup$ Even though these are Euclidean [sic] distances, it's possible that you're seeing multimodality in the distribution e.g. distances of $1$, $\sqrt{2}$, etc. When only certain values are possible, smoothing them over with kernel density estimation isn't always the best thing to do. Your dataset is not too large to rule out posting it or say a 25% sample. $\endgroup$
    – Nick Cox
    Commented Nov 12, 2019 at 13:31
  • $\begingroup$ @German Demidov gave a very good answer on this information, which you should accept if it satisfies you. Otherwise saying more depends on seeing the data directly. $\endgroup$
    – Nick Cox
    Commented Nov 12, 2019 at 15:31

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At first, what is important is what your whiskers mean - https://en.wikipedia.org/wiki/Box_plot - it can be standard deviation (I would say no), or Tukey boxplot (I'd say this is what you have), or something else - check this out in the manual of your statistical toolbox. At second, these boxplots may be a bit "misleading" in some sense. These "outliers" may be just a part of your distribution and not "outliers" - if your distribution is highly skewed. I'd recommend you to use Violin plots and compare density mass in the regions of interest, assuming that there is no outliers. However, the decision on how to interpret the extreme dots is always up to you since you know your data better, I can just give an advice. You may also try log-transform your data and check what will happen in this case. Anyways, these plots are exploratory, and the answer to "Can I make a conclusions about this?" is, I would say, "no". I'd go with something like Dunn test to make conclusions.

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  • $\begingroup$ Good advice. I'd really recommend as a first step log transforming the y variable and plotting the box plots with that variable. That will give you a much better visual of the difference in distributions between groups. (Simply changing the y-axis of the current plot to log scale will do the same thing.) $\endgroup$ Commented Nov 10, 2019 at 14:47
  • $\begingroup$ Agree, log-transform is a good first step almost always (even thou he may have 0s). In this case it is some Euclidean distance and I am not sure if the shape of the distribution will become closer to normal after log-transform - but worth to try. Only Violin plots of - may be transformed data - may help. Adding to my advice about Dunn's test - graphpad.com/guides/prism/7/statistics/… - only careful exploration of the density plots may show it is applicable. $\endgroup$ Commented Nov 10, 2019 at 14:52
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    $\begingroup$ What points lie more than 1.5 IQR from the nearer quartile needs to be calculated afresh if you use a transformed scale. $\endgroup$
    – Nick Cox
    Commented Nov 10, 2019 at 19:42
  • $\begingroup$ I have added the violin plots. The natural log transform really outputs a nice graph. I can say that the distribution is somewhat equal for the first 3. Base and DR have an opposite shape, which I can explain in the results. Any other insights that I can make from this? $\endgroup$
    – jgcbrouns
    Commented Nov 11, 2019 at 16:58

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