Better document meaning of notches in boxplots

[rasbt]

Hi,
I found a problem regarding the boxplot function when the notch shape is being used (matplotlib 1.4.0).

I uploaded an self-contained example as IPython notebook with more details.

[tacaswell]

cc @phobson

[tacaswell]

Digging into the code a bit, it looks like it is using the confidence intervals to determine the size of the notch and what is happening is that the internal extends past the 1st or 3rd quartile.

I can see two ways to fix this:

1. draw the q{1,3} lines at their full widths and make the slopes of the notes shallower to make that work
2. draw the q{1,3} lines at the width they are where they hit the notch lines

This is a relatively easy code fix (around L3426 in _axes.py), but I think we need a domain expert (as in someone who uses box plots!) to make the call as to which solution to use.

[phobson]

If that's where the confidence limits are, then there's nothing wrong. Mathematically it's perfectly plausible that the lower CL on the median is less than the first quartile. My boxplots appear like this all the time and seeing the notch inversion is a very useful visual key.

[tacaswell]

Fair enough. I did not consider that this was the correct behaviour....

[phobson]

Just for thoroughness, I'm going to jump into -- ::deep breath:: -- R and confirm

[WeatherGod]

Whatever decision is made, it might make sense to add an image test
codifying the behavior. It certainly looks "wrong" to me at first. Perhaps
documentation and examples might be prudent?

On Fri, Oct 10, 2014 at 12:35 PM, Paul Hobson notifications@github.com
wrote:

Just for thoroughness, I'm going to jump into -- ::deep breath:: -- R and
confirm

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Reply to this email directly or view it on GitHub
#3631 (comment)
.

[phobson]

Yup, same behavior with a different dataset in R

[phobson]

worth noting that R raises a warning:

Warning message:
In bxp(list(stats = c(0.67, 0.70, 0.76, 0.78,  :
  some notches went outside hinges ('box'): maybe set notch=FALSE

But I think that's a poor message as it essentially tells the user that they should hide the fact that the values of the medians are uncertain.

To @rasbt, you can use:

bplot = plt.boxplot(data, notch=True, bootstrap=20000)  

to maybe tighten up the medians' confidence limit

[tacaswell]

I am convinced that this is correct behaviour and just needs some documentation and a test to make sure that confused people like me don't try to 'fix' it in the future.

[rasbt]

Sorry for the confusion, you are absolutely right. This was actually a very stupid question in retrospect and this "flipping" behavior is quite useful information as @phobson pointed out :). Maybe it would be worthwhile to add this to documentation though. Or maybe a warning message that the confidence interval is very uncertain in those cases where upper CI > quartile 3 and lower CI < quartile 1.

[lofidevops]

I think "won't fix" label needs to be removed, now that this is a documentation ticket? (Thanks for the thorough investigation here and at https://stackoverflow.com/questions/26291082 btw.)

[WeatherGod]

good point. tag removed.