Re: [Matplotlib-users] boxplot -- how (more)

[Jeffrey B. <jbl...@al...>]

On Aug 22, 2012, at 10:04 AM, Virgil Stokes wrote:

> On 21-Aug-2012 17:52, Jeffrey Blackburne wrote:
>>
>> On Aug 21, 2012, at 10:58 AM, Virgil Stokes wrote:
>>
>>> In reference to my previous email.
>>>
>>> How can I find the outliers (samples points beyond the whiskers)  
>>> in the data
>>> used for the boxplot?
>>>
>>> Here is a code snippet that shows how it was used for the timings  
>>> data (a list
>>> of 4 sublists (y1,y2,y3,y4), each containing 400,000 real data  
>>> values),
>>>    ...
>>>    ...
>>>    ...
>>>    # Box Plots
>>>    plt.subplot(2,1,2)
>>>    timings = [y1,y2,y3,y4]
>>>    pos = np.array(range(len(timings)))+1
>>>    bp = plt.boxplot( timings, sym='k+', patch_artist=True,
>>>                     positions=pos, notch=1, bootstrap=5000 )
>>>
>>>    plt.xlabel('Algorithm')
>>>    plt.ylabel('Exection time (sec)')
>>>    plt.ylim(0.9*ymin,1.1*ymax)
>>>
>>>    plt.setp(bp['whiskers'], color='k',  linestyle='-' )
>>>    plt.setp(bp['fliers'], markersize=3.0)
>>>    plt.title('Box plots (%4d trials)' %(n))
>>>    plt.show()
>>>    ...
>>>    ...
>>>    ...
>>>
>>> Again my questions:
>>> 1) How to get the value of the median?
>>
>> This is easily calculated from your data. Numpy will even do it  
>> for you: np.median(timings)
>>
>>> 2) How to find the outliers (outside the whiskers)?
>>
>> From the boxplot documentation: the whiskers extend to the most  
>> extreme data point within distance X of the bottom or top of the  
>> box, where X is 1.5 times the extent of the box. Any points more  
>> extreme than that are the outliers. The box itself of course  
>> extends from the 25th percentile to the 75th percentile of your  
>> data. Again, you can easily calculate these values from your data.
>>
>>> 3) How to find the width of the notch?
>>
>> Again, from the docs: with bootstrap=5000, it calculates the width  
>> of the notch by bootstrap resampling your data (the timings array)  
>> 5000 times and finding the 95% confidence interval of the median,  
>> and uses that as the notch width. You can redo that yourself  
>> pretty easily. Here is some bootstrap code for you to adapt:
>> http://mail.scipy.org/pipermail/scipy-user/2009-July/021704.html
>>
>> I encourage you to read the documentation! This page is very  
>> useful for reference:
>> http://matplotlib.sourceforge.net/api/pyplot_api.html
>>
>> -Jeff
>>
> Yes Jeff,
> These are very useful links; however, box plots have a parameter  
> called the "adjacent value" (from the McGill reference),
>
> "The plotted whisker extends to the adjacent value,  which is the  
> most extreme data value that is not an outlier."
>
> It seems there should be one for the lower and one for the upper  
> whisker --- how can one get these two values from boxplot?

Look at bp['whiskers']

For those who got here by searching: bp is the object returned by  
plt.boxplot()

> Also, is there anyway to directly get the indices of the outliers?

Look into np.where()