notBoxPlot - alternative to box plots.

This function visualizes raw (grouped) data along with the mean, 95% confidence interval, and 1 SD.

Description

Whilst box plots have their place, it's sometimes nicer to see all the data making up a distribution rather than hiding them with summary statistics such as the inter-quartile range. This function (with a tongue in cheek name) addresses this problem. To the best of my knowledge there aren't similar functions here on the FEX.

Jittered raw data are plotted for each group. Also shown are the mean, and 95% confidence intervals for the mean. This allows one to eyeball the data to look for significant differences between means (non-overlapping confidence intervals indicate a significant difference at the chosen p-value, which here is 5%). Also see: http://jcb.rupress.org/cgi/content/abstract/177/1/7 Finally, 1 SD is also shown. Note that if data are not normally distributed then these statistics will be less meaningful.

The function has several examples and there are various visualization possibilities in addition to those shown in the above screenshot. For instance, the coloured areas can be replaced by lines.

Although it's worked well for situations I've needed it, I will be happy to modify the function if users come up against problems.

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Included functions
notBoxPlot.m - generates plots as shown in screenshot
SEM_calc.m - calculate standard error of the mean. Provided as a separate function file so that it can be used for other purposes.
tInterval_Calc.m - calculate a t-interval. Right now notBoxPlot doesn't make use of this (unless the user edits the code, of course), but it still might be useful. For small sample sizes, the t-interval is larger than the SEM.

* NOTE *
The statistics toolbox is not required if you install the nantoolbox from here: http://pub.ist.ac.at/~schloegl/matlab/NaN/ Otherwise you will need the statistics toolbox for nan-handling.

• MATLAB release: MATLAB 7.8 (R2009a)

[Michael Ashby]

I like the idea but it seems to be missing the required "SEM_calc" function.

[Rob Campbell]

Really? I thought I zipped it in there. Thanks for letting me know. I shall re-upload.

[Rossella Blatt]

Very nice and useful. Thanks!

[Mahmoud]

Very Useful!
Two questions,
1) How do you add labels to the x-axis like you would with the 'label' option in the boxplot function?
2) How can you specify what range should be plotted on the y-axis of notboxPlot?

[Rob Campbell]

Mahmoud,
You can achieve these things in exactly the same way as you would for most other plotting commands. I try to avoid having functions behave too idiosyncratically. So, to answer your question:
clf
h=notBoxPlot(randn(10,2));
set(gca,'XTickLabel',{'GrpA','GrpB'})
ylim([-5,5])

The last two lines are obviously standard ways of setting labels and changing the axis limits. These work with any plot. Note that the notBoxPlot function returns the handles to the plot objects so that you can change their properties or even delete them. For example, you could remove all the data points by doing: delete([h.data])

[Dylan]

Very useful, code is very well written.

[J G]

This is very useful thanks! Is it possible to plot the SD as error bars instead of the box?

[Rob Campbell]

Normally I'd say you should modify the plotted objects with the handles returned by the function. However, it would be awkward to do what you requested in this way. Consequently I've just submitted an update which should do what you want. The 4th argument can how have the values "sdline." If you want to alter the line properties, I recommend doing so by modifying the object properties via the handle returned by the function.

[Andrea]

 

[Harry MacDowel]

Thanks Rob. Love it.

[Kelvin]

I’m wondering how noBoxPlot can plot vectors of different lengths.

i.e.
x = rand(5,1);
y = rand(10,1);
z = rand(15,1);
group = [repmat({'First'}, 5, 1); repmat({'Second'}, 10, 1); repmat({'Third'}, 15, 1)];
boxplot([x;y;z], group)

Thanks in advance!

[Rob Campbell]

Almost the same way: just don't code your groups as a cell array of strings. To modify your example:
 
group = [repmat(1, 5, 1); repmat(2, 10, 1); repmat(3, 15, 1)];
notBoxPlot([x;y;z], group)

You can then change the XTickLabels to strings if needed. I've not found I do this often enough to add cell arrays as an input possibility. Perhaps I should, though (when time allows!).

[Ted P Teng]

At the moment, I am admiring what I just made with your function. Love it, thank you.
You guys may also want to use this function in conjunction with XTICKLABEL_ROTATE.

[Alexander]

In opinion, a better replacement for the builtin boxplot is "Violin Plots for plotting multiple distributions (distributionPlot.m)" which does no require any additional toolboxes. Check:
http://www.mathworks.com/matlabcentral/fileexchange/23661-violin-plots-for-plotting-multiple-distributions-distributionplot-m

[Rob Campbell]

I will soon be modifying this function to require no additional toolboxes. Otherwise, which function is best probably depends on the size of the data set. For large sample sizes the violin plots work best. For small sample sizes I prefer the plot style on this page, since it doesn't bin the data.

[Ian Shapiro]

Great tool. It's an excellent way to visualize the distribution in a set of data. However, I've found that it does not appear work with 'gname' for labeling individual data points, whereas boxplot is able to do this. Any idea why that's the case?

[Rob Campbell]

Hmmm... Don't know. I will look into it.

[Rob Campbell]

Ok... For some reason adding a patch object causes gname to fail. If you run notBoxPlot using the "line" plotting style then gname works.

[J G]

Great function! Is there a way to have a trend line through the means, i.e. using polyval/polyfit? Thanks!

[J G]

How can I use this function with continuous spacing on x-axis?
For example,
p = [0.1 0.25 0.5 0.75 0.9];
boxplot(A,'position',p)
will place the boxplots unevenly spaced along x-axis. Is there a way to do this with this function?

[Rob Campbell]

JG:
Q1. The function will return the coordinates of the means so you can use these with polyval. e.g.
H=notBoxPlot(randn(10),[],[],'line');
x=get([H.mu],'XData'), y=get([H.mu],'YData');
Without "line" the above will return two data points for each mean (since the means are lines), but it's easy enough to work with that too. Does that work for you?

Q2. You can do this as follows:
notBoxPlot(randn(10,5),[1,2,5,9,10])