# How to create variability charts?

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Eric Sampson on 1 Feb 2013
Commented: Eric Sampson on 18 Oct 2013
I'm trying to find a way to recreate JMP-style variability charts using MATLAB.
I've tried looking through the Stats Toolbox and the File Exchange, and can't find anything that would do the trick. Anyone have an idea?
Thanks!
Shashank Prasanna on 1 Feb 2013
If you know how the 'understanding is included' in that chart, you can use that information and create a boxplot. There is nothing this specialized that is offered in the statistics toolbox. You could put in a ticket with the mathworks as a suggested enhancement along with your usecase.

Matt Tearle on 1 Feb 2013
Edited: Matt Tearle on 22 Mar 2013
EDIT: file added to MATLAB File Exchange. Share and enjoy!
Based on your comment above, boxplot with nominal grouping variables will do it:
x = randn(400,1);
y1 = nominal(round(rand(400,1)),{'little','lots'});
y2 = nominal(round(rand(400,1)),{'large','small'});
y3 = nominal(round(rand(400,1)),{'gourmet','plain'});
boxplot(x,[y1,y2,y3])
Hopefully this is basically how your data is already arranged. x contains all 400 observations of the response variable. y1, y2, and y3 are nominal arrays that record each observation's status for the three categories.
The boxplot labeling doesn't emphasize the hierarchy, but the results are correct.
EDIT TO ADD Oops, I got the grouping variables backward. Anyway, this is getting close to what you posted:
boxplot(x,[y3,y2,y1],...
'plotstyle','compact','labelorientation','horizontal',...
'factorseparator',[1,2])
The only problem is that the vertical arrangement of the group labels is backwards, for showing the hierarchy. This can be hacked, though, if you need:
h = findobj(get(gca,'children'),'type','text');
tl = get(h,'position');
tl = cat(1,tl{:});
tl(:,2) = flipud(tl(:,2));
for k = 1:length(h)
set(h(k),'position',tl(k,:))
end
EDIT TO ADD (2): Not pretty, but here's a function that does a reasonable job of approximating the graphic:
function variabilityplot(x,y)
n = size(y,2);
numgrps = zeros(1,n);
for k = 1:n
numgrps(k) = numel(unique(y(:,k)));
end
numgrps = cumprod(numgrps);
N = numgrps(n);
y = fliplr(y);
boxplot(x,y,...
'plotstyle','compact','labelorientation','horizontal',...
'factorseparator',1:n);
hbxplt = get(gca,'children');
hall = get(hbxplt,'children');
halltype = get(hall,'type');
hsepln = hall(end-n+1:end);
htxt = hall(strcmpi('text',halltype));
set(htxt,'units','data')
txtpos = get(htxt,'position');
txtpos = cat(1,txtpos{:});
txtpos(:,2) = flipud(txtpos(:,2));
x = reshape(txtpos(:,1),N,n);
for k = 2:n
m = numgrps(k-1);
for j = 1:N
ii = floor((j-1)/m);
i1 = 1 + m*ii;
i2 = m*(1+ii);
x(j,k) = mean(x(i1:i2,1));
end
end
txtpos(:,1) = x(:);
for k = 1:length(htxt)
set(htxt(k),'position',txtpos(k,:))
end
tlcol = 0.5*[1,1,1];
txtpos = get(htxt,'extent');
txtpos = cat(1,txtpos{:});
xl = xlim;
yl = ylim;
y1 = min(yl);
y2 = min(txtpos(:,2));
y = linspace(y1,y2,n+1);
for k = 2:(n+1)
line(xl,[y(k),y(k)],'parent',gca,'clipping','off','color',tlcol)
end
line(xl(1)*[1,1],[y1,y2],'parent',gca,'clipping','off','color',tlcol)
line(xl(2)*[1,1],[y1,y2],'parent',gca,'clipping','off','color',tlcol)
for j = 1:n
newy = get(hsepln(j),'YData');
newy(newy==yl(2)) = y(j+1);
line(get(hsepln(j),'XData'),newy,'parent',gca,'clipping','off','color',tlcol)
end
delete(hsepln(1))
Trying it out:
x = randn(400,1);
y1 = nominal(randi(2,400,1),{'little','lots'});
y2 = nominal(randi(3,400,1),{'large','medium','small'});
y3 = nominal(randi(2,400,1),{'gourmet','plain','aardvark','potato'},[1,2,3,4]);
y = [y1,y2,y3];
variabilityplot(x,y)
If you think it's useful, I'll clean it up a bit and put it on the File Exchange soon.
Eric Sampson on 18 Oct 2013
@Matt thanks very much! Somehow I missed seeing your last comment, so my reply is even later :) Best, Eric

Shashank Prasanna on 1 Feb 2013
You can certainly use boxplots: http://www.mathworks.com/help/stats/boxplot.html
But I am not certain there is something that generates a plot that looks exactly like that. You may have to generate a boxplot and add all the labels below them after that.