Boxplot for both x and y axis with different box widths.

How can we make a boxplot like the one below for both x and y data (the box widths of each group that are x-data related are different). I tried boxplot(X,Y, group) but it did not work.

[Jonas]

i think you can not specify mutiple different box widths directly, you would have to edit the box sizes manually by accesing the XData of the boxes

[Benjamin Kraus]

boxchart does offer a setting for the box width.

[Adam Danz]

I missed that since BoxWidth is not mentioned on the documentation page for boxchart, however it is listed in the properties page.

Thanks, Benjamin.

[Gechang Cao]

Thanks for your nice suggestions! boxchart works

Answer 1

[Benjamin Kraus]

The boxplot command creates a group of lines, so if you wanted to adjust the box widths you would need to manually adjust the XData properties on each line to move them to the desired locations.

The better alternative is to use the new boxchart command. The object created by the the boxchart command has a BoxWidth property, but I suspect you won't need it, because even when you specify x values, the boxes created by the boxchart command have uniform widths.

boxchart(randn(1000,1), 'BoxWidth', 0.3);

or

boxchart(randi(10,1000,1),randn(1000,1));

[Adam Danz]

An extension of Benjamin Kraus's example where the width of each box is specified using boxchart.

rng('default')
y = rand(20,5).*randi(4,1,5) + rand(1,5)*2; 
x = 1:size(y,2); % x position of each box
widths = [.25 .6 .1 .9, .45]; % width of each box (0:1)

figure(); 
ax = axes();

% X-axis limits must be set prior to adding the boxes
% and they are apparently categorical even if the 
% inputs are numeric.  Here's an easy way to set 
% the x-limits to the range of your data (deleted later)
temp = plot(ax, categorical(x), nan(1,5)); 
hold(ax,'on')
xl = xlim(ax); % Store original axis limits, boxchart may change them
for i = 1:size(y,2)
    xdata = repelem(x(i),size(y,1),1); % Specify x=coordinate of box
    boxchart(ax,y(:,i),'XData',xdata,'BoxWidth',widths(i))
end
xlim(ax,xl) % Restore xlimits
delete(temp)

[Benjamin Kraus]

@Adam Danz The reason the x-axis is categorical is because you are setting the XData using a name-value pair. If you specify the x-data before the y-data, it will create a numeric ruler.

Do this:

boxchart(ax,xdata,y(:,i),'BoxWidth',widths(i))

Instead of this:

boxchart(ax,y(:,i),'XData',xdata,'BoxWidth',widths(i))

With that tweak, your code now becomes:

rng('default')
y = rand(20,5).*randi(4,1,5) + rand(1,5)*2; 
x = 1:size(y,2); % x position of each box
widths = [.25 .6 .1 .9, .45]; % width of each box (0:1)
figure(); 
ax = axes();
hold(ax,'on')
for i = 1:size(y,2)
    xdata = repelem(x(i),size(y,1),1); % Specify x=coordinate of box
    boxchart(ax,xdata,y(:,i),'BoxWidth',widths(i))
end

[Adam Danz]

Thanks for the explanation, Benjamin.

I wonder what the logic is in converting numeric inputs to categorical under one syntax but not the other.

[Gechang Cao]

Thank you very much! Cool, the box widths now are controlled by some numbers. I tried some means but did not make it. The locations of x-data are also controlled by the real values not by even distance. Thanks a lot! This is really cool!!