Boxplot and histogram in one plot

Hey,

I think this question has been asked before:

How to overlay box plot with distribution histogram in the same graph - MATLAB Answers - MATLAB Central (mathworks.com)

But I could not find any proper solution;

so is there a way to achieve something like this:

I'm looking forward to hear your suggestions :)

[Sambit Supriya Dash]

Yes it is possible to get boxplot and histogram in one plot,

Example,

x = [1 2 3;4 5 6;7 8 9];
y = [5 4 3; 5 7 9; 1 9 3];
figure(1)
hist(x)
hold on
boxplot(y)
hold off

Hope, it helps.

Answer 1

[Adam Danz]

This method uses patch objects to display histograms next to each boxplot. It's based on another answer that displays probability density distributions next to vertical scatter plots.

You only need to replace the x and y data and can copy-paste the rest of the code.

Inputs.

x : 1xn vector defining the x coordinate of n boxplots.

y : mxn matrix of raw data for n boxplots

rng('default') % for reproducibility
x = 0:5:30; 
y = (randn(300, numel(x)) + linspace(.5,5,numel(x))) .* linspace(.5,2,numel(x));

Set spacing

binWidth = 0.4;  % histogram bin widths
hgapGrp = .05;   % horizontal gap between pairs of boxplot/histograms (normalized)
hgap = 0.2;      % horizontal gap between boxplot and hist (normalized)

Compute histogram counts & edges

hcounts is an nx2 cell array containing the {counts, edges} for each distribution.

maxCount is the maximum bin count across all distributionts, used to normalize patch heights

hcounts = cell(size(y,2),2); 
for i = 1:size(y,2)
    [hcounts{i,1}, hcounts{i,2}] = histcounts(y(:,i),'BinWidth',binWidth); 
end
maxCount = max([hcounts{:,1}]);

Plot boxplots

fig = figure();
ax = axes(fig); 
hold(ax,'on')

xInterval = mean(diff(sort(x))); % x-interval (best if x is at a fixed interval)
normwidth = (1-hgapGrp-hgap)/2;  
boxplotWidth = xInterval*normwidth;
boxplot(ax,y,'Positions',x,'Widths',boxplotWidth,'OutlierSize',3,'Labels',compose('%d',x))

Add vertical histograms (patches)

histX0 = x + boxplotWidth/2 + hgap;    % histogram base
maxHeight = xInterval*normwidth;       % max histogram height
patchHandles = gobjects(1,size(y,2)); 
for i = 1:size(y,2)
    % Normalize heights 
    height = hcounts{i,1}/maxCount*maxHeight;
    % Compute x and y coordinates 
    xm = [zeros(1,numel(height)); repelem(height,2,1); zeros(2,numel(height))] + histX0(i);
    yidx = [0 0 1 1 0]' + (1:numel(height));
    ym = hcounts{i,2}(yidx);
    % Plot patches
    patchHandles(i) = patch(xm(:),ym(:),[0 .75 1],'FaceAlpha',.4);
end

xlim([-2.5, 32.5])

Method 2 with color control

With just a few changes to the code above, you can use boxplotGroup() from the file exchange to set up colors of boxplots and histogram similar to the example in your question.

%% Inputs
rng('default') % for reproducibility
x = 0:5:30; 
y = (randn(300, numel(x)) + linspace(.5,5,numel(x))) .* linspace(.5,2,numel(x));

%% Set Spacing
binWidth = 0.4;  % histogram bin widths
hgapGrp = .15;   % horizontal gap between pairs of boxplot/histograms (normalized)
hgap = 0.06;      % horizontal gap between boxplot and hist (normalized)

%% Compute histogram counts & edges
hcounts = cell(size(y,2),2); 
for i = 1:size(y,2)
    [hcounts{i,1}, hcounts{i,2}] = histcounts(y(:,i),'BinWidth',binWidth); 
end
maxCount = max([hcounts{:,1}]);

%% Plot boxplotsGroup()
fig = figure();
ax = axes(fig); 
hold(ax,'on')

% Convert y (mxn matrix) to 1xn cell array of mx1 vectors, required by boxplotWidths
yc = mat2cell(y,size(y,1),ones(1,size(y,2))); 

xInterval = 1; %x-interval is always 1 with boxplot groups
normwidth = (1-hgapGrp-hgap)/2;     
boxplotWidth = xInterval*normwidth; 

% Define colors for each boxplot
colors = lines(size(y,2)); 

% Plot colored boxplots
bph = boxplotGroup(ax,yc,'Widths',boxplotWidth,'OutlierSize',3,'PrimaryLabels',compose('%d',x),'Colors',colors);
set(findobj(bph.boxplotGroup,'-property','LineWidth'), 'LineWidth', 1) % increase line widths

%% Add vertical histograms (patches) with matching colors
xCoordinate = 1:size(y,2);  %x-positions is always 1:n with boxplot groups
histX0 = xCoordinate + boxplotWidth/2 + hgap;    % histogram base
maxHeight = xInterval*normwidth;       % max histogram height
patchHandles = gobjects(1,size(y,2)); 
for i = 1:size(y,2)
    % Normalize heights 
    height = hcounts{i,1}/maxCount*maxHeight;
    % Compute x and y coordinates 
    xm = [zeros(1,numel(height)); repelem(height,2,1); zeros(2,numel(height))] + histX0(i);
    yidx = [0 0 1 1 0]' + (1:numel(height));
    ym = hcounts{i,2}(yidx);
    % Plot patches
    patchHandles(i) = patch(xm(:),ym(:),colors(i,:),'EdgeColor',colors(i,:),'LineWidth',1,'FaceAlpha',.45);
end

[Jakob Seifert]

This is insane, thank you very much.

[Adam Danz]

Later I realized my boxplotGroup() function could be used to control the color so I added a 2nd version to my answer. The same could be achieved using boxchart but I haven't worked out those details.

[RJ]

This seems great and exactly what I was looking for too.

I wondered if there is a way to do this with boxplot y vectors of different lengths or am I missing something? And to add x labels? Thanks!!

[Adam Danz]

An easy workaround when using vectors of unequal length is to pad the shorter vectors with NaN values so all vecs are the same length and then you can combine them into a matrix. padarray may be helpful.

For labels, use text() function or labelpoints().

[RJ]

Awesome thanks, I got it working with padcat.

Answer 2

[Scott MacKenzie]

This solution uses tiledlayout and boxchart, but you can adjust to use subplot and boxplot if you are running an older version of MATLAB:

n = 7;
y = randn(100,n);

tiledlayout(1, 2*n);

for i=1:n
    nexttile;
    boxchart(y(:,i));
    set(gca,'visible', 'off', 'ylim', [-4 4]);
    nexttile;
    histogram(y(:,i), 20, 'orientation', 'horizontal');
    set(gca,'visible', 'off', 'ylim', [-4 4]);
end

f = gcf;
f.Color = 'w';
f.Units = 'normalized';
f.Position = [.1 .2 .8 .4];

[Jakob Seifert]

Thank you for your answer, but this isn't what I am exactly looking for.

I want the y-axis to be the possible outputs for the boxplot, as well as the histogram. That is, I want the histogram to be rotated by 90° degrees. (look at the picture embedded in my original post)

[Scott MacKenzie]

I just adjusted my answer so the histograms are horizontal. Is that what you are looking for?

[Jakob Seifert]

Yes this looks much better! But as I understand it, you turned off the individual axes. I need two "overall" axes; meaning something like this:

https://www.mathworks.com/help/examples/stats/win64/CreateBoxPlotsForGroupedDataExample_01.png

But this soultions is already pretty good ! thank you

[Scott MacKenzie]

You're right. My solution creates 14 plots in 14 axes, all of which are made invisible. To get exacly what you want, you'd need to add all the plots to a single axis or add axes to the parent tiledlayout or figure. I don't know if that's possible.

[Adam Danz]

One more step: it's important to set ylim so that the extent of the histograms align with the extent of the boxplots/outliers. For example, in the 5th pair of axes the boxplot does not show any outliers at the top but the histogram extends beyond the upper cap. This is because of a difference in y-limits between the neighboring axes.

Also, the ylim needs to match for all axes so that vertical differenced between columns of data are preserved.

For example, compare these two figures using the exact same data.

n = 7;
y = randn(100,n) .* [1:3:19];

figure()
boxchart(y)

figure()
tiledlayout(1, 2*n);
for i=1:n
    nexttile;
    boxchart(y(:,i));
    set(gca,'visible', 'off');
    nexttile;
    histogram(y(:,i), 20, 'orientation', 'horizontal');
    set(gca,'visible', 'off');
end
f = gcf;
f.Color = 'w';
f.Units = 'normalized';
f.Position = [.1 .2 .8 .4];

[Scott MacKenzie]

Hey, good point. Thanks. I just adjusted my solution to prevent this -- by setting the y-axis limits.