How to get a normal box plot graph we get in origin software which consist of box plot with data points scattered and normal distribution curve in MATLAB

I am trying to plot a boxplot in matlab which should contain boxplot with data points in the right with normal distribution curve in matlab. Like the one above

Answer 1

[Voss]

Maybe something like this. This fits distributions to the data, but if you have the distributions already you can plot them the same way.

% random normal data
data = randn(100,3);
% box plot and distribution colors
colors = [0 0.6 0; 0.8 0.8 0; 0.8 0 0];
% box plot width
w = 0.3;

[N,m] = size(data);

% make the box plot
h = boxplot(data,'Widths',w);

% shift box plots to the left by w/2
xd = arrayfun(@(obj)get(obj,'XData')-w/2,h,'UniformOutput',false);
set(h,{'XData'},xd(:))

% set box plot colors
for ii = 1:m
    set(h(:,ii),'Color',colors(ii,:),'MarkerEdgeColor',colors(ii,:))
end

hold on

% fit and plot the distributions

[xmin,xmax] = bounds(data(:));
x = linspace(xmin,xmax);

for ii = 1:m
    plot(ii+w/4+w/2*rand(N,1),data(:,ii),'.','Color',colors(ii,:))
    pd = fitdist(data(:,ii),'Normal');
    plot(pdf(pd,x)+ii,x,'Color',colors(ii,:))
end

% set axes xticks and xticklabels
set(gca(),'XTick',1:m,'XTickLabels',string(char('A'+(0:m-1).')))

[Deepan Jayakumar]

Thank you. The code works for me as well

[Voss]

You're welcome!

Answer 2

[Aquatris]

I dont think there is a builtin plot like this. You can create your own functions for it or modify the community provided ones such as this.

Answer 3

[Malay Agarwal]

Hi Deepan,

I understand that you want to create a boxplot with the normal distribution and the datapoints for each category overlayed to the right of each box.

Please try the following code:

% Step 1: Generate Sample Data
rng(10); % For reproducibility
dataA = normrnd(20, 5, [100, 1]);
dataB = normrnd(30, 10, [100, 1]);
dataC = normrnd(40, 15, [100, 1]);
categories = [repmat({'A'}, 100, 1); repmat({'B'}, 100, 1); repmat({'C'}, 100, 1)];
values = [dataA; dataB; dataC];

% Define colors for each category
colors = {'magenta', 'green', 'blue'}; % Magenta for A, Green for B, Blue for C

% Step 2: Create Boxplot
boxplot(values, categories, 'Whisker', Inf);
hold on;

% Step 3: Plot Normal Distributions next to each boxplot
uniqueCats = unique(categories, 'stable');
for i = 1:length(uniqueCats)
    category = uniqueCats{i};
    subset = values(strcmp(categories, category));
    
    % Creating a range of values for plotting the normal distribution
    x = linspace(min(subset), max(subset), 100);
    
    % Calculating the normal distribution with the same mean and std as the data
    pd = fitdist(subset, 'Normal');
    y = pdf(pd, x);
    
    % Scaling the y-values to match the boxplot size
    y = y / max(y) * 0.15; % 0.15 is the scaling factor, adjust as needed
    
    % Plotting the normal distribution with specified color
    plot(i + y, x, 'Color', colors{i});
    
    % Step 4: Overlay scatter plot for the actual data points
    % Adjust position of each data point to align with the distribution curve
    % We scatter the points with a slight random offset horizontally to avoid overlap
    rng(10); % For consistent scatter positions
    scatter_x = normrnd(i, 0.03, size(subset)) + max(y); % Adjust scatter_x for alignment
    
    % Scatter with specified color and transparency
    scatter(scatter_x, subset, [], colors{i}, 'filled', 'MarkerFaceAlpha', 0.3);
end

title('Boxplot with Normal Distribution and Data Points');
hold off;

The code:

• Uses the “boxplot” function to create the initial boxplot.
• Uses “hold on” to ensure that all subsequent plots are on the same figure.
• Loops over each category and fits a normal distribution to the category’s data using the “fitdist” function.
• Creates a PDF from the normal distribution using the “pdf” function and plots it.
• Creates a scatter plot for the category’s data using the “scatter” function and plots it.

Please refer to the following resources for more information:

• “boxplot” function - https://www.mathworks.com/help/releases/R2022a/stats/boxplot.html.
• “fitdist” function - https://www.mathworks.com/help/releases/R2022a/stats/fitdist.html.
• “pdf” function - https://www.mathworks.com/help/releases/R2022a/stats/prob.normaldistribution.pdf.html.
• “scatter” function - https://www.mathworks.com/help/releases/R2022a/matlab/ref/scatter.html.
• “hold” command - https://www.mathworks.com/help/releases/R2022a/matlab/ref/hold.html.

Hope this helps!