Matlab创建三维箱线图-EW帮帮网

1、箱线图介绍

统计指标一般包括：四分位数、均值、中位数、众数、方差、标准差等，箱线图作为一种数据统计的方法，内容包括：最小值，第一分位，中位数，第三分位数，最大值。

箱线图于1977年由美国著名统计学家约翰·图基（John Tukey）发明，能够明确的展示离群点的信息，同时能够让我们了解数据是否对称，数据如何分组、数据的峰度。

箱线图（Box- plot）是一种用于显示一组数据分散情况的统计图，多用于多组数据的比较，相对于直方图，既可以节省空间，还可以展示更多信息（如均值、四分位数等）。

箱线图包含数学统计量，能够分析不同类别数据各层次水平差异，还可以揭示数据间离散程度、异常值、分布差异等。

箱线图内容详细介绍：

四分位数：

一组数据按照从小到大顺序排列后，把该组数据四等分的数，称为四分位数。第一四分位数 (Q1)、第二四分位数 (Q2，也叫“中位数”)和第三四分位数 (Q3)分别等于该样本中所有数值由小到大排列后第25%、第50%和第75%的数字。第三四分位数与第一四分位数的差距又称四分位距（interquartile range, IQR）。

（1）第一个四分位数Q1：也称作25th百分位数，表示最小数（不是“最小值”）和数据集的中位数之间的中间数。

（2）第二四分位数Q2：也称作中位数Median/50th百分位数，表示数据集的中间值。

（3）第三四分位数Q3：也称作75th百分位数，表示数据集的中位数和最大值之间的中间值（不是“最大值”）。

（4）四分位间距IQR：第25至第75个百分点的距离。

（5）离群值：Outliers

（6）最大值max、最小值min

利用正态分布的箱线图，可以帮助理解箱线图：

2 完整代码

function boxPlot3D(xx,g1,g2,quantDistribution)

%function boxPlot3D(xx,g1,g2,quantDistribution)

%--------------------------------------------------------------------------

% boxPlot3D(x) creates a three dimensional box plot of the data in x. If x

% is 3D a matrix, boxPlot3D creates one box for each column. Example,

% create a 3D matrix with normal distributions with different means:

% xx=randn(50,2,4)+repmat((permute([0 1 2 -2;1 2 3 4],[3 1 2])),[50,1,1]);

% boxPlot3D(xx)

% boxPlot3D(x,g1,g2) groups the data of x, with the grouping variables of

% g1, and g2. Example, create a 1D Matrix with different values and the

% corresponding grouping parameters:

% xx=randn(500,1)+linspace(0,5,500)';

% g1= [0.1*ones(250,1);0.2*ones(250,1)];

% g2= [3*ones(150,1);4*ones(150,1);5*ones(200,1)];

% boxPlot3D(xx,g1,g2)

% boxPlot3D(x,[],[],quantDistribution) allows the selection of the

% quantiles to select, e.g. [0 0.25 0.5 0.75 1]

% [0 0.25 0.5 0.75 1] (default) creates a box between 0.25 and 0.75

% with a line in 0.5 and two planes at 0 and 1

% connected with a dashed line. These values can be

% changed.

% [ 0 1] creates a box within the extremes of the values

% selected. These values can be changed, e.g.

% [0.25 0.75]

% [ 0.25 0.5 0.75] creates a box and a line, same as the option with

% 5 values, but will not draw the planes with the

% dashed line.

% The colours of the boxes can be changed in the code.

%--------------------------------------------------------------------------

if nargin <1

else

figure

hold on;

if ~exist('quantDistribution','var')

% Calculate the positions of the edges of the boxplot, and the

% quantiles at 25,50 75%

quantDistribution = [0 0.25 0.50 0.75 1 ];

end

if ~exist('g1','var')

% Only one parameter received, the data is in a 3D Matrix with one

% column per group.

[rows,columns,levels] = size( xx);

for counterCols = 1:columns

for counterLevs = 1:levels

% Select columns, extract positions, and call display

% The column is directly extracted from the matrix

currentColumn = xx(:,counterCols,counterLevs);

% The positions correspond to the extreme, median and 25%/75%

% positions of the distribution, these are obtained with

% quantile

currentPositions = quantile(currentColumn,quantDistribution);

display3Dbox(counterCols,counterLevs,currentPositions);

end

else

% Three arguments, the data and two grouping parameters

% all should be the same size. First, detect the unique cases of

% each of the grouping parameters

cases_g1=unique(g1);

cases_g2=unique(g2);

% Count how many cases there are for each dimension

num_g1 = numel(cases_g1);

num_g2 = numel(cases_g2);

% The separation may vary and not necessarily be 0,1,2,3...

width_g1 = min(diff(cases_g1));

width_g2 = min(diff(cases_g2));

for counterCols = 1:num_g1

current_g1 = cases_g1(counterCols);

address_g1 = (g1==current_g1);

for counterLevs = 1:num_g2

current_g2 = cases_g2(counterLevs);

address_g2 = (g2==current_g2);

% Select columns, extract positions, and call display

% The column is directly extracted from the matrix

currentColumn = xx((address_g1)&(address_g2));

% The positions correspond to the extreme, median and 25%/75%

% positions of the distribution, these are obtained with

% quantile

currentPositions = quantile(currentColumn,quantDistribution);

% Call the display with the extra parameters for width

display3Dbox(current_g1,current_g2,currentPositions,width_g1,width_g2);

end

view(3)

rotate3d on

axis tight

grid on

end

function display3Dbox(counterCols,counterLevs,currentPositions,width_g1,width_g2)

if ~exist('width_g1','var')

width_g1 = 1;

end

if ~exist('width_g2','var')

width_g2 = 1;

end

if ~exist('colourFace','var')

colourFace='red';

end

if ~exist('colourFace2','var')

colourFace2='cyan';

end

lenZStats=length(currentPositions);

% to avoid overlap between boxes, use only 35% to each dimension

x=width_g1 * 0.35*[-1 1 1 -1 -1 1 1 -1]';

y=width_g2 * 0.35*[-1 -1 1 1 -1 -1 1 1]';

% This are the parameters to create the boxes and faces

z=[1 1 1 1]';

face_Mat=[1 2 6 5;2 3 7 6;3 4 8 7;4 1 5 8;4 1 5 8;1 2 3 4; 5 6 7 8];

switch lenZStats

case 2

%----- a single box with extremes (.25 .75 / 0 1) to be plotted

vert_Mat=[counterCols+x counterLevs+y [currentPositions(1)*z;currentPositions(2)*z]];