Matlab boxplot adjacent values

I found that calculating an index to specify outliers of a dataset according to how the boxplot works does not give the same results. Please find below an example where I create some data, extract the values from the boxplot (as seen in datatips in the figure window) and compare them to the values I calculated.

While the median and quartiles match up the upper and lower adjacent values do not. According to the Matlab help under 'Whisker', the adjacent values are calculated as q3 + w*(q3-q1) where q3 and q1 are the quantiles and w is the specified whisker length.

Am I calculating this wrong or is there any other mistake? I would like to be able to explain the error.

Screenshot of results table (please note the results vary due to random data)

%Boxplot test



% create random, normally distributed dataset

data = round(randn(1000,1)*10,2);



figure(10)

clf

boxplot(data,'Whisker',1.5)



clear stats tmp



% read data from boxplot, same values as can be seen in datatips in the figure window

h = findobj(gcf,'tag','Median');

tmp = get(h,'YData');

stats(1,1) = tmp(1);

h = findobj(gcf,'tag','Box');

tmp = get(h,'YData');

stats(1,2) = tmp(1);

stats(1,3) = tmp(2);

h = findobj(gcf,'tag','Upper Adjacent Value');

tmp = get(h,'YData');

stats(1,4) = tmp(1);

h = findobj(gcf,'tag','Lower Adjacent Value');

tmp = get(h,'YData');

stats(1,5) = tmp(1);



% calculated data

stats(2,1) = median(data);

stats(2,2) = quantile(data,0.25);

stats(2,3) = quantile(data,0.75);

range = stats(2,3) - stats(2,2);

stats(2,4) = stats(2,3) + 1.5*range;

stats(2,5) = stats(2,2) - 1.5*range;



% error calculation

for k=1:size(stats,2)

    stats(3,k) = stats(2,k)-stats(1,k);

end %for k



% convert results to table with labels

T = array2table(stats,'VariableNames',{'Median','P25','P75','Upper','Lower'}, ...

    'RowNames',{'Boxplot','Calculation','Error'});

edited Nov 22 '18 at 9:42

asked Nov 20 '18 at 12:51

Lukas W.

166

add a comment |

Am I calculating this wrong or is there any other mistake? I would like to be able to explain the error.

Screenshot of results table (please note the results vary due to random data)

%Boxplot test



% create random, normally distributed dataset

data = round(randn(1000,1)*10,2);



figure(10)

clf

boxplot(data,'Whisker',1.5)



clear stats tmp



% read data from boxplot, same values as can be seen in datatips in the figure window

h = findobj(gcf,'tag','Median');

tmp = get(h,'YData');

stats(1,1) = tmp(1);

h = findobj(gcf,'tag','Box');

tmp = get(h,'YData');

stats(1,2) = tmp(1);

stats(1,3) = tmp(2);

h = findobj(gcf,'tag','Upper Adjacent Value');

tmp = get(h,'YData');

stats(1,4) = tmp(1);

h = findobj(gcf,'tag','Lower Adjacent Value');

tmp = get(h,'YData');

stats(1,5) = tmp(1);



% calculated data

stats(2,1) = median(data);

stats(2,2) = quantile(data,0.25);

stats(2,3) = quantile(data,0.75);

range = stats(2,3) - stats(2,2);

stats(2,4) = stats(2,3) + 1.5*range;

stats(2,5) = stats(2,2) - 1.5*range;



% error calculation

for k=1:size(stats,2)

    stats(3,k) = stats(2,k)-stats(1,k);

end %for k



% convert results to table with labels

T = array2table(stats,'VariableNames',{'Median','P25','P75','Upper','Lower'}, ...

    'RowNames',{'Boxplot','Calculation','Error'});

edited Nov 22 '18 at 9:42

asked Nov 20 '18 at 12:51

Lukas W.

166

add a comment |

Am I calculating this wrong or is there any other mistake? I would like to be able to explain the error.

Screenshot of results table (please note the results vary due to random data)

%Boxplot test



% create random, normally distributed dataset

data = round(randn(1000,1)*10,2);



figure(10)

clf

boxplot(data,'Whisker',1.5)



clear stats tmp



% read data from boxplot, same values as can be seen in datatips in the figure window

h = findobj(gcf,'tag','Median');

tmp = get(h,'YData');

stats(1,1) = tmp(1);

h = findobj(gcf,'tag','Box');

tmp = get(h,'YData');

stats(1,2) = tmp(1);

stats(1,3) = tmp(2);

h = findobj(gcf,'tag','Upper Adjacent Value');

tmp = get(h,'YData');

stats(1,4) = tmp(1);

h = findobj(gcf,'tag','Lower Adjacent Value');

tmp = get(h,'YData');

stats(1,5) = tmp(1);



% calculated data

stats(2,1) = median(data);

stats(2,2) = quantile(data,0.25);

stats(2,3) = quantile(data,0.75);

range = stats(2,3) - stats(2,2);

stats(2,4) = stats(2,3) + 1.5*range;

stats(2,5) = stats(2,2) - 1.5*range;



% error calculation

for k=1:size(stats,2)

    stats(3,k) = stats(2,k)-stats(1,k);

end %for k



% convert results to table with labels

T = array2table(stats,'VariableNames',{'Median','P25','P75','Upper','Lower'}, ...

    'RowNames',{'Boxplot','Calculation','Error'});

edited Nov 22 '18 at 9:42

asked Nov 20 '18 at 12:51

Lukas W.

166

Am I calculating this wrong or is there any other mistake? I would like to be able to explain the error.

Screenshot of results table (please note the results vary due to random data)

%Boxplot test



% create random, normally distributed dataset

data = round(randn(1000,1)*10,2);



figure(10)

clf

boxplot(data,'Whisker',1.5)



clear stats tmp



% read data from boxplot, same values as can be seen in datatips in the figure window

h = findobj(gcf,'tag','Median');

tmp = get(h,'YData');

stats(1,1) = tmp(1);

h = findobj(gcf,'tag','Box');

tmp = get(h,'YData');

stats(1,2) = tmp(1);

stats(1,3) = tmp(2);

h = findobj(gcf,'tag','Upper Adjacent Value');

tmp = get(h,'YData');

stats(1,4) = tmp(1);

h = findobj(gcf,'tag','Lower Adjacent Value');

tmp = get(h,'YData');

stats(1,5) = tmp(1);



% calculated data

stats(2,1) = median(data);

stats(2,2) = quantile(data,0.25);

stats(2,3) = quantile(data,0.75);

range = stats(2,3) - stats(2,2);

stats(2,4) = stats(2,3) + 1.5*range;

stats(2,5) = stats(2,2) - 1.5*range;



% error calculation

for k=1:size(stats,2)

    stats(3,k) = stats(2,k)-stats(1,k);

end %for k



% convert results to table with labels

T = array2table(stats,'VariableNames',{'Median','P25','P75','Upper','Lower'}, ...

    'RowNames',{'Boxplot','Calculation','Error'});

matlab statistics boxplot

edited Nov 22 '18 at 9:42

asked Nov 20 '18 at 12:51

Lukas W.

166

edited Nov 22 '18 at 9:42

asked Nov 20 '18 at 12:51

Lukas W.

166

edited Nov 22 '18 at 9:42

asked Nov 20 '18 at 12:51

Lukas W.

166

asked Nov 20 '18 at 12:51

Lukas W.

166

asked Nov 20 '18 at 12:51

Lukas W.

166

add a comment |

1 Answer
1

active

oldest

votes

While the calculation of the boundaries, e.g. q3 = q3 + w*(q3-q1), is correct, it is not displayed in the boxplot. What is actually displayed and marked as upper/lower adjacent value is the minimum and maximum of the values within the aforementioned boundaries.

Regarding the initial task leading to the question: For applying the same filtering of outliers as in the boxplot the calculated boundaries can be used.

answered Nov 21 '18 at 12:50

Lukas W.

166

add a comment |

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1 Answer
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1 Answer
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Regarding the initial task leading to the question: For applying the same filtering of outliers as in the boxplot the calculated boundaries can be used.

answered Nov 21 '18 at 12:50

Lukas W.

166

add a comment |

Regarding the initial task leading to the question: For applying the same filtering of outliers as in the boxplot the calculated boundaries can be used.

answered Nov 21 '18 at 12:50

Lukas W.

166

add a comment |

Regarding the initial task leading to the question: For applying the same filtering of outliers as in the boxplot the calculated boundaries can be used.

answered Nov 21 '18 at 12:50

Lukas W.

166

Regarding the initial task leading to the question: For applying the same filtering of outliers as in the boxplot the calculated boundaries can be used.

answered Nov 21 '18 at 12:50

Lukas W.

166

answered Nov 21 '18 at 12:50

Lukas W.

166

answered Nov 21 '18 at 12:50

Lukas W.

166

answered Nov 21 '18 at 12:50

Lukas W.

166

add a comment |

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