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Box Plots

The graph below, created with the boxplot command, compares petal lengths in samples from two species of iris.

load fisheriris
s1 = meas(51:100,3);
s2 = meas(101:150,3);
figure;
boxplot([s1 s2],'notch','on',...
        'labels',{'versicolor','virginica'})

This plot has the following features:

  • The tops and bottoms of each "box" are the 25th and 75th percentiles of the samples, respectively. The distances between the tops and bottoms are the interquartile ranges.

  • The line in the middle of each box is the sample median. If the median is not centered in the box, it shows sample skewness.

  • The whiskers are lines extending above and below each box. Whiskers are drawn from the ends of the interquartile ranges to the furthest observations within the whisker length (the adjacent values).

  • Observations beyond the whisker length are marked as outliers. By default, an outlier is a value that is more than 1.5 times the interquartile range away from the top or bottom of the box, but this value can be adjusted with additional input arguments. Outliers are displayed with a red + sign.

  • Notches display the variability of the median between samples. The width of a notch is computed so that box plots whose notches do not overlap (as above) have different medians at the 5% significance level. The significance level is based on a normal distribution assumption, but comparisons of medians are reasonably robust for other distributions. Comparing box-plot medians is like a visual hypothesis test, analogous to the t test used for means.

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