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Construction of a Box-and-Whisker plot

Box-and-whisker plot

Construction of Box-and-Whisker plot

A Box‑and‑Whisker plot (Tukey, 1977) is constructed as follows:

Note that John Tukey did not use the term 'outlier' for 'outside' and 'far out' values.

Notched Box-and-Whisker plot

Construction of notched Box-and-Whisker plot

A notched Box‑and‑Whisker plot (McGill et al., 1978) is constructed in the same way as a Box-and-Whisker plot (described above), but in this variation of the box-and-whisker plot a confidence interval(*) for the median is provided by means of notches surrounding the medians.

(The illustration does not show all the details of the regular Box-and-Whisker plot)

The notches surrounding the medians provide a measure of the rough significance of differences between the values. Specifically, if the notches about two medians do not overlap in the display, the medians are, roughly, significantly different at about a 95% confidence level (McGill et al., 1978).

In the following example, there is probably no significant difference between the medians in the two samples because the notches overlap.

Comparison of medians using Notched Box-and-Whisker plot

MedCalc calculates the notches according to McGill et al. (1978), as follows:

$$ Median\;±\;1.7\;\frac{1.25\;IQR}{ 1.35\;\sqrt{N}} $$

where IQR is the Interquartile range and N is the number of cases in the sample.

(*) Important: this confidence interval is not a 95% confidence interval of the median. It is a confidence interval that allows comparison of the medians.


MedCalc procedures that offer Box-and-Whisker plots

See also

Recommended book

Book cover

Exploratory Data Analysis
John W. Tukey

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The approach in this introductory book is that of informal study of the data. Methods range from plotting picture-drawing techniques to rather elaborate numerical summaries. Several of the methods are the original creations of the author, and all can be carried out either with pencil or aided by hand-held calculator.