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Construction of a Box-and-Whisker plot

Box-and-whisker plot

Description 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

Description 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.

Literature

MedCalc procedures that offer Box-and-Whisker plots

See also