Box-and-whisker plot

Command

Statistics Distribution plot Box-and-whisker plot

Description

The box-and-whisker plot (Tukey, 1977), or boxplot, displays a statistical summary of a variable: median, quartiles, range and possibly extreme values.

Required input

The Define variable dialog box for Box-and-whisker plot is similar to the one for Summary statistics:

If the data require a logarithmic transformation, then select the Logarithmic transformation option.

You can choose between vertical and horizontal orientation of the box-and-whisker plot.

Results

This is the box-and-whisker plot for the variable Weight:

In the Box-and-whisker plot, the central box represents the values from the lower to upper quartile (25 to 75 percentile). The middle line represents the median. The horizontal line extends from the minimum to the maximum value, excluding outside and far out values which are displayed as separate points.

• An outside value is defined as a value that is smaller than the lower quartile minus 1.5 times the interquartile range, or larger than the upper quartile plus 1.5 times the interquartile range (inner fences).

• A far out value is defined as a value that is smaller than the lower quartile minus 3 times the interquartile range, or larger than the upper quartile plus 3 times the interquartile range (outer fences). These values are plotted using a different marker in the warning color (see Format graph).

As an option, you may select to plot all individual data points. This enables you to obtain a diagram representing a statistical summary of the data without the disadvantage of concealing the real data.

When you click an individual observation in the graph, the corresponding case is identified in a popup window (see also Select variable for case identification command). If you double-click an observation, the spreadsheet window will open with the corresponding case highlighted. If the value is an outlier, you can exclude the value or the entire case from further statistical analysis by selecting the value Exclude command in the Data menu.

For multiple box-and-whisker plots see Multiple comparison graphs and Multiple variables graphs.

Presentation of results

The description of the data (summary statistics) in the text or table may be complemented by a graphical representation of the data: either a histogram, cumulative distribution or box-and-whisker plot. The histogram is not very effective to display location and spread. The cumulative distribution has the advantage that it makes it easy to estimate the median (or other percentile) by reading off the horizontal value at which the curve attains 50% (or other percentage) (Moses, 1987). Secondly, the plot can contain the individual observations (cumulative dot plot). Finally, the box-and-whisker plot may be preferable because it can combine a display of all the data together with a statistical summary.

Literature

• Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
• Tukey JW (1977) Exploratory data analysis. Reading, Mass: Addison-Wesley Publishing Company.

More box-and-whisker plots including notched box-and-whisker plots

• Multiple comparison graphs: box-and-whisker plots for subgroups of one variable
• Clustered multiple comparison graphs: box-and-whisker plots for subgroups (two-way classification) of one variable
• Multiple variables graphs: box-and-whisker plots for several variables
• Clustered multiple variables graphs: box-and-whisker plots for subgroups of several variables

See also

• Outlier detection
• Histogram
• Cumulative frequency distribution
• Normal plot
• Dot plot
• Format graph
• Graph legend
• Add graphical objects
• Reference lines