Boxplots—409

Boxplots

What is a boxplot?

A boxplot, also known as a box and whisker diagram, summarizes the distribution of a set of data by displaying the centering and spread of the data using a few primary elements.

Data points outside the inner fence are known as outliers. To further characterize outliers, we define the outer fences as the first quartile minus 3.0*IQR and the third quartile plus 3.0*IQR. Data between the inner and outer fences are termed near outliers, and those outside the outer fence are referred to as far outliers. A data point lying on an outer fence is considered a near outlier.

A shaded region or notch may be added to the boxplot to display approximate confidence intervals

for the median (under certain restrictive statistical assump-

tions). The bounds of the shaded or notched area are defined by the median +/- 1.57*IQR/ N ,

where N is the number of observations. Notching is useful in indicating whether two samples were drawn from populations with the same median; roughly speaking, if the notches of two boxes do not overlap, then the medians may be said to differ with 95% confidence. It is worth noting that in some cases, most likely involving small numbers of observations, the notches may be bigger than the boxes.

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Boxplots are often drawn so that the widths of the boxes are uniform. Alternatively, the box widths can be varied as a measure of the sample size for each box, with widths drawn proportional to N , or proportional to the square root of N .

Creating a boxplot

The boxplot view can be created from a series for various subgroups of your sample, or from a group.

Boxplots by Classification

From a series, select View/Descriptive Statistics/Boxplots by Classification… to display the Boxplots by Classification dialog.

In the Series/Group for classify field, enter series or group names that define your subgroups. You may type more than one series or group name; separate each name by a space.

If the classification field is left blank, statistics will be calculated for the entire sample of observations, otherwise, descriptive statistics will be calculated for each unique value of the classification series (unless automatic binning is performed).

You may specify the NA handling, and the grouping options as described in “Stats by Classification” beginning on page 312. The Show boxplot for total option allows you to include a box of the summary statistics for (ungrouped) series the boxplot view.

The set of options provided in Display in boxplot allows you to customize the initialize appearance of the boxplot. By default, the Fixed Width boxplots will show Medians, Means, Near outliers and Far outliers, as well as Shaded confidence intervals for the medians. You need not make final decisions here, since all box display elements may subsequently be shown or hidden by modifying the resulting view.

Lastly, the Options button may be used to open a dialog allowing you to customize the calculation of your quartiles.

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It is worth pointing out that the Graph Options dialog for boxplots does not include a Type or a Legend tab. Boxplots, like a number of other statistical graphs, do not allow you to change the graph type. In addition, boxplots use text objects in place of legends for labeling the graph.

To specify the axis labels for a boxplot, click on the Axes & Scaling tab, and select the Bottom - Dates or Observations axis in the Edit Axis combo box. You may use the listbox on the right side of the dialog to edit, display, or hide individual box labels. You may also change the box label font or display the labels at an angle.

Boxplots for a Group of Series

To display a boxplot for each series in a group, open a group window and select View/ Descriptive Statistics/Boxplots…. EViews will open the Group Boxplots dialog. You may use the dialog to customize the initialize appearance of the boxplot.

By default, the Display options are set to show all of the boxplot components: Medians, Means, Near outliers and Far outliers, and Shaded confidence intervals for the medians. You may elect to hide any of the basic elements by unchecking the corresponding checkbox, and you may use the radio buttons to change the display of the median confidence intervals: None or Notched.

The Boxwidth settings are, by default, set to show

Fixed Width boxes, but you may elect to draw