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Pareto dot plot

pdplotcatvar[[if] [in]] [weight] [,aiopts(options)dotsonlyhorizontallevel(#)nreps(#)options]

fweights are allowed; see help weights.

Description

pdplotproduces a Pareto dot plot as proposed by Wilkinson (2006). The frequencies of the categories ofcatvarare shown in order by a series of dots against a magnitude scale. As backdrop, corresponding acceptance intervals are shown by bars.The command is more flexible than this description of default behaviour implies. The intervals can be suppressed and the dot plot can be recast() to another kind of twoway plot.

RemarksWilkinson (2006) briefly reviews Pareto charts which commonly combine two displays in one. Frequencies in various categories are shown by a series of bars arranged in frequency order, from most common downwards. On that is often superimposed a rising curve showing cumulative frequency. Frequency and cumulative frequency may or may not have consistent scales. Examples from quality management studies often show categories of accidents, complaints, defects, failures, rejects, returns, or other such unwelcome phenomena. Wilkinson gives several cogent criticisms of this design and suggests an alternative: show frequencies in order, but by a dot plot, but add as reference a series of acceptance intervals.

The acceptance intervals are calculated by simulation. Imagine as benchmark a population in which k categories are equally probable, and imagine taking samples of size n. Here k and n are the same as those in the data under consideration. Just by chance the observed frequencies of the k categories will typically differ. For each sample we can label the frequencies f_(1) >= f_(2) > ... >= f_(k-1) >= f_(k): thus f_(1) is the frequency of the most abundant category, and so forth. Across several samples we can get order statistics for each f_(j) and use those to calculate intervals with desired coverage.

The acceptance intervals should not be overinterpreted, for various different reasons. First, the reference distribution is just an agnostic guess assuming that we know just the numbers of values and categories and that we have no reason to suppose that categories differ in probability. More commonly, we would not really expect that the categories are equal in probability; it is just that we would rarely know how to make our expectations precise. Second, although making the sample size bigger will stabilise results, some variability will always be experienced in intervals produced by simulation. Third, there are various slightly different recipes for producing percent points from order statistics and only one is wired in here.

Vilfredo Pareto (1848-1923) was an Italian sociologist, economist and philosopher, perhaps best remembered for his work on income distributions and what is now called Pareto efficiency. See http://en.wikipedia.org/wiki/Vilfredo_Pareto. Contrary to many statements, there appears to be no evidence that he used what is now known as the Pareto chart, which seems to have emerged in quality management after 1951. See Wilkinson (2006) for more on the latter point.

Pareto charts are commonly shown as vertical bar charts with the awkward consequence that long text labels are aligned vertically or obliquely, and so made difficult to read. The

horizontaloption allows you to override the default.

Options

aiopts(options)are options tuning the appearance of the acceptance intervals. Note that the default options arebarw(0.2) bcolor(none). The bars are laid down before the dots, so more colourful bars are possible. For comparison note that the bars are centred at ranks 1, 2, etc., so that the default bar width is 20% of the possible.

dotsonlysuppresses the simulation and the addition of acceptance intervals. In that case anyaiopts(),level()ornreps()has no effect.

horizontalspecifies that the display should be aligned horizontally. The default is vertical. Note thathorizontalwithrecast()works but is not useful.

level(#)specifies a coverage level as a percent for the acceptance intervals. The default is given byc(level), which in turn defaults to 95. See help on level if desired.

nreps(#)specifies the number of repetitions of random drawing of a sample of size n from a population with k equally frequent categories. The default is 10000. For indicative, exploratory work, fewer repetitions may be adequate. Note that large numbers of repetitions, especially with large n, have implications for time and memory. Positively,pdplotis most needed and most useful when the sample number is small. For reproducible results, set seed beforehand.

optionsare other twoway options tuning the appearance of the graph. For example, note that a dot display is not compulsory and can be replaced using with the recast() option.

Examples

. pdplot category. pdplot category, recast(bar) barw(0.1). pdplot category, dotsonly

AcknowledgementsWilliam Gould and Vince Wiggins made very helpful suggestions.

AuthorNicholas J. Cox, Durham University n.j.cox@durham.ac.uk

ReferencesWilkinson, Leland. 2006. Revising the Pareto chart.

AmericanStatistician60(4): 332-334.

Also seeOn-line: help for graph bar, graph dot, catplot (if installed)