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Tutorial for polyPlot

The following code demonstrates the various options of PolyPlot. It also explains the basic statistics used. Finally, it demonstrates how the PolyPlot does a good job of approximating the shape of the underlying distribution.

The Basic PolyPlot

First, simulate a set of 100 scores from a normal distribution. Then call polyStats to get the summary statistics and polyPlot to get the associated plot.

Scores <- round(rnorm(100, 10, 2), 0)
polyStats(Scores, digits = 3)
          Lower Middle  Upper Spread
Quartiles 9.000  10.00 11.000  1.000
Means     8.600  10.13 11.660  1.530
Z Scores  8.225  10.13 12.035  1.905
Range     6.000  10.50 15.000  4.500

polyPlot(Scores)

Generally speaking, each level/row provides a different category of measures of location and spread:

  • First/Top: Provides the quartiles (and median as the center) of the distribution, with the interquartile range divided by 2 as the measure of spread
  • Second: Provides the means of the halves (and the whole set as the center) of the distribution, with the mean absolute deviation from the median as the measure of spread
  • Third: Provides the mean (as the center) of the distribution and points +/- one standard deviation from the mean (i.e, z scores of -1 and 1), with the standard deviation as the measure of spread
  • Fourth/Bottom: Provides the range (and midrange as the center) of the distribution, with the range divided by 2 as the measure of spread

Further explanation of the math behind the PolyPlot is available in Seier and Bonett (2011).

Exploring Distributional Shapes

To see the relationship between the PolyPlot and the underlying distribution, either a frequency distribution (histogram) or a density curve can be added in the background. If the desire is to focus on shape, the value labels can be supressed. Colors and titles can be altered to further enhance the plot.

For example, simulate some positively skewed data. Use polyPlot to get the statistics plot and a frequency histogram.

Scores <- round(rbeta(100, 2, 5) * 20, 0)
polyPlot(Scores, values = FALSE, type = "frequency", main = "PolyPlot and Histogram for Positively Skewed Data")

As another example, simulate some negatively skewed data. Use polyPlot to get the statistics plot and a density curve.

Scores <- round(rbeta(100, 5, 2) * 20, 0)
polyPlot(Scores, values = FALSE, type = "density", main = "PolyPlot and Density for Negatively Skewed Data")

As a final example, simulate some bimodal data. Here the values are presented on each polyPlot to show their utility in explaining the underlying data.

Scores <- c(round(rnorm(50, 7, 1), 0), round(rnorm(50, 13, 1), 0))
polyPlot(Scores, type = "frequency", col = "blue", bg = "goldenrod", values = TRUE, main = "PolyPlot and Histogram for Bimodal Data")

polyPlot(Scores, type = "density", col = "blue", bg = "goldenrod", values = TRUE, main = "PolyPlot and Density for Bimodal Data")