ORD PLOT

ORD PLOT

Graphics Command

Generates an Ord plot.

An Ord plot can be used to distinguish whether a data set follows a Poisson, binomial, negative binomial, or logarithmic series distribution.

If x and n_x denote the class value and the corresponding class frequency, then the Ord plot is a plot of

\( \frac{x n_{x}} {n_{x-1}} \)   versus x

If this plot is approximately linear, then it can help distinguish between these four distributions based on the following table:

Distribution	Slope b	Intercept a	Parameter Estimate
Poisson	0	+	\( \lambda \) = a
Binomial	-	+	p = b/(b-1)
Negative Binomial	+	+	p = 1 - b
Logarithmic Series	+	-	\( \theta \) = -a

The slope and intercept can be determined by fitting a line to the plotted points. We follow the suggestion of Friendly of using the weights

\( w_{x} = \sqrt{n_{x} - 1} \)

This compensates for the fact that classes with small frequency have large variance.

The primary disadvantage of this plot is that a discrepant frequency affects the points for both x and x+1. For this reason, the Ord plot does not have good resistance properties.

ORD PLOT <y>             <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used for the case where you have raw data. Dataplot will automatically create the frequency table.

ORD PLOT <y> <x>             <SUBSET/EXCEPT/FOR qualification>
where <y> is a variable containing frequencies;
            <x> is a variable containing the class value;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used for the case where your data is already in the form of a frequency table.

ORD PLOT Y
ORD PLOT Y X

The appearance of the plot can be controlled with the LINE and CHARACTER commands. The first setting is for the plot points and the second setting is for the fitted line. This is demonstrated with the sample plot below.

The following internal parameters are saved by this plot:
PPA0 - the intercept of the fitted line
PPA1 - the slope of the fitted line

None

None

POSSION PLOT	= Generates a Poisson plot.
PROBABILITY PLOT	= Generates a probability plot.
PPCC PLOT	= Generates a ppcc plot.
KS PLOT	= Generates a Kolmogorov-Smirnov (or chi-square) plot.
ORD PLOT	= Generate an Ord plot.
HISTOGRAM	= Generates a histogram.
LINES	= Sets the type for plot lines.
CHARACTER	= Sets the type for plot characters.

Friendly (2000), "Visualizing Categorical Data", SAS Publishing Inc., Cary, NC, pp. 49-56.

Distributional Modeling

2007/5

 
. Data from p. 47 of Friendly
read x y
0  109
1   65
2   22
3    3
4    1
end of data
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title case asis
title offset 2
label case asis
title Ord Plot
y1label Frequency Ratio
x1label x
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tic offset units screen
tic offset 3 3
xlimits 1 4
major xtic mark number 4
minor xtic mark number 0
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character x blank
line blank dotted
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ord plot y x