FREQUENCY PLOT

... FREQUENCY PLOT

Graphics Command

Generates a frequency plot.

A frequency plot is a graphical data analysis technique for summarizing the distributional information of a variable. The response variable is divided into equal sized intervals (or bins). The number of occurrences of the response variable is calculated for each bin. The frequency plot then consists of:

Vertical axis	=	frequencies or relative frequencies;
Horizontal axis	=	response variable (i.e., the mid-point of each interval).

There are 4 types of frequency plots:

1. frequency plot (absolute counts);
2. relative frequency plot (converts counts to proportions);
3. cumulative frequency plot;
4. cumulative relative frequency plot.

The frequency plot and the histogram have the same information except the frequency plot has lines connecting the frequency values whereas the histogram has bars at the frequency values.

<type> <y>             <SUBSET/EXCEPT/FOR qualification>
where <type> is one of FREQUENCY, RELATIVE FREQUENCY, CUMULATIVE FREQUENCY, CUMULATIVE RELATIVE FREQUENCY;
            <y> is the variable of raw data values which will appear on the horizontal axis;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used when you have raw data. Note that <y> can be either a variable or a matrix. If <y> is a matrix, then a frequency plot will be generated for all values in that matrix.

<type> <y> <x>             <SUBSET/EXCEPT/FOR qualification>
where <type> is one of FREQUENCY, RELATIVE FREQUENCY, CUMULATIVE FREQUENCY, CUMULATIVE RELATIVE FREQUENCY;
            <y> is a variable containing pre-computed frequencies;             <x> is a variable containing the bin mid-points;
and where the <SUBSET/EXCEPT/FOR qualification is optional.

This syntax is used when you have grouped data with equi-sized bins.

<type> <y> <xlow> <xhigh>             <SUBSET/EXCEPT/FOR qualification>
where <type> is one of FREQUENCY, RELATIVE FREQUENCY, CUMULATIVE FREQUENCY, CUMULATIVE RELATIVE FREQUENCY;
            <y> is a variable containing pre-computed frequencies;
            <xlow> is a variable containing the lower limits for the bins;
            <xhigh> is a variable containing the upper limits for the bins;
and where the <SUBSET/EXCEPT/FOR qualification is optional.

This syntax is used when you have grouped data with unequal sized bins.

MULTIPLE <type> <y1> ... <yk>             <SUBSET/EXCEPT/FOR qualification>
where <type> is one of FREQUENCY, RELATIVE FREQUENCY, CUMULATIVE FREQUENCY, CUMULATIVE RELATIVE FREQUENCY;
            <y1> ... <yk> is a list of response variables;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax will overlay multiple frequency plots on the same plot.

Note that the response variables (<y1> ... <yk> can be either variables or matrices (or a mix of variables and matrices). For matrices, a frequency plot will be generated for all values in the matrix.

REPLICATED <type> <y> <x1>             <SUBSET/EXCEPT/FOR qualification>
where <type> is one of FREQUENCY, RELATIVE FREQUENCY, CUMULATIVE FREQUENCY, CUMULATIVE RELATIVE FREQUENCY;
            <y> is the response variable;
            <x1> is a group-id variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax will generate a frequency plot for each distinct value in the group-id variable. The frequency plots will be generated on the same page.

REPLICATED <type> <y> <x1> <x2>             <SUBSET/EXCEPT/FOR qualification>
where <type> is one of FREQUENCY, RELATIVE FREQUENCY, CUMULATIVE FREQUENCY, CUMULATIVE RELATIVE FREQUENCY;
            <y> is the response variable;
            <x1> is the first group-id variable;
            <x2> is the second group-id variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax will cross tabulate the group-id variables and generate a frequency plot for each unique combination of values for the <x1> and <x2> group-id variables. The frequency plots will be generated on the same page.

FREQUENCY PLOT TEMP
RELATIVE FREQUENCY PLOT TEMP
CUMULATIVE FREQUENCY PLOT TEMP
CUMULATIVE RELATIVE FREQUENCY PLOT TEMP
FREQUENCY PLOT COUNTS STATE
RELATIVE FREQUENCY PLOT COUNTS STATE
CUMULATIVE FREQUENCY PLOT COUNTS STATE
CUMULATIVE RELATIVE FREQUENCY PLOT COUNTS STATE

Although DATAPLOT does not have a FREQUENCY TABLE command, one can be generated with the following commands:
FREQUENCY PLOT Y
LET YFREQ = YPLOT
LET XVAL = XPLOT


Then the variables YFREQ and XVAL essentially contain a frequency table. There is a LET subcommand called FREQUENCY. However, it does not generate a frequency table in the sense that a frequency plot does. You can also use the command

LET Y2 X2 = BINNED Y

for this purpose.

By default, Dataplot uses a class width of 0.3 X the standard deviation of the variable. Use the CLASS WIDTH command to override this default. Dataplot also tends to generate a large number of zero frequency classes at the lower and upper tails. This tends to compress the frequency plot on the horizontal axis. Use the XLIMITS command or the CLASS LOWER and CLASS UPPER commands to avoid plotting these zero frequency classes.

A number of alternative choices for class width can be set with the command

HISTOGRAM CLASS WIDTH

Enter HELP HISTOGRAM CLASS WIDTH for details.

By default, Dataplot sets the lower and upper class limits to xbar -/+ 6*s (with xbar and s denoting the sample mean and standard deviation, respectively). This can occassionally result in a few outlying points being excluded from the frequency plot. To adjust the lower and upper class limits so that these outlying points are included, enter the command
SET HISTOGRAM OUTLIERS ON

To revert to the default, enter

SET HISTOGRAM OUTLIERS OFF

The FREQUENCY PLOT supports the TO syntax for the list of variable names. This is most useful for the MULTIPLE case.

None

A synonym for CUMULATIVE RELATIVE FREQUENCY PLOT is RELATIVE CUMULATIVE FREQUENCY PLOT.

HISTOGRAM	= Generates a histogram.
KERNEL DENSITY PLOT	= Generate a kernel density plot.
PERCENT POINT PLOT	= Generate a percent point plot.
PROBABILITY PLOT	= Generate a probability plot.
PPCC PLOT	= Generates probability plot correlation coefficient plot.
PLOT	= Generate a data or function plot.
CLASS LOWER	= Set the lower class minimum for histograms, frequency plots, and pie charts.
CLASS UPPER	= Set the upper class maximum for histograms, frequency plots, and pie charts.
CLASS WIDTH	= Set the class width for histograms, frequency plots, and pie charts.
HISTOGRAM CLASS WIDTH	= Specify alternative default class wdith algorithms for histograms.
MINIMUM	= Set the frame minima for all plots.
MAXIMUM	= Set the frame maxima for all plots.
LIMITS	= Set the frame limits for all plots.
BARS	= Set the on/off switches for plot bars.
BAR WIDTH	= Set the widths for plot bars.
BAR FILL	= Set the on/off switches for plot bar fills.
BAR PATTERN	= Set the types for bar fill patterns.
BAR BORDER LINE	= Set the types for bar border lines.

Most introductory statistics book discuss frequency polygons and histograms.

David Scott (1992), "Multivariate Density Estimation", John Wiley, (chapter 3).

Exploratory Data Analysis, Distributional Analysis

Pre-1987

 
LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 1000
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
MULTIPLOT SCALE FACTOR 2
TITLE CASE ASIS
TITLE OFFSET 2
.
XLIMITS -5 5
TITLE Counts Frequency Plot
FREQUENCY PLOT Y
TITLE Relative Frequency Plot
RELATIVE FREQUENCY PLOT Y
TITLE Cumulative Counts Frequency Plot
CUMULATIVE FREQUENCY PLOT Y
TITLE Cumulative Relative Frequency Plot
CUMULATIVE RELATIVE FREQUENCY PLOT Y
END OF MULTIPLOT