Previous: Functions and Variables for descriptive statistics, Up: descriptive [Contents][Index]
Plots bars diagrams for discrete statistical variables, both for one or multiple samples.
data can be a list of outcomes representing one sample, or a matrix of m rows and n columns, representing n samples of size m each.
Available options are:
3/4): relative width of rectangles. This
value must be in the range [0,1].
clustered): indicates how multiple samples are
shown. Valid values are: clustered and stacked.
1): a positive integer number representing
the gap between two consecutive groups of bars.
[]): a list of colors for multiple samples.
When there are more samples than specified colors, the extra necessary colors
are chosen at random. See color to learn more about them.
absolute): indicates the scale of the
ordinates. Possible values are: absolute, relative,
and percent.
orderlessp): possible values are orderlessp or ordergreatp,
indicating how statistical outcomes should be ordered on the x-axis.
[]): a list with the strings to be used in the legend.
When the list length is other than 0 or the number of samples, an error message is returned.
0): indicates where the plot begins to be plotted on the
x axis.
draw options, except xtics, which is
internally assigned by barsplot.
If you want to set your own values for this option or want to build
complex scenes, make use of barsplot_description. See example below.
key, color_draw,
fill_color, fill_density and line_width.
See also
barsplot.
There is also a function wxbarsplot for creating embedded
histograms in interfaces wxMaxima and iMaxima. barsplot in a
multiplot context.
Examples:
Univariate sample in matrix form. Absolute frequencies.
(%i1) load ("descriptive")$
(%i2) m : read_matrix (file_search ("biomed.data"))$
(%i3) barsplot(
col(m,2),
title = "Ages",
xlabel = "years",
box_width = 1/2,
fill_density = 3/4)$
Two samples of different sizes, with relative frequencies and user declared colors.
(%i1) load ("descriptive")$
(%i2) l1:makelist(random(10),k,1,50)$
(%i3) l2:makelist(random(10),k,1,100)$
(%i4) barsplot(
l1,l2,
box_width = 1,
fill_density = 1,
bars_colors = [black, grey],
frequency = relative,
sample_keys = ["A", "B"])$
Four non numeric samples of equal size.
(%i1) load ("descriptive")$
(%i2) barsplot(
makelist([Yes, No, Maybe][random(3)+1],k,1,50),
makelist([Yes, No, Maybe][random(3)+1],k,1,50),
makelist([Yes, No, Maybe][random(3)+1],k,1,50),
makelist([Yes, No, Maybe][random(3)+1],k,1,50),
title = "Asking for something to four groups",
ylabel = "# of individuals",
groups_gap = 3,
fill_density = 0.5,
ordering = ordergreatp)$
Stacked bars.
(%i1) load ("descriptive")$
(%i2) barsplot(
makelist([Yes, No, Maybe][random(3)+1],k,1,50),
makelist([Yes, No, Maybe][random(3)+1],k,1,50),
makelist([Yes, No, Maybe][random(3)+1],k,1,50),
makelist([Yes, No, Maybe][random(3)+1],k,1,50),
title = "Asking for something to four groups",
ylabel = "# of individuals",
grouping = stacked,
fill_density = 0.5,
ordering = ordergreatp)$
For bars diagrams related options, see barsplot of package draw
See also functions histogram and piechart.
Function barsplot_description creates a graphic object
suitable for creating complex scenes, together with other
graphic objects.
Example: barsplot in a multiplot context.
(%i1) load ("descriptive")$
(%i2) l1:makelist(random(10),k,1,50)$
(%i3) l2:makelist(random(10),k,1,100)$
(%i4) bp1 :
barsplot_description(
l1,
box_width = 1,
fill_density = 0.5,
bars_colors = [blue],
frequency = relative)$
(%i5) bp2 :
barsplot_description(
l2,
box_width = 1,
fill_density = 0.5,
bars_colors = [red],
frequency = relative)$
(%i6) draw(gr2d(bp1), gr2d(bp2))$
This function plots box-and-whisker diagrams. Argument data can be a list,
which is not of great interest, since these diagrams are mainly used for
comparing different samples, or a matrix, so it is possible to compare
two or more components of a multivariate statistical variable.
But it is also allowed data to be a list of samples with
possible different sample sizes, in fact this is the only function
in package descriptive that admits this type of data structure.
The box is plotted from the first quartile to the third, with an horizontal
segment situated at the second quartile or median. By default, lower and
upper whiskers are plotted at the minimum and maximum values,
respectively. Option range can be used to indicate that values greater
than quantile(x,3/4)+range*(quantile(x,3/4)-quantile(x,1/4)) or
less than quantile(x,1/4)-range*(quantile(x,3/4)-quantile(x,1/4))
must be considered as outliers, in which case they are plotted as
isolated points, and the whiskers are located at the extremes of the rest of
the sample.
Available options are:
3/4): relative width of boxes.
This value must be in the range [0,1].
vertical): possible values: vertical
and horizontal.
inf): positive coefficient of the interquartilic range
to set outliers boundaries.
1): circle size for isolated outliers.
draw options, except points_joined, point_size, point_type,
xtics, ytics, xrange, and yrange, which are
internally assigned by boxplot.
If you want to set your own values for this options or want to build
complex scenes, make use of boxplot_description.
draw options: key, color,
and line_width.
There is also a function wxboxplot for creating embedded
histograms in interfaces wxMaxima and iMaxima.
Examples:
Box-and-whisker diagram from a multivariate sample.
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix(file_search("wind.data"))$
(%i3) boxplot(s2,
box_width = 0.2,
title = "Windspeed in knots",
xlabel = "Stations",
color = red,
line_width = 2)$
Box-and-whisker diagram from three samples of different sizes.
(%i1) load ("descriptive")$
(%i2) A :
[[6, 4, 6, 2, 4, 8, 6, 4, 6, 4, 3, 2],
[8, 10, 7, 9, 12, 8, 10],
[16, 13, 17, 12, 11, 18, 13, 18, 14, 12]]$
(%i3) boxplot (A, box_orientation = horizontal)$
Option range can be used to handle outliers.
(%i1) load ("descriptive")$
(%i2) B: [[7, 15, 5, 8, 6, 5, 7, 3, 1],
[10, 8, 12, 8, 11, 9, 20],
[23, 17, 19, 7, 22, 19]] $
(%i3) boxplot (B, range=1)$ (%i4) boxplot (B, range=1.5, box_orientation = horizontal)$
(%i5) draw2d(
boxplot_description(
B,
range = 1.5,
line_width = 3,
outliers_size = 2,
color = red,
background_color = light_gray),
xtics = {["Low",1],["Medium",2],["High",3]}) $
Function boxplot_description creates a graphic object
suitable for creating complex scenes, together with other
graphic objects.
Constructs and displays a histogram from a data sample. Data must be stored as a list of numbers, or a matrix of one row or one column.
Optional arguments:
nclasses (default, 10):
the number of classes (also called bins) in the histogram,
or a list of two numbers (the least and greatest values included in the histogram),
or a list of three numbers (the least and greatest values included in the histogram, and the number of classes),
or a set containing the endpoints of the class intervals,
or a symbol specifying the name of one of three algorithms to automatically determine the number of classes:
fd (Ref. [1]), scott (Ref. [2]), or sturges (Ref. [3]).
A class interval excludes its left endpoint and includes its right endpoint, except for the first interval, which includes both the left and right endpoints. It is assumed that class intervals are contiguous. That is, the right endpoint of one interval is equal to the left endpoint of the next.
frequency (default, absolute): indicates the scale of the vertical axis.
Possible values are: absolute (heights of bars add up to number of data),
relative (heights of bars add up to 1),
percent (heights of bars add up to 100),
and density (total area of histogram is 1).
htics (default, auto): format of tic marks on the horizontal axis.
Possible values are: auto (tics are placed automatically),
endpoints (tics are placed at the divisions between classes),
intervals (classes are labeled with the corresponding intervals),
or a list of labels, one for each class.
draw options, except xrange, yrange,
and xtics, which are internally assigned by histogram.
If you want to set your own values for these options, make use of
histogram_description.
key,
fill_color, fill_density, and line_width.
Note that the outlines of bars,
as well as the interior of bars when fill_density is nonzero,
are drawn with fill_color, not color.
histogram honors the global option histogram_skyline.
When histogram_skyline is true,
histogram and histogram_description construct "skyline" plots,
which shows the outline of the histogram bars,
instead of drawing all the vertical segments.
Otherwise (the default), histograms are displayed with bars showing vertical segments.
There is also a function wxhistogram for creating embedded
histograms in interfaces wxMaxima and iMaxima.
See also continuous_freq,
which, like histogram,
counts data in intervals,
but returns the counts instead of displaying a graphic representation.
See also barsplot.
Examples:
A simple histogram with eight classes:
(%i1) load ("descriptive")$
(%i2) s1 : read_list (file_search ("pidigits.data"))$
(%i3) histogram (
s1,
nclasses = 8,
title = "pi digits",
xlabel = "digits",
ylabel = "Absolute frequency",
fill_color = grey,
fill_density = 0.6)$
Setting the limits of the histogram to -2 and 12, with 3 classes. Also, we introduce predefined tics:
(%i1) load ("descriptive")$
(%i2) s1 : read_list (file_search ("pidigits.data"))$
(%i3) histogram (
s1,
nclasses = [-2,12,3],
htics = ["A", "B", "C"],
terminal = png,
fill_color = "#23afa0",
fill_density = 0.6)$
Bounds for varying class widths.
(%i1) load ("descriptive")$
(%i2) s1 : read_list (file_search ("pidigits.data"))$
(%i3) histogram (s1, nclasses = {0,3,6,7,11})$
Freedman-Diaconis formula for the number of classes.
(%i1) load ("descriptive")$
(%i2) s1 : read_list (file_search ("pidigits.data"))$
(%i3) histogram(s1, nclasses=fd) $
References:
[1] Freedman, D., and Diaconis, P. (1981) On the histogram as a density estimator: L_2 theory. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 57, 453-476.
[2] Scott, D. W. (1979) On optimal and data-based histograms. Biometrika 66, 605-610.
[3] Sturges, H. A. (1926) The choice of a class interval. Journal of the American Statistical Association 21, 65-66.
Creates a graphic object which represents a histogram.
Such an object is suitable for creating complex scenes together with other graphic objects,
to be displayed by draw2d.
histogram_description takes the same arguments
as the stand-alone function histogram.
See histogram for more information.
Example:
We make use of histogram_description for setting
xrange and adding an explicit curve into the scene:
(%i1) load ("descriptive")$
(%i2) ( load("distrib"),
m: 14, s: 2,
s2: random_normal(m, s, 1000) ) $
(%i3) draw2d(
grid = true,
xrange = [5, 25],
histogram_description(
s2,
nclasses = 9,
frequency = density,
fill_density = 0.5),
explicit(pdf_normal(x,m,s), x, m - 3*s, m + 3* s))$
Default value: false
When histogram_skyline is true,
histogram and histogram_description construct "skyline" plots,
which shows the outline of the histogram bars,
instead of drawing all the vertical segments.
The outline is drawn with the current fill_color (not the current color).
The interior of the histogram is filled with fill_color,
but only if fill_density is nonzero.
Otherwise, histograms are displayed with bars showing vertical segments.
Example:
Construct a skyline histogram, and an ordinary histogram for comparison, on the same plot.
(%i1) load ("descriptive") $
(%i2) L: read_list (file_search ("pidigits.data")) $
(%i3) histogram_skyline: true $
(%i4) skyline_hist: histogram_description (L) $
(%i5) histogram_skyline: false $
(%i6) ordinary_hist: histogram_description (L) $
(%i7) draw (gr2d (skyline_hist), gr2d (ordinary_hist)) $
Continuing the preceding example.
Set display options for fill_color and fill_density.
(%i8) histogram_skyline: true $ (%i9) skyline_hist: histogram_description (L, fill_color = blue, fill_density = 0.2) $ (%i10) histogram_skyline: false $ (%i11) ordinary_hist: histogram_description (L, fill_color = blue, fill_density = 0.2) $ (%i12) draw (gr2d (skyline_hist), gr2d (ordinary_hist)) $
Similar to barsplot, but plots sectors instead of rectangles.
Available options are:
[]): a list of colors for sectors.
When there are more sectors than specified colors, the extra necessary colors
are chosen at random. See color to learn more about them.
[0,0]): diagram’s center.
1): diagram’s radius.
draw options, except key, which is
internally assigned by piechart.
If you want to set your own values for this option or want to build
complex scenes, make use of piechart_description.
draw options: key, color,
fill_density and line_width. See also
ellipse
There is also a function wxpiechart for
creating embedded histograms in interfaces wxMaxima and iMaxima.
Example:
(%i1) load ("descriptive")$
(%i2) s1 : read_list (file_search ("pidigits.data"))$
(%i3) piechart(
s1,
xrange = [-1.1, 1.3],
yrange = [-1.1, 1.1],
title = "Digit frequencies in pi")$
See also function barsplot.
Function piechart_description creates a graphic object
suitable for creating complex scenes, together with other
graphic objects.
Plots scatter diagrams both for univariate (list) and multivariate (matrix) samples.
Available options are the same admitted by histogram.
There is also a function wxscatterplot for
creating embedded histograms in interfaces wxMaxima and iMaxima.
Examples:
Univariate scatter diagram from a simulated Gaussian sample.
(%i1) load ("descriptive")$
(%i2) load ("distrib")$
(%i3) scatterplot(
random_normal(0,1,200),
xaxis = true,
point_size = 2,
dimensions = [600,150])$
Two dimensional scatter plot.
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix (file_search ("wind.data"))$
(%i3) scatterplot(
submatrix(s2, 1,2,3),
title = "Data from stations #4 and #5",
point_type = diamant,
point_size = 2,
color = blue)$
Three dimensional scatter plot.
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix (file_search ("wind.data"))$
(%i3) scatterplot(submatrix (s2, 1,2), nclasses=4)$
Five dimensional scatter plot, with five classes histograms.
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix (file_search ("wind.data"))$
(%i3) scatterplot(
s2,
nclasses = 5,
frequency = relative,
fill_color = blue,
fill_density = 0.3,
xtics = 5)$
For plotting isolated or line-joined points in two and three dimensions,
see points. See also histogram.
Function scatterplot_description creates a graphic object
suitable for creating complex scenes, together with other
graphic objects.
Plots star diagrams for discrete statistical variables, both for one or multiple samples.
data can be a list of outcomes representing one sample, or a matrix of m rows and n columns, representing n samples of size m each.
Available options are:
[]): a list of colors for multiple samples.
When there are more samples than specified colors, the extra necessary colors
are chosen at random. See color to learn more about them.
absolute): indicates the scale of the
radii. Possible values are: absolute and relative.
orderlessp): possible values are orderlessp or ordergreatp,
indicating how statistical outcomes should be ordered.
[]): a list with the strings to be used in the legend.
When the list length is other than 0 or the number of samples, an error message is returned.
[0,0]): diagram’s center.
1): diagram’s radius.
draw options, except points_joined, point_type,
and key, which are internally assigned by starplot.
If you want to set your own values for this options or want to build
complex scenes, make use of starplot_description.
draw option: line_width.
There is also a function wxstarplot for
creating embedded histograms in interfaces wxMaxima and iMaxima.
Example:
Plot based on absolute frequencies. Location and radius defined by the user.
(%i1) load ("descriptive")$
(%i2) l1: makelist(random(10),k,1,50)$
(%i3) l2: makelist(random(10),k,1,200)$
(%i4) starplot(
l1, l2,
stars_colors = [blue,red],
sample_keys = ["1st sample", "2nd sample"],
star_center = [1,2],
star_radius = 4,
proportional_axes = xy,
line_width = 2 ) $
Function starplot_description creates a graphic object
suitable for creating complex scenes, together with other
graphic objects.
Plots stem and leaf diagrams.
Unique available option is:
1): indicates the unit of the leaves; must be a
power of 10.
Example:
(%i1) load ("descriptive")$
(%i2) load("distrib")$
(%i3) stemplot(
random_normal(15, 6, 100),
leaf_unit = 0.1);
-5|4
0|37
1|7
3|6
4|4
5|4
6|57
7|0149
8|3
9|1334588
10|07888
11|01144467789
12|12566889
13|24778
14|047
15|223458
16|4
17|11557
18|000247
19|4467799
20|00
21|1
22|2335
23|01457
24|12356
25|455
27|79
key: 6|3 = 6.3
(%o3) done
Previous: Functions and Variables for descriptive statistics, Up: descriptive [Contents][Index]