g01asf produces a specified number of box and whisker plots on a character printing device, with a chosen number of character positions in each direction.

2 Specification

Fortran Interface

Subroutine g01asf (

prt, m, n, x, ldx, nstepx, nstepy, plot, ldplot, fivept, iwork, ifail)

Integer, Intent (In)	::	m, n(m), ldx, nstepx, nstepy, ldplot
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	iwork(ldx)
Real (Kind=nag_wp), Intent (In)	::	x(ldx,m)
Real (Kind=nag_wp), Intent (Out)	::	fivept(5*m)
Character (1), Intent (In)	::	prt
Character (1), Intent (InOut)	::	plot(ldplot,nstepx)

C Header Interface

#include <nag.h>

void	g01asf_ (const char prt, const Integer m, const Integer n[], const double x[], const Integer ldx, const Integer nstepx, const Integer nstepy, char plot[], const Integer ldplot, double fivept[], Integer iwork[], Integer *ifail, const Charlen length_prt, const Charlen length_plot)

The routine may be called by the names g01asf or nagf_stat_plot_box_whisker.

3 Description

g01asf produces a series of box and whisker plots representing

m

data batches each of size

n_{i}

, for

i = 1, 2, \dots, m

. A box and whisker plot is a diagrammatic representation of the five-point summary of a data batch. The plot consists of a box spanning the hinges with the median indicated by a third line and two whiskers to represent the extreme values. The five-point summary is calculated internally and is returned in the workspace array.

The plot is returned in the character array plot. The size of the plot may be controlled using the arguments nstepx and nstepy. Optionally the plot can be output to an external file, in which case output is directed to the current advisory message unit as defined by x04abf.

An axis corresponding to the

y

axis is drawn and annotated and data points are plotted to the nearest character position.

4 References

Erickson B H and Nosanchuk T A (1985) Understanding Data Open University Press, Milton Keynes

Tukey J W (1977) Exploratory Data Analysis Addison–Wesley

5 Arguments

1: $prt$ – Character(1) Input

On entry: indicates whether the box and whisker plot is to be output to an external file.

$prt ='N'$: The box and whisker plot is not output to an external file.
$prt ='P'$: The box and whisker plot is output to the current advisory message unit as defined by x04abf.

Constraint:

prt ='P'

'N'

2: $m$ – Integer Input

On entry:

m

, the number of data batches that are to be represented.

Constraint:

m > 0

3: $n (m)$ – Integer array Input

On entry:

n (i)

contains the number of observations in the

i

th batch,

n_{i}

, for

i = 1, 2, \dots, m

n_{i} < 5

the

i

th batch is omitted from the plot.

Constraint: at least one

n (i)

must be greater than or equal to

5

, for

i = 1, 2, \dots, m

4: $x (ldx, m)$ – Real (Kind=nag_wp) array Input

On entry: the

i

th column of x must contain the data for the

i

th batch, that is

x (j, i)

must contain the

j

th observation of the

i

th batch, for

i = 1, 2, \dots, m

and

j = 1, 2, \dots, n_{i}

5: $ldx$ – Integer Input

On entry: the first dimension of the array x and the dimension of the array iwork as declared in the (sub)program from which g01asf is called.

Constraint:

ldx \geq \max {n (i)}

6: $nstepx$ – Integer Input

On entry: the number of character positions to be plotted in the

x

-direction.

Constraint:

nstepx \geq \max (19, (15 \times m / 4 + 9))

7: $nstepy$ – Integer Input

On entry: the number of character positions to be plotted in the

y

-direction.

Constraint:

nstepy \geq 9

8: $plot (ldplot, nstepx)$ – Character(1) array Output

On exit: contains the box and whisker plots.

9: $ldplot$ – Integer Input

On entry: the first dimension of the array plot as declared in the (sub)program from which g01asf is called.

Constraint:

ldplot \geq nstepy

10: $fivept (5 \times m)$ – Real (Kind=nag_wp) array Output

On exit:

fivept (j)

, for

j = (i - 1) \times 5 + 1, \dots, (i - 1) \times 5 + 5

, contains the five-point summary of the

i

th batch.

11: $iwork (ldx)$ – Integer array Workspace

12: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

1

to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of

0

causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of

−1

means that an error message is printed while a value of

1

means that it is not.

If halting is not appropriate, the value

−1

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, at least one element of $n < 5$ .

$ifail = 2$: On entry, $nstepx = ⟨ value ⟩$ .
Constraint: $nstepx \geq 19$ .

On entry, $nstepx = ⟨ value ⟩$ is too small for $⟨ value ⟩$ plots.

$ifail = 3$: On entry, $nstepy = ⟨ value ⟩$ .
Constraint: $nstepy \geq 9$ .

$ifail = 4$: On entry, $ldplot = ⟨ value ⟩$ and $nstepy = ⟨ value ⟩$ .
Constraint: $ldplot \geq nstepy$ .

$ifail = 5$: On entry, $prt = ⟨ value ⟩$ .
Constraint: $prt ='P'$ or $'N'$ .

$ifail = 6$: On entry, $ldx = ⟨ value ⟩$ .
Constraint: $ldx \geq ⟨ value ⟩$ .

$ifail = 7$: On entry, all batches have $n < 5$ .

$ifail = 8$: On entry, the data values are all identical.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

If the range of observations in a particular batch is too small to allow each item of the five-point summary to be plotted separately, then a sequence of stars are plotted at the median point of the batch to indicate that the full box-plot could not be plotted.

8 Parallelism and Performance

g01asf is not threaded in any implementation.

9 Further Comments

The time taken by g01asf increases with

m

and

n_{i}

, for

i = 1, 2, \dots, m

10 Example

The following program produces a box and whisker plot for each one of

5

data batches of sizes

5

6

8

8

and

7

respectively and prints the

5

box and whisker plots on the current advisory message unit.

g01as: FL CL CPP AD

NAG FL Interfaceg01asf (plot_​box_​whisker)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g01asf (plot_box_whisker)