NAG Library Routine Document

G11BCF

INTEGER	NCELLS, NDIM, IDIM(NDIM), ISDIM(NDIM), MAXST, MCELLS, MDIM, MLEVEL(NDIM), IWK(3*NDIM), IFAIL
REAL (KIND=nag_wp)	TABLE(NCELLS), STABLE(MAXST), AUXT(*), WK(NCELLS)
CHARACTER(1)	STAT

3 Description

For a dataset containing classification variables (known as factors) the routines G11BAF and G11BBF compute a table using selected statistics, for example the mean or the median. The table is indexed by the levels of the selected factors, for example if there were three factors A, B and C with

3

2

and

4

levels respectively and the mean was to be tabulated the resulting table would be

3 \times 2 \times 4

with each cell being the mean of all observations with the appropriate combination of levels of the three factors. In further analysis the table of means averaged over C for A and B may be required; this can be computed from the full table by taking the mean over the third dimension of the table, C.

In general, given a table computed by G11BAF or G11BBF, G11BCF computes a sub-table defined by a subset of the factors used to define the table such that each cell of the sub-table is the selected statistic computed over the remaining factors. The statistics that can be used are the total, the mean, the median, the variance, the smallest and the largest value.

4 References

John J A and Quenouille M H (1977) Experiments: Design and Analysis Griffin

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin

West D H D (1979) Updating mean and variance estimates: An improved method Comm. ACM 22 532–555

5 Parameters

1: $STAT$ – CHARACTER(1)Input

On entry: indicates which statistic is to be used to compute the marginal table.

$STAT ='T'$: The total.
$STAT ='A'$: The average or mean.
$STAT ='M'$: The median.
$STAT ='V'$: The variance.
$STAT ='L'$: The largest value.
$STAT ='S'$: The smallest value.

Constraint:

STAT ='T'

'A'

'M'

'V'

'L'

'S'

2: $TABLE (NCELLS)$ – REAL (KIND=nag_wp) arrayInput

On entry: the table as computed by G11BAF or G11BBF.

3: $NCELLS$ – INTEGERInput

On entry: the number of cells in TABLE as returned by G11BAF or G11BBF.

4: $NDIM$ – INTEGERInput

On entry: the number of dimensions for TABLE as returned by G11BAF or G11BBF.

Constraint:

NDIM \geq 2

5: $IDIM (NDIM)$ – INTEGER arrayInput

On entry: the number of levels for each dimension of TABLE as returned by G11BAF or G11BBF.

Constraint:

IDIM (i) \geq 2

, for

i = 1, 2, \dots, NDIM

6: $ISDIM (NDIM)$ – INTEGER arrayInput

On entry: indicates which dimensions of TABLE are to be included in the sub-table. If

ISDIM (i) > 0

the dimension or factor indicated by

IDIM (i)

is to be included in the sub-table, otherwise it is excluded.

7: $STABLE (MAXST)$ – REAL (KIND=nag_wp) arrayOutput

On exit: the first MCELLS elements contain the sub-table computed using the statistic indicated by STAT. The table is stored in a similar way to TABLE with the MCELLS cells stored so that for any two dimensions the index relating to the dimension given later in IDIM changes faster. For further details see Section 9.

8: $MAXST$ – INTEGERInput

On entry: the maximum size of sub-table to be computed.

Constraint:

MAXST \geq

the product of the levels of the dimensions of TABLE included in the sub-table, STABLE.

9: $MCELLS$ – INTEGEROutput

On exit: the number of cells in the sub-table in STABLE.

10: $MDIM$ – INTEGEROutput

On exit: the number of dimensions to the sub-table in STABLE.

11: $MLEVEL (NDIM)$ – INTEGER arrayOutput

On exit: the first MDIM elements contain the number of levels for the dimensions of the sub-table in STABLE. The remaining elements are not referenced.

12: $AUXT (*)$ – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array AUXT must be at least

MAXST

STAT ='V'

, and at least

1

otherwise.

On exit: if

STAT ='V'

AUXT contains the sub-table of means corresponding to the sub-table of variances in STABLE. Otherwise AUXT is not referenced.

13: $IWK (3 \times NDIM)$ – INTEGER arrayWorkspace

14: $WK (NCELLS)$ – REAL (KIND=nag_wp) arrayWorkspace

15: $IFAIL$ – INTEGERInput/Output

On entry: IFAIL must be set to

0

- 1 ​ or ​ 1

. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value

- 1 ​ or ​ 1

is recommended. If the output of error messages is undesirable, then the value

1

is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is

0

. 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,	$NDIM < 2$ ,
or	$STAT \neq'T'$ , $'A'$ , $'M'$ , $'V'$ , $'L'$ or $'S'$ .

$IFAIL = 2$

On entry,	$IDIM (i) \leq 1$ , for some $i = 1, 2, \dots, NDIM$ ,
or	NCELLS is incompatible with IDIM,
or	the requested sub-table is of dimension $0$ ,
or	the requested sub-table is the full table,
or	MAXST is too small, the minimum value is returned in MDIM.

$IFAIL = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.8 in the Essential Introduction for further information.

$IFAIL = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.7 in the Essential Introduction for further information.

$IFAIL = - 999$: Dynamic memory allocation failed.
See Section 3.6 in the Essential Introduction for further information.

7 Accuracy

Only applicable when

STAT ='V'

. In this case a one pass algorithm is used as describe in West (1979).

8 Parallelism and Performance

G11BCF is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

The sub-tables created by G11BCF and stored in STABLE and, depending on STAT, also in AUXT are stored in the following way. Let there be

m

dimensions defining the table with dimension

k

having

l_{k}

levels, then the cell defined by the levels

i_{1}, i_{2}, \dots, i_{m}

of the factors is stored in

s

th cell given by

s = 1 + \sum_{k = 1}^{m} [(i_{k} - 1) c_{k}],

where

c_{j} = \prod_{k = j + 1}^{m} l_{k} for ​ j = 1, 2, \dots, n - 1 and c_{m} = 1 .

10 Example

The data, given by John and Quenouille (1977), is for 3 blocks of a

3 \times 6

factorial experiment. The data can be considered as a

3 \times 6 \times 3

table (i.e., blocks

\times

treatment with

6

levels

\times

treatment with

3

levels). This table is input and the

6 \times 3

table of treatment means for over blocks is computed and printed.

NAG Library Routine DocumentG11BCF

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

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 Library Routine Document

G11BCF