nag_contab_tabulate_margin (g11bc) computes a marginal table from a table computed by nag_contab_tabulate_stat (g11ba) or nag_contab_tabulate_percentile (g11bb) using a selected statistic.

Syntax

[stable, mcells, mdim, mlevel, auxt, ifail] = g11bc(stat, table, idim, isdim, maxst, 'ncells', ncells, 'ndim', ndim)

[stable, mcells, mdim, mlevel, auxt, ifail] = nag_contab_tabulate_margin(stat, table, idim, isdim, maxst, 'ncells', ncells, 'ndim', ndim)

Description

For a dataset containing classification variables (known as factors) the functions nag_contab_tabulate_stat (g11ba) and nag_contab_tabulate_percentile (g11bb) 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 nag_contab_tabulate_stat (g11ba) or nag_contab_tabulate_percentile (g11bb), nag_contab_tabulate_margin (g11bc) 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.

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

Parameters

Compulsory Input Parameters

1: $stat$ – string (length ≥ 1)

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: $table (ncells)$ – double array

The table as computed by nag_contab_tabulate_stat (g11ba) or nag_contab_tabulate_percentile (g11bb).

3: $idim (ndim)$ – int64int32nag_int array

The number of levels for each dimension of table as returned by nag_contab_tabulate_stat (g11ba) or nag_contab_tabulate_percentile (g11bb).

Constraint:

idim (i) \geq 2

, for

i = 1, 2, \dots, ndim

4: $isdim (ndim)$ – int64int32nag_int array

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.

5: $maxst$ – int64int32nag_int scalar

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.

Optional Input Parameters

1: $ncells$ – int64int32nag_int scalar: Default: the dimension of the array table.
The number of cells in table as returned by nag_contab_tabulate_stat (g11ba) or nag_contab_tabulate_percentile (g11bb).
2: $ndim$ – int64int32nag_int scalar: Default: the dimension of the arrays idim, isdim. (An error is raised if these dimensions are not equal.)
The number of dimensions for table as returned by nag_contab_tabulate_stat (g11ba) or nag_contab_tabulate_percentile (g11bb).

Constraint: $ndim \geq 2$ .

Output Parameters

1: $stable (maxst)$ – double array: 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 Further Comments.
2: $mcells$ – int64int32nag_int scalar: The number of cells in the sub-table in stable.
3: $mdim$ – int64int32nag_int scalar: The number of dimensions to the sub-table in stable.
4: $mlevel (ndim)$ – int64int32nag_int array: The first mdim elements contain the number of levels for the dimensions of the sub-table in stable. The remaining elements are not referenced.
5: $auxt (:)$ – double array: The dimension of the array auxt will be $maxst$ if $stat ='V'$ and $1$ otherwise

If $stat ='V'$ auxt contains the sub-table of means corresponding to the sub-table of variances in stable. Otherwise auxt is not referenced.
6: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$

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.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Only applicable when

stat ='V'

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

Further Comments

The sub-tables created by nag_contab_tabulate_margin (g11bc) 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 .

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.

Open in the MATLAB editor: g11bc_example

function g11bc_example


fprintf('g11bc example results\n\n');

y   = [ 274;   361;   253;   325;   317;   339;
        326;   402;   336;   379;   345;   361;
        352;   334;   318;   339;   393;   358;
        350;   340;   203;   397;   356;   298;
        382;   376;   355;   418;   387;   379;
        432;   339;   293;   322;   417;   342;
         82;   297;   133;   306;   352;   361;
        220;   333;   270;   388;   379;   274;
        336;   307;   266;   389;   333;   353];

idim   = [int64(3); 6; 3];
isdim  = [int64(0); 1; 1];
maxt   = prod(idim(isdim~=0));
maxt   = int64(maxt);

% Compute marginal table
stat = 'A';
[table, mcells, mdim, mlevel, auxt, ifail] = ...
  g11bc( ...
         stat, y, idim, isdim, maxt);

% Display results
fprintf(' Marginal Table\n\n');
ncol = mlevel(mdim);
nrow = mcells/ncol;
table  = transpose(reshape(table,[ncol,nrow]));
for i = 1:nrow
  fprintf('%8.2f', table(i,:));
  fprintf('\n');
end

g11bc example results

 Marginal Table

  235.33  332.67  196.33
  342.67  341.67  332.67
  309.33  370.33  320.33
  395.00  370.33  338.00
  373.33  326.67  292.33
  350.00  381.00  351.00

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox