Represents a factor by factorial combinations of a set of factors (R.W. Payne).

### Option

`OLDFACTOR` = factor |
Factor whose levels are to be represented by the factorial combinations of the `NEWFACTOR` s |
---|

### Parameters

`NEWFACTOR` = factors |
Factors formed to represent `OLDFACTOR` |
---|---|

`LEVELS` = scalars or variates |
Levels of the `NEWFACTOR` s |

### Description

`FACDIVIDE`

allows a set of factors to be formed with a set of levels for every level of another factor. (It is thus provides the opposite operation to the procedure `FACPRODUCT`

, which forms a factor with a level for every combination of the levels of a set of factors.) `FACDIVIDE`

may be useful, for example, if a design for a single factor, such as a Latin square, is to be used to study several factors and their interactions: e.g. a 12 by 12 Latin square could be used to study the main effects and interaction of factors A and B with 3 and 4 levels respectively.

The original factor is specified by the `OLDFACTOR`

option, and the `NEWFACTOR`

and `LEVELS`

parameters specify the new factors and their levels. So, to represent the 12-level factor `Treat`

by factors `A`

and `B`

as above, would require

`FACDIVIDE [OLDFACTOR=Treat] NEWFACTOR=A,B; LEVELS=3,4`

As in the `FACTOR`

directive, the `LEVELS`

parameter can be set to a scalar if the new factor is to have the standard levels 1, 2 and so on, or to a variate if you want to specify some other levels.

Options: `OLDFACTOR`

. Parameters: `NEWFACTOR`

, `LEVELS`

.

### Method

`FACDIVIDE`

uses `GENERATE`

to form a set of mapping vectors containing the levels of the new factors, in standard order. It then uses these in the `NEWLEVELS`

function to calculate the levels of the new factors.

### Action with `RESTRICT`

If any `OLDFACTOR`

is restricted, the levels will be formed only for the units not excluded by the restriction.

### See also

Procedures: `AFUNITS`

, `FACPRODUCT`

, `FACCOMBINATIONS`

, `FBASICCONTRASTS`

, `FDISTINCTFACTORS`

.

Commands for: Calculations and manipulation, Design of experiments.

### Example

CAPTION 'FACDIVIDE example'; STYLE=meta FACTOR [LEVELS=12; VALUES=2,10,5,6,11,3,8,1,9,4,12,7] Factor12 FACDIVIDE [OLDFACTOR=Factor12] Factor3,Factor4; LEVELS=3,4 PRINT Factor12,Factor3,Factor4 " sort the levels to see how they have been allocated " SORT Factor12,Factor3,Factor4 PRINT Factor12,Factor3,Factor4