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# FACDIVIDE procedure

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 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.

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
```
Updated on March 8, 2019