Forms factors to define terms representing the effects of one factor within another factor (R.W. Payne).

### Options

`LEVNULL` = scalar |
Numerical value to represent the null level assigned to units not involved in the comparison of the levels of one of the factors within a particular level of the other factor; default 0 |

`LABNULL` = text |
String to label the null level; default `'-'` |

### Parameters

`F1` = factors |
First factor |

`F2` = factors |
Second factor |

`F1WITHINF2` = pointers |
Pointer containing a factor for each level of the second factor, used to estimate the effects of the first factor within that level |

`F2WITHINF1` = pointers |
Pointer containing a factor for each level of the first factor, used to estimate the effects of the second factor within that level |

### Description

When there is an interaction between two factors, it may be interesting to compare the effects of one factor within each level of the other factor. `FWITHINTERMS`

forms factors to define terms to enable you to do this.

The two factors are specified by the `F1`

and `F2`

parameters. The `F1WITHINF2`

parameter saves a pointer containing a factor for each level of the `F2`

factor, to be used to assess the effects of `F1`

within that level. To do this you can specify a model formula of

`F2 / F1WITHINF2[]`

The term `F2`

represents the main effect of factor `F2`

. Subsequent terms like `F2.F1WITHINF2[i]`

represent the effects of `F1`

within level `i`

of factor `F2`

. To help make the output clear, the elements of `F1WITHINF2`

are labelled by the levels of `F2`

(or its labels if available). Each factor has the levels of `F1`

for the units with its corresponding level of `F2`

, and a “null” level elsewhere. The numerical value to represent the null level is specified by the `LEVNULL`

option (default 0). If `F1`

has labels, the label for the null level is specified by the `LABNULL`

option (default `'-'`

).

Similarly, the `F2WITHINF1`

parameter saves a pointer containing factors to assess the effects of `F2`

within `F1`

.

Options: `LEVNULL`

, `LABNULL`

.

Parameters: `F1`

, `F2`

, `F1WITHINF2`

, `F2WITHINF1`

.

### See also

Procedure: `FBETWEENGROUPVECTORS`

.

Commands for: Calculations and manipulation, Analysis of variance.

### Example

CAPTION 'FWITHINTERMS example',\ !t('Experiment on canola with two treatment factors,',\ 'N (nitrogen) and S (sulphur), in a randomized-block design');\ STYLE=meta,plain SPLOAD [PRINT=*] '%data%/Canola.gsh' BLOCK block / plot TREATMENTS N * S ANOVA [PRINT=aovtable,means; FPROBABILITY=yes] yield FWITHINTERMS F1=S; F2=N; F1WITHINF2=SwithinN; F2WITHINF1=NwithinS PRINT N,S,SwithinN[],NwithinS[]; DECIMALS=0 " sulphur within nitrogen " TREATMENTS N / SwithinN[] ANOVA [PRINT=aovtable,means; FPROBABILITY=yes] yield " nitrogen within sulphur " TREATMENTS S / NwithinS[] ANOVA [PRINT=aovtable,means; FPROBABILITY=yes] yield