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# FWITHINTERMS procedure

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`.

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
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```
Updated on February 4, 2022