Forms information about aliased model terms in analysis of variance (R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output (`aovtable` , `aliasedterms` ); default `alia` |
---|---|

`TREATMENTSTRUCTURE` = formula |
Treatment model for the design; if this is not set, the default is taken from any existing setting defined by the `TREATMENTSTRUCTURE ` directive |

`BLOCKSTRUCTURE` = formula |
Block model for the design; if this is not set, the default is taken from any existing setting defined by the `BLOCKSTRUCTURE` directive |

`FACTORIAL` = scalar |
Limit on number of factors in a treatment term; default 3 |

`RESTRICTION` = variate |
Defines a restriction on the units for the analysis; default * i.e. none |

### Parameters

`TERMS` = formula |
Model terms whose aliased terms are to be identified; the default is to take all the terms in the treatment model |
---|---|

`ALIASTERMS` = formula or pointer |
New factors, with levels (and labels) that exclude those that Saves the aliased terms |

### Description

When a term is aliased in an analysis of variance, it is listed in the *Information summary* produced by

`ANOVA [PRINT=information]`

under the heading “Aliased model terms”. However, `ANOVA`

does not indicate the terms with which it is aliased. This information can be obtained using procedure `FALIASTERMS`

.

The block structure of the design can be specified by the `BLOCKSTRUCTURE`

option. If this is not set, the default is taken from any existing setting defined by the `BLOCKSTRUCTURE`

directive. Similarly, the treatments are specified by the `TREATMENTSTRUCTURE`

option, with a default taken from any existing setting defined by the `TREATMENTSTRUCTURE`

directive. As in `ANOVA`

, the `FACTORIAL`

option sets a limit on the number of factors in a treatment term; default 3. The `RESTRICTION`

option can supply a variate to define a restriction on the units of the design. (Units where the variate contains a zero value are excluded from the analysis.)

The terms whose aliasing is to be investigated are specified by the `TERMS`

parameter. If this is not specified, all the terms in the treatment model are investigated.

The terms to which they are aliased can be saved using the `ALIASEDTERMS`

parameter. They are saved in a formula structure if a single term has been specified by `TERMS`

, or in a pointer containing a formula structure for each term if it has specified several.

Printed output is controlled by the `PRINT`

option with settings:

`aovtable` |
to print the analysis-of-variance table; and |

`aliasterms` |
to print the terms to which each term is aliased (default). |

Options: `PRINT`

, `TREATMENTSTRUCTURE`

, `BLOCKSTRUCTURE`

, `FACTORIAL`

, `RESTRICTION`

.

Parameters: `TERM`

, `ALIASTERMS`

.

### Method

The procedure calculates a set of dummy effects for the aliased model term, and then forms and analyses a variate in which only these effects are present. The analysis detects the model terms to which the term is aliased as those that have non-zero sums of squares.

### Action with RESTRICT

A restriction can be specified using the `RESTRICTION`

option.

### See also

Directives: `ANOVA`

, `FPSEUDOFACTORS`

.

Procedures: `AEFFICIENCY`

, `ALIAS`

.

Commands for: Analysis of variance, Design of experiments.

### Example

CAPTION 'FALIASTERMS example'; STYLE=meta FACTOR [NVALUES=32; LEVEL=2] A,B,C & [LEVEL=4] D,Blocks & [ LEVEL=8] Plots GENERATE A,B,C & D & Blocks,Plots VARIATE [VALUES=13,17,25,33,18,19,22,14,26,23,31,29,25,21,18,34, \ 23,19,33,36,25,23,29,18,31,30,37,33,29,27,20,36] Y BLOCKSTRUCTURE Blocks/Plots TREATMENTS A*B*C+D ANOVA [PRINT=aovtable,information] Y CAPTION !T('The aov table and information summary show that D is aliased;',\ 'FALIASTERMS indicates that the aliasing is with B, C and B.C ') FALIASTERMS D PRINT !T('The printout below confirms this:', \ 'D level 1 corresponds to B level 1 and C level 1,', \ 'D level 2 corresponds to B level 1 and C level 2,', \ 'D level 3 corresponds to B level 2 and C level 1,', \ 'D level 4 corresponds to B level 2 and C level 2.'); \ JUSTIFICATION=left & [RLWIDTH=3; ORIENTATION=across] D,B,C; FIELDWIDTH=2; JUST=left PRINT !T('Use RESTRICT to analyse only the first 3 blocks;', \ 'the main effect D is still aliased, exactly as before...'); \ JUSTIFICATION=left RESTRICT Y; Blocks < 4 ANOVA [PRINT=aovtable,information] Y FALIASTERMS [RESTRICTION=Blocks<4] D