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Plots single-factor polynomial contrasts fitted by `ANOVA` (R.W. Payne).

### Option

`SAVE` = `ANOVA` save structure Save structure (from `ANOVA`) to provide details of the analysis from which the polynomials are to be plotted; default uses the save structure from the most recent `ANOVA`

### Parameters

`XFACTOR` = factors Factor over which the polynomial contrasts have been formed Factor(s) for which different polynomial coefficients should be plotted in the same graph Factor or factors for which different polynomial coefficients should be plotted in a trellis plot Title for the graph; default defines a title automatically Title for the y-axis; default `' '` Title for the x-axis; default is to use the identifier of the `XFACTOR` Defines the pen to use to plot the points and/or line for each group defined by the `GROUPS` factors

### Description

`ADPOLYNOMIAL` plots polynomials fitted in analyses by the `ANOVA` directive. (These are included in the treatment model for `ANOVA` by the functions `POL` or `POLND`.) It also plots the corresponding means so that you can see how well the polynomials fit. By default, the polynomials are plotted from the most recent analysis performed by `ANOVA`, but the `SAVE` option can be used to supply the save structure from an earlier analysis to use instead.

The `XFACTOR` parameter specifies the factor over whose effects the polynomial contrasts have been fitted. If the analysis contains interactions between the `XFACTOR` and other factors, you can plot the polynomials for all the combinations of levels of these other factors by setting the `GROUPS` and `TRELLISGROUPS` parameters. If only `GROUPS` is specified, all the polynomials are plotted in a single graph. Alternatively, you can set the `TRELLISGROUPS` parameter to one or more of the factors to produce a trellis plot; there is then a graph for each of the combination of levels of the trellis factors (and each of these graphs plots the polynomials for every level of the group factors, at the relevant levels of the trellis factors). You should set `GROUPS` or `TRELLISGROUPS` to the factor if there is only one factor, or to a pointer containing all the factors if there are several.

The `TITLE`, `YTITLE` and `XTITLE` parameters can supply titles for the graph, the y-axis and the x-axis, respectively. The symbols, colours and line styles that are used in a high-resolution plot are usually set up by `ADPOLYNOMIAL` automatically. If you want to control these yourself, you should use the `PEN` directive to define a pen with your preferred symbol, colour and line style, for each of the groups defined by combinations of the `GROUPS` factors. The pen numbers should then be supplied to `ADPOLYNOMIAL`, in a variate with a value for each group, using the `PENS` parameter.

Option: `SAVE`.

Parameters: `XFACTOR`, `GROUPS`, `TRELLISGROUPS`, `TITLE`, `YTITLE`, `XTITLE`, `PENS`.

### Method

The coefficients of the polynomials are obtained using the `APOLYNOMIAL` procedure.

Directives: `ANOVA`, `TREATMENTSTRUCTURE`.

Procedure: `APOLYNOMIAL`.

Functions: `POL`, `POLND`.

Commands for: Analysis of variance.

### Example

```CAPTION     'ADPOLYNOMIAL example',!t('Split plot design, see the',\
'Guide to Genstat, Part 2, Section 4.2.1.'); STYLE=meta,plain
FACTOR      [NVALUES=72; LEVELS=6] Blocks
&           [LEVELS=3] Wplots
&           [LEVELS=4] Subplots
GENERATE    Blocks,Wplots,Subplots
FACTOR      [LABELS=!T('0 cwt','0.2 cwt','0.4 cwt','0.6 cwt')] Nitrogen
&           [LABELS=!T(Victory,'Golden rain',Marvellous)] Variety
VARIATE     Yield
4 3 2 1 1 2 4 3 1 2 3 4 3 1 2 4 4 1 2 3 2 1 3 4
2 3 4 1 4 2 3 1 1 4 2 3 3 4 1 2 1 3 4 2 2 3 4 1
4 1 3 2 3 4 1 2 3 4 2 1 3 1 4 2 4 3 1 2 1 2 3 4 :
3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2
2 2 2 2 3 3 3 3 1 1 1 1 3 3 3 3 2 2 2 2 1 1 1 1
2 2 2 2 1 1 1 1 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 :
156 118 140 105 111 130 174 157 117 114 161 141
104  70  89 117 122  74  89  81 103  64 132 133
108 126 149  70 144 124 121  96  61 100  91  97
109  99  63  70  80  94 126  82  90 100 116  62
96  60  89 102 112  86  68  64 132 124 129  89
118  53 113  74 104  86  89  82  97  99 119 121 :
TREATMENTS  Variety*Nitrogen
BLOCKSTRUCTURE Blocks/Wplots/Subplots
VARIATE     [VALUES=0,0.2,0.4,0.6] Nitlev
" Polynomial effects of nitrogen to order 2 (lin. and quad.)."
TREATMENTS  POL(Nitrogen;2;Nitlev) * Variety
" Analysis printing contrasts to order 4 and the aov table."
ANOVA       [PRINT=aov,contrasts] Yield