Provides further output following an analysis of variance by `A2WAY`

(R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output from the analysis (`aovtable` , `information` , `covariates` , `effects` , `residuals` , `means` , `%cv` , `missingvalues` ); default `*` |
---|---|

`FPROBABILITY` = string token |
Probabilities for variance ratio (`yes` , `no` ); default `no` |

`PLOT` = string tokens |
Which residual plots to provide (`fittedvalues` , `normal` , `halfnormal` , `histogram` , `absresidual` ); default `*` |

`GRAPHICS` = string token |
Type of graphs (`lineprinter` , `highresolution` ); default `high` |

`COMBINATIONS` = string token |
Factor combinations for which to form predicted means (`present` , `estimable` ); default `esti` |

`ADJUSTMENT` = string token |
Type of adjustment to be made when predicting means (`marginal` , `equal` , `observed` ); default `marg` |

`PSE` = string tokens |
Types of standard errors to be printed with the means (`differences` , `lsd` , `means` , `alldifferences` , `alllsd` ); default `diff` |

`LSDLEVEL` = scalar |
Significance level (%) for least significant differences; default 5 |

`RMETHOD` = string token |
Type of residuals to display (`simple` , `standardized` ); default `simp` |

### Parameter

`SAVE` = pointers |
Save structure (from `A2WAY` ) for the analysis; if omitted, output is from the most recent `A2WAY` analysis |
---|

### Description

The procedure `A2WAY`

provides specialized facilities for analysis of variance with either one or two treatment factors. There can also be a blocking factor. It automatically determines the type of design and uses the appropriate method: the `ANOVA`

directive if the design is balanced, or the regression directives (`FIT`

, `ADD`

and so on) if it is unbalanced.

Procedure `A2DISPLAY`

allows you to display further output from the analysis. By default the output is from the most recent analysis performed by `A2WAY`

. Alternatively, you can set the `SAVE`

parameter to a save structure (saved using the `SAVE`

parameter of `A2WAY`

) to obtain output from an earlier analysis.

Printed output is controlled by the `PRINT`

option, with settings:

`aovtable` |
analysis-of-variance table (probabilities are given for the variance ratios if option `FPROBABILITY=yes` ); |
---|---|

`information` |
information about the design (non-orthogonality &c); |

`covariates` |
covariate regression coefficients; |

`effects` |
treatment parameters in the linear model; |

`means` |
table of means; |

`%cv` |
the coefficient of variation; |

`missingvalues` |
estimates for any missing values; |

`residuals` |
residuals and fitted values. |

The `PSE`

option controls the types of standard errors that are produced to accompany the tables of means, with settings:

`differences` |
summary of standard errors for differences between pairs of means; |
---|---|

`alldifferences` |
standard errors for differences between all pairs of means (unbalanced designs only); |

`lsd` |
summary of least significant differences between pairs of means; |

`alllsd` |
least significant differences between all pairs of means (unbalanced designs only); |

`means` |
standard errors of the means – for unbalanced designs, these are approximate effective standard errors formed by procedure `SED2ESE` with the aim of allowing good approximations to the standard errors for differences to be calculated by the usual formula of sed = √(ese_{ij}_{i}^{2} + ese_{j}^{2}) |

The default is `differences`

. The `LSDLEVEL`

option sets the significance level (as a percentage) for the least significant differences.

For unbalanced designs (analysed by `A2WAY`

using Genstat regression) the means are produced using the `PREDICT`

directive. The first step (A) of the calculation forms the full table of predictions, classified by all the treatment and blocking factors. The second step (B) averages the full table over the factors that do not occur in the table of means. The `COMBINATIONS`

option specifies which cells of the full table are to be formed in Step A. The default setting, `estimable`

, fills in all the cells other than those that involve parameters that cannot be estimated. Alternatively, setting `COMBINATIONS=present`

excludes the cells for factor combinations that do not occur in the data. The `ADJUSTMENT`

option then defines how the averaging is done in Step B. The default setting, `marginal`

, forms a table of marginal weights for each factor, containing the proportion of observations with each of its levels; the full table of weights is then formed from the product of the marginal tables. The setting `equal`

weights all the combinations equally. Finally, the setting `observed`

uses the `WEIGHTS`

option of `PREDICT`

to weight each factor combination according to its own individual replication in the data.

The `PLOT`

option allows up to four of the following residual plots to be requested:

`fittedvalues` |
for a plot of residuals against fitted values; |
---|---|

`normal` |
for a Normal plot; |

`halfnormal` |
for a half-Normal plot; |

`histogram` |
for a histogram of residuals; and |

`absresidual` |
for a plot of the absolute values of the residuals against the fitted values. |

By default the first four are produced. The `GRAPHICS`

option determines the type of graphics that is used, with settings `highresolution`

(the default) and `lineprinter`

.

The `RMETHOD`

option controls whether simple or standardized residuals are printed or plotted; by default `RMETHOD=simple`

.

Options: `PRINT`

, `FPROBABILITY`

, `PLOT`

, `GRAPHICS`

, `COMBINATIONS`

, `ADJUSTMENT`

, `PSE`

, `LSDLEVEL`

, `RMETHOD`

.

Parameter: `SAVE`

.

### Method

`A2DISPLAY`

uses `ADISPLAY`

or `AUDISPLAY`

when appropriate. Otherwise, it saves the information, using `AKEEP`

or `RKEEP`

, and prints the output in the required format.

### Action with `RESTRICT`

If the `Y`

variate in `A2WAY`

was restricted, only the units not excluded by the restriction will have been analysed.

### See also

Procedures: `A2WAY`

, `A2KEEP`

, `A2RESULTSUMMARY`

Commands for: Analysis of variance.

### Example

CAPTION 'A2DISPLAY example',\ !t('Data from Snedecor & Cochran (1980), Statistical Methods',\ '(7th edition), page 216 and also see page 252.');\ STYLE=meta,plain FACTOR [LEVELS=4; VALUES=(1...4)6] Fat VARIATE [VALUES=64,78,75,55, 72,91,93,66, 68,97,78,49,\ 77,82,71,64, 56,85,63,70, 95,77,76,68] Absorbed A2WAY [PRINT=*; PLOT=*; TREATMENTS=Fat; FPROBABILITY=yes] Absorbed A2DISPLAY [PRINT=aovtable,means] CAPTION !t('Experiment on foster feeding of rats from Scheffe (1959)',\ 'The Analysis of Variance; also see McConway, Jones & Taylor (1999)',\ 'Statistical Modelling using GENSTAT, Example 7.6.') FACTOR [NVALUES=61; LABELS=!t(A,B,I,J)] Litter,Mother VARIATE [NVALUES=61] Littwt READ Litter,Mother,Littwt; FREPRESENTATION=labels A A 61.5 A A 68.2 A A 64.0 A A 65.0 A A 59.7 A B 55.0 A B 42.0 A B 60.2 A I 52.5 A I 61.8 A I 49.5 A I 52.7 A J 42.0 A J 54.0 A J 61.0 A J 48.2 A J 39.6 B A 60.3 B A 51.7 B A 49.3 B A 48.0 B B 50.8 B B 64.7 B B 61.7 B B 64.0 B B 62.0 B I 56.5 B I 59.0 B I 47.2 B I 53.0 B J 51.3 B J 40.5 I A 37.0 I A 36.3 I A 68.0 I B 56.3 I B 69.8 I B 67.0 I I 39.7 I I 46.0 I I 61.3 I I 55.3 I I 55.7 I J 50.0 I J 43.8 I J 54.5 J A 59.0 J A 57.4 J A 54.0 J A 47.0 J B 59.5 J B 52.8 J B 56.0 J I 45.2 J I 57.0 J I 61.4 J J 44.8 J J 51.5 J J 53.0 J J 42.0 J J 54.0 : A2WAY [PRINT=*; PLOT=*; TREATMENTS=Litter,Mother] Littwt A2DISPLAY [PRINT=aovtable,means,%cv;\ PSE=differences,lsd,means,alldifferences,alllsd]