Aims to give useful advice if a design that is thought to be balanced fails to be analysed by `ANOVA`

(R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output (`advice` , `suspects` ); default `advi` |
---|---|

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

`METHOD` = string tokens |
Method to use to predict the correct pattern of replication (`median` , `mode` , `proportional` ); default `mode` |

`WEIGHTS` = variate |
Weights for the analysis; default `*` i.e. all units have weight one |

`SUSPECTS` = variate |
Saves the numbers of the units whose factor values are suspected to be incorrect |

### Parameter

`Y` = variates |
Data values to be analysed (this is needed only if the analysis is to take place on a restricted set of units) |
---|

### Description

The `ANOVA`

directive analyses “balanced” designs. These include most of the commonly occurring experimental designs such as randomized blocks, Latin squares, split plots and other orthogonal designs, as well as designs with balanced confounding like balanced incomplete blocks or balanced lattices. Details of the necessary condition of *first-order balance* are given by Wilkinson (1970), Payne & Wilkinson (1976) and Payne & Tobias (1992). However, `ANOVA`

can itself detect whether or not a design can be analysed, so if you are not sure whether or not a particular design is analysable, you can run it through `ANOVA`

and see whether it succeeds or fails with an “AN 1” diagnostic. Sometimes the design will genuinely be unbalanced, but on other occasions it may be that errors have been made in entering the data. So the aim of `AN1ADVICE`

is to give useful advice if you find that a set of data that you had expected to be balanced fails to be analysed by `ANOVA`

.

The use of `AN1ADVICE`

is very similar to `ANOVA`

. You must first define the model that is to be fitted in the analysis, using the `BLOCKSTRUCTURE`

and `TREATMENTSTRUCTURE`

directives. As in `ANOVA`

, the treatment terms to be included in the model are controlled by the `FACTORIAL`

option, and the `WEIGHT`

option can specify weights for a weighted analysis of variance.

`AN1ADVICE`

has a parameter `Y`

to specify the variate whose values are being analysed. However, this is required only if you are analysing a subset of the units. (You would then have used the `RESTRICT`

directive, directly or through a menu, to restrict `Y`

to the units concerned.)

In a balanced design, the joint replications of sets of factors in the design will usually have a systematic pattern. Often there will be equal replication. Then, for example, if you look at the replication table for any pair of factors, it will contain a single value (the number of times each pair of their levels occurs in the design). Alternatively, the replications may have a proportional pattern. For example, you may have a “control” level of one of the factors with perhaps twice as many replicates as the other, “test”, levels. Then, in every replication table involving that factor, the cells for the “control” level will have values twice as large as those in the corresponding “test” cells. So `AN1ADVICE`

examines the factors in the model terms that `ANOVA`

has found to be unbalanced, and examines their replications to try to identify cells whose values seem to be too small or too large.

The `METHOD`

option controls how `AN1ADVICE`

works out what the replication in each table ought to be. The default setting, `mode`

, assumes that the values should all be equal, and that the non-zero value that occurs most often in the table is the correct one. The setting `median`

is similar except that the right value is assumed to be the median of the non-zero values. Finally, the `proportional`

setting estimates the correct values for each table by assuming that the replication has a proportional pattern.

The `PRINT`

option controls the printed output, with settings:

The default is `PRINT=advice`

. The list of suspect units can also be saved, in a variate, using the `SUSPECTS`

option.

If you believe that the design should be balanced, you may find that the factor values (or weights) of some of suspect units have been entered incorrectly. Alternatively, you may find that some units with the factor combinations whose replication has been highlighted as too low have been accidentally omitted from the data. If these mistakes can be corrected, the design may become balanced. Alternatively, if you cannot find any mistakes in the data, you will need to use regression or `REML`

instead of `ANOVA`

.

Options: `PRINT`

, `FACTORIAL`

, `METHOD`

, `WEIGHTS`

, `SUSPECTS`

.

Parameter: `Y`

.

### Action with `RESTRICT`

You can restrict the set of units used for the analysis by applying a restriction to the y-variate.

### References

Payne, R.W. & Wilkinson, G.N. (1977). A general algorithm for analysis of variance. *Applied Statistics*, 26, 251-260.

Payne, R.W. & Tobias, R.D. (1992). General balance, combination of information and the analysis of covariance. *Scandinavian Journal of Statistics*, 19, 3-23.

Wilkinson, G.N. (1970). A general recursive algorithm for analysis of variance. *Biometrika*, 57, 19-46.

### See also

Directives: `ANOVA`

, `BLOCKSTRUCTURE`

, `TREATMENTSTRUCTURE`

.

Commands for: Analysis of variance.

### Example

CAPTION 'AN1ADVICE 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 [NVALUES=72; LABELS=!T(Victory,'Golden rain',Marvellous)] Variety & [LABELS=!T('0 cwt','0.2 cwt','0.4 cwt','0.6 cwt')] Nitrogen READ [SERIAL=yes] Nitrogen,Variety 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 : TREATMENTS Variety*Nitrogen BLOCKS Blocks/Wplots/Subplots CAPTION 'With the correct factor values, the design is balanced.' ANOVA CAPTION !t('Now switch the Nitrogen values in units 43 & 44',\ 'with those in 45 & 46 so that it becomes unbalanced.') CALCULATE nn1,nn2 = Nitrogen$[!(43,44),!(45,46)] & Nitrogen$[!(43,44),!(45,46)] = nn2,nn1 AN1ADVICE [PRINT=advice,suspects]