A2DISPLAY procedure

Provides further output following an analysis of variance by A2WAY (R.W. Payne).

Options

PRINT = strings

Controls printed output from the analysis (aovtable, information, covariates, effects, residuals, means, %cv, missingvalues); default *

FPROBABILITY = string

Probabilities for variance ratio (yes, no); default no

PLOT = strings

Which residual plots to provide (fittedvalues, normal, halfnormal, histogram, absresidual); default *

GRAPHICS = string

Type of graphs (lineprinter, highresolution); default high

COMBINATIONS = string

Factor combinations for which to form predicted means (present, estimable); default esti

ADJUSTMENT = string

Type of adjustment to be made when predicting means (marginal, equal, observed); default marg

PSE = strings

Types of standard errors to be printed with the means (differences, lsd, means); default diff

LSDLEVEL = scalar

Significance level (%) for least significant differences; default 5

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 standard errors printed with the tables of means. The default setting is differences, which gives standard errors of differences of means. The setting means produces standard errors of means, lsd produces least significant differences, and by setting PSE=* the standard errors can be suppressed altogether. The significance level to use in the calculation of least significant differences can be changed from the default of 5% using the LSDLEVEL option.

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 of 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.

Options: PRINT, FPROBABILITY, PLOT, GRAPHICS, COMBINATIONS, ADJUSTMENT, PSE, LSDLEVEL.

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.