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, alldifferences, alllsd); default diff

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

RMETHOD = string
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 sedij = √(esei2 + esej2)

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 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.

   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.