AONEWAY procedure

Performs one-way analysis of variance (R.W. Payne).


Options

PRINT = strings
Controls printed output from the analysis of variance (aovtable, information, covariates, effects, residuals, contrasts, means, cbeffects, cbmeans, stratumvariances, %cv, missingvalues, homogeneity, permutationtest); default aovt, mean, miss

GROUPS = factor
Defines the treatments for the analysis

COVARIATES = variates
Covariates (if any) for analysis of covariance

PLOT = strings
Which residual plots to provide (fittedvalues, normal, halfnormal, histogram, absresidual); default fitt, norm, half, hist

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

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

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

NTIMES = scalar
Number of random allocations to make when PRINT=perm; default 999

SEED = scalar
Seed for the random number generator used to make the allocations; default 0 continues from the previous generation or (if none) initializes the seed automatically


Parameters

Y = variates
Each of these contains the data values for an analysis

RESIDUALS = variates
Saves the residuals from each analysis

FITTEDVALUES = variates
Saves the fitted values from each analysis


Description

AONEWAY provides customized facilities and output for one-way analysis of variance. For example, if the treatments have unequal replication, a standard error is printed for each mean, rather than the summary for comparisons of means with minimum and maximum replication as given by ANOVA. Similarly, any missing values are excluded from the analysis by AONEWAY. Conversely, in ANOVA they need to be included, to ensure balance in the more general situations that it covers, and are estimated as part of the analysis. In addition, AONEWAY provides residual plots directly, instead of requiring you to use procedure APLOT after the analysis, and it can test the homogeneity of the variances within the groups.

   The Y parameter supplies a variate containing the data values to be analysed. The factor defining the groups to be compared is supplied by the GROUPS option. You can either specify just the factor to produce a simple one-way anova, or you can put it within a POL, REG or COMPARISON function to fit some contrasts at the same time. There is also a COVARIATES option which can supply one or more variates to be used as covariates in an analysis of covariance.

   Printed output is requested by listing the required components with the PRINT option. The most relevant settings are:

    aovtable
to print the analysis-of-variance table;

    means
to print the table of means;

    effects
to print the effects (means minus grand mean);

    %cv
to print the coefficient of variation;

    missingvalues
to print estimates for missing values (if any);

    homogeneity
to print tests for the homogeneity of the variances within the groups; and

    permutationtest
analysis-of-variance table with the probabilities calculated by a random permutation test.

However, for compatibility, all the settings of the PRINT option of ANOVA are included. By default, when PRINT=perm, AONEWAY makes 999 random allocations of the data to the two samples (using a default seed), and determines the probabilities of the variance ratios from their distribution over these randomly generated datasets. (It therefore makes no assumptions about the distribution of the data values.) The NTIMES option allows you to request another number of allocations, and the SEED option allows you to specify another seed. AONEWAY checks whether NTIMES is greater than the number of possible ways in which the data values can be allocated. If so, it does an exact test instead, which takes each possible allocation once.

   The FPROBABILITY option can be set to yes to print of probabilities for variance ratios in the analysis-of-variance table. 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 the least significant differences can be changed from the default of 5% using the LSDLEVEL option.

   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.

   Variates of residuals and fitted values can be saved using the RESIDUALS and FITTEDVALUES parameters, respectively. Directive AKEEP can be used to save other information from the analysis of the last data variate to be analysed by the procedure (see the Guide to GenStat, Part 2, Section 4.6.1 for details).

 

Options: PRINT, GROUPS, COVARIATES, PLOT, GRAPHICS, FPROBABILITY, PSE, LSDLEVEL.

Parameters: Y, RESIDUALS, FITTEDVALUES .


Method

AONEWAY uses the standard GenStat facilities for analysis of variance, except that the standard errors and lsd's for the means are saved by AKEEP and then printed, rather than being printed directly (as just a summary) by ADISPLAY. Permutation tests are performed by APERMTEST, residual plots are produced by APLOT, and the homogeneity of variances is tested by VHOMOGENEITY.


Action with RESTRICT

If the Y variate is restricted, only the units not excluded by the restriction will be analysed.