AMCOMPARISON procedure

Performs pairwise multiple comparison tests for ANOVA means (D.M. Smith).


Options

PRINT = strings
Controls printed output (comparisons, description, lines, letters); default lett

METHOD = string
Test to be performed (Tukey, SNK, REGWMR, Duncan, Scheffe, FPLSD, FULSD, Bonferroni, Sidak); default FPLSD

FACTORIAL = scalar
Limit on the number of factors in each term; default 3

DIRECTION = string
How to sort means (ascending, descending); default asce

PROBABILITY = scalar
The required significance level; default 0.05

STUDENTIZE = string
Whether to use the alternative LSD test where the Studentized Range statistic is used instead of Student's t (yes, no); default no

SAVE = ANOVA save structure
Save structure to provide the table of means; default save structure uses the from the most recent ANOVA


Parameters

TERMS = formula
Treatment terms whose means are to be compared

MEANS = pointer or variate
Saves the (sorted) means

LABELS = pointer or text
Saves labels for the (sorted) means

LETTERS = pointer or text
Saves letters indicating groups of means that do not differ significantly

SIGNIFICANCE = pointer or symmetric matrix
Indicators to show significant comparisons between (sorted) means


Description

AMCOMPARISON performs a range of all pairwise multiple comparison tests (see Hsu 1996 and Bechhofer, Santner & Goldsman 1995). The methodology implemented in the procedure closely follows that described in Chapter 5 of Hsu (1996).

   The TERMS parameter specifies a model formula to define the treatment terms whose means are to be compared. The means are usually taken from the most recent analysis of variance (performed by ANOVA), but you can set the SAVE option to a save structure from another ANOVA if you want to examine means from an earlier analysis. As in ANOVA, the FACTORIAL option sets a limit on the number of factors in each term (default 3).

   Printed output is controlled by the PRINT option, with settings:

    comparisons
indicates the signifance or non-significance of the comparison between each pair of means;

    description
provides a description including information such as the experiment-wise and compartment-wise error rates;

    lines
gives the means, with lines joining those that do not differ significantly;

    letters
gives the means, with identical letters (a, b etc.) alongside those that do not differ significantly.

By default, PRINT=letters.

   The means are usually sorted into ascending order, but you can set option DIRECTION=descending for descending order, or DIRECTION=* to leave them in their original order. Note, though, that the lines joining means with non-significant differences may then be broken.

   The type of test to be performed is specified by the METHOD option, with settings Tukey, SNK (Student-Newman-Keuls), REGWMR (Ryan/Einot-Gabriel/Welsch multiple range test), Duncan, Scheffe, FPLSD (Fisher's Protected Least Significant Difference), FULSD (Fisher's Unprotected Least Significant Difference), Bonferroni and Sidak. The PROBABILITY option allows the experiment-wise significance level for the intervals to be changed from the default 0.05 (e.g. to 0.01). The STUDENTIZE option can specify that the Fisher's protected or unprotected LSD tests should use the Studentized Range statistic rather than Student's t (for further information see Hsu 1996, page 139).

   The MEANS parameter can save the means, sorted according to the DIRECTION option and omitting any that were non-estimable. If the TERMS parameter specifies a single term, MEANS should be set to a variate. If TERMS specifies several terms, you must supply a pointer which will then be set up to contain as many variates as there are terms. Similarly the LABELS parameter can save labels to identify the means, in either a text (for a single term) or in a pointer of texts (for several). Likewise the LETTERS parameter can save texts with the letters identifying mean that do not differ significantly, and the SIGNIFICANCE parameter can save symmetric matrices containing ones or zeros according to whether the various comparisons were significant or non-significant.

 

Options: PRINT, METHOD, FACTORIAL, DIRECTION, PROBABILITY, STUDENTIZE, SAVE.

Parameter: TERMS, MEANS, LABELS, LETTERS, SIGNIFICANCE.


Method

The methodology implemented is based on that described and reviewed in Hsu (1996), and Bechhofer, Santner & Goldsman (1995). For specific details of the tests these books should be referred to.


References

Bechhofer, R.E., Santner, T.J. & Goldsman, D.M. (1995). Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons. Wiley, New York.

Hsu, J.C. (1996). Multiple Comparisons Theory and Methods. Chapman & Hall, London.