Performs a range of all pairwise multiple comparison tests (D.M. Smith).
Options
METHOD = string token |
Test to be performed (Tukey, SNK, REGWMR, Duncan, Scheffe, FPLSD, FULSD, Bonferroni, Sidak); default * |
|---|---|
DIRECTION = string token |
How to sort means (ascending, descending); default asce |
PROBABILITY = scalar |
The required significance level; default=0.05 |
ALSD = string token |
Whether to use the alternative LSD test where the Studentized Range statistic is used instead of Student’s t (yes, no); default no |
Parameters
MEANS = variates or tables |
Mean values |
|---|---|
REPLICATIONS = scalars or tables or variates |
Number(s) of observations per mean |
VARIANCE = scalars |
Estimate of variance |
DF = scalars |
Degrees of freedom |
LABELS = texts |
Identifiers of mean values |
Description
ALLPAIRWISE 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 means are input using the MEANS parameter, either in a table saved e.g. from AKEEP, or in a variate. The replication (or number of observations in each mean) is supplied by the REPLICATIONS parameter, either in a scalar (if all the replications are equal) or in a structure of the same type as the means. The estimate of the variance (usually a pooled estimate as given by the residual mean square in ANOVA, and accessible using the VARIANCE parameter of AKEEP) and its corresponding degrees of freedom are input as scalars using the VARIANCE and DF parameters respectively. The LABELS parameter can be used to supply labels for the means.
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 DIRECTION option allows the means to be arranged in ascending or descending order.
The PROBABILITY option allows the pair-wise significance level for the intervals intervals from the Fisher tests to be changed from the default 0.05 (e.g. to 0.01). For the other tests, it changes the experiment-wise significance level.
The ALSD allows the LSD test asked for (FPLSD or FULSD) to use the Studentized Range statistic rather than Student’s t (for further information see Hsu, 1996, page 139).
Options: METHOD, DIRECTION, PROBABILITY, ALSD.
Parameter: MEANS, REPLICATION, VARIANCE, DF, LABELS.
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.
See also
Procedures: AMCOMPARISON, AUMCOMPARISON, AMDUNNETT, CONFIDENCE, MCOMPARISON, VMCOMPARISON.
Commands for: Analysis of variance.
Example
CAPTION 'ALLPAIRWISE example',\
'Data from Duncan (1955) Biometrics paper.'; STYLE=meta,plain
VARIATE Mean
TEXT Meanid
READ [SETNVALUES=YES] Meanid,Mean
A 49.6 B 71.2 C 67.6 D 61.5 E 71.3 F 58.1 G 61.0 :
FACTOR [LABELS=!t(A,B,C,D,E,F,G)] Labels
" means in a variate with accompanying labels "
ALLPAIRWISE [METHOD=Bonferroni]\
MEANS=Mean; REPLICATION=6; VARIANCE=79.64; DF=30; LABELS=Meanid
TABLE [CLASS=Labels] Meantab; VALUES=Mean
" means in a table "
ALLPAIRWISE [METHOD=Bonferroni; DIRECTION=descending; PROBABILITY=0.01]\
MEANS=Meantab; REPLICATION=6; VARIANCE=79.64; DF=30