Performs a range of all pairwise multiple comparison tests (D.M. Smith).
||Test to be performed (
||How to sort means (
||The required significance level; default=0.05|
||Whether to use the alternative LSD test where the Studentized Range statistic is used instead of Student’s t (
||Number(s) of observations per mean|
||Estimate of variance|
||Degrees of freedom|
||Identifiers of mean values|
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
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
REGWMR (Ryan/Einot-Gabriel/Welsch multiple range test),
FPLSD (Fisher’s Protected Least Significant Difference),
FULSD (Fisher’s Unprotected Least Significant Difference),
DIRECTION option allows the means to be arranged in ascending or descending order.
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.
ALSD allows the LSD test asked for (
FULSD) to use the Studentized Range statistic rather than Student’s t (for further information see Hsu, 1996, page 139).
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.
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.
Commands for: Analysis of variance.
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