pairwise(factorname,lev [,method:T] [,error:term]), CHARACTER scalar factorname, positive REAL scalar lev < 1, positive integer or CHARACTER scalar term, keyword phrase method:T one of 'lsd:T', 'bsd:T', 'snk:T', 'hsd:T', 'regwb:T', or 'regwr:T' pairwise(factorname,critval:val), positive REAL scalar val |

pairwise(factorname,siglevel) prints a summary of all paired comparisons between the levels of the factor given in factorname at the level of significance siglevel. Comparisons are done using the Bonferroni method. factorname must be a CHARACTER scalar or quoted string naming a factor in the current GLM model and siglevel must be a REAL scalar between 0 and 1. It is an error if there is no current GLM model or if the current GLM model does not contain the named factor. pairwise(factorname,siglevel,METHOD:T), where METHOD:T is one of 'bsd:T', 'lsd:T', 'snk:T', 'hsd:T', 'regwb:T', or 'regwr:T', does the same, except METHOD specifies the multiple comparison method to be used. METHOD Description bsd Bonferroni method (the default) lsd Least significant difference method hsd Tukey's honestly significant difference or Studentized range method snk Student-Newman-Keuls method regwb Step down Bonferroni using REGW tail probabilities regwrs Step down Studentized range using REGW tail probabilities. The REGW tail probabilities were proposed in papers by Ryan, Einot and Gabriel, and Welsch. pairwise(factorname,critval:val) does the same, except it uses val as the critical value for a t-test between the levels of factorname rather than a computed cutoff. Examples: After anova("y=trt"), Cmd> pairwise("trt",.01,hsd:T) does paired comparisons between the levels of trt at signficance .01 using the HSD method. Cmd> pairwise("trt",\ critval:invstudrng("trt",1 - .01, max(trt), DF[3])/sqrt(2)) does the same, directly computing the HSD critical value. See invstudrng(). pairwise() prints only a summary of the results and returns no value. The printed output consists of one row for each level of the term, sorted from smallest to largest effect, giving the "underlines" identifying effects that are not significantly different, level number, and effect. By default, the error mean square used in the comparison tests is taken from the last error term of the current model (the last line of the ANOVA table). You may specify a different error term with keyword phrase error:term. term must be a CHARACTER scalar or positive integer which specifies the name or number of the line in the ANOVA table to be used as the error mean square. Examples are 'error:4' (use line 4 as error term) or 'error:"a.b.c"' (use the ABC interaction as error term). The contrast() command is used to make each comparison. In particular this implies that the comparisons are adjusted for any other terms in the model and that there should be no missing degrees of freedom in the factor. Examples: Cmd> anova("y=a") Model used is y=a DF SS MS CONSTANT 1 15.082 15.082 a 4 67.535 16.884 ERROR1 15 20.132 1.3421 Cmd> pairwise("a",.05,hsd:T) #hsd method | 5 -1.86 | | 2 -1.18 | | 4 -1.15 | | 3 1.13 | 1 3.07 Cmd> pairwise("a",.05,lsd:T) #lsd w/ alpha=.05 | 5 -1.86 | 2 -1.18 | 4 -1.15 3 1.13 1 3.07 Cmd> pairwise("a",critval:2.13) #lsd w/ alpha=.05 a different way | 5 -1.86 | 2 -1.18 | 4 -1.15 3 1.13 1 3.07

Gary Oehlert 2003-01-15