Post-hoc nonparametric pairwise comparisons of a one-way within subjects factor
The syntax below performs a specified pairwise comparison between a subset pair of groups representing the within subject factor. The overall one-way repeated measures ANOVA, using ranked outcomes to compute and compare group rank sums, should be carried out first using Friedman's test (Siegal and Castellan, 1988).
References
Siegel, S., & Castellan, N. J. Jr. (1988, 2nd ed.). Nonparametric statistics for the behavioral sciences. New York: McGraw–Hill. (First edition (1981) in CBSU library).
Sprent P., Smeetom, NC (2001) Applied nonparametric statistical methods. Chapman and Hall:London. Details of the post-hoc tests.
* Compares test performance (rows)
* over time at pre, mid and post (columns)
*
*
data list free/
t1 t2 t3.
begin data
1 3 5
21 25 27
0.2 0.1 0.1
2 1 3
end data.
* macro assumes columns called t1 to tn
* contain matched scores on the within subject
* factor e.g. time.
*
* pairf takes as inputs: the two columns to compare
* and the total number of columns
*
* output is a t-statistic, its df, p-value
* and the two columns which have been compared
define pairf( !pos !tokens(1)
/!pos !tokens(1)
/!pos !tokens(1)).
VARSTOCASES /ID = id
/MAKE test FROM t1 to !concat(t,!3)
/INDEX = time(3)
/KEEP =
/NULL = KEEP.
RANK VARIABLES=test (A) by id
/RANK
/PRINT=YES
/TIES=MEAN .
compute rtestsq=rtest*rtest.
exe.
aggregate outfile=*
/break = time
/rtsum rtsumsq=sum(rtest rtestsq)
/nsize = n(rtest).
matrix.
get m /variables=time rtsum rtsumsq nsize.
compute stsum=make(1,1,0).
loop i = 1 to mmax(m(:,1)).
compute stsum=stsum+((m(i,2))**2)/m(i,4).
end loop.
compute srsum=csum(m(:,3)).
compute tn=mmax(m(:,1)).
compute bn=mmax(m(:,4)).
compute #ct1=m(!1,2)-m(!2,2).
compute ct2=#ct1 / sqrt((2*bn*(srsum-stsum))/((bn-1)*(tn-1))).
compute ct3=1-fcdf(ct2*ct2,1,(bn-1)*(tn-1)).
save {ct2, (bn-1)*(tn-1), ct3, !1, !2} /outfile=*
/variables=tstat, df, pvalue, group_1, group_2.
end matrix.
formats tstat (f7.3) df (f4.0) pvalue (f5.3) group_1 (f2.0) group_2 (f2.0).
report format=list automatic align(center)
/variables=tstat df pvalue group_1 group_2
/title "Unadjusted comparisons for method"
"of Sprent and Smeeton (2001) for Friedman test"
" " " NB: This test is only valid if the Friedman test is statistically"
" significant overall using all the groups".
!enddefine.
pairf 1 3 3.