The programs below assume each person has three conditions, c1, c2 and c3 with the number of conditions entered as ncon and sub denoting control group (1) or case (2). They compare the average change over the three conditions to the change in the single case.
In SPSS you have to enter the contrast corresponding to a linear change over the three conditions. These are available in appendix polynomial of Howell DC (2002) Statistical Methods for Psychology Fifth Edition. Wadsworth:Pacific Grove, CA
compute linsum = -c1 + c3. exe. aggregate outfile='Y:\R_Work\aggemp.sav' /break=sub /avglin = mean(linsum) /sdlin= sd(linsum) /nlin=n. get file='Y:\R_Work\aggemp.sav' . if(sub eq 1) cbeta=avglin. if(sub eq 2) pbeta=avglin. if(sub eq 1) secbeta=cbeta/sqrt(nlin). compute const=1. exe. aggregate outfile=* /break=const /cb = first(cbeta) /pb= first(pbeta) /nb=first(nlin) /seb=first(secbeta). compute tout=(cb-pb)/seb. compute df=nb-1. compute pv2=2*(1-cdf.t(abs(tout),nb-1)). exe.
This can more elegantly be performed in R.
c1 <- c(2,1,4,5,2,3,4,1,2,3,4) c2 <- c(1,6,5,4,3,4,5,6,7,8,9) c3 <- c(2,1,3,4,5,6,7,8,9,3,11) sub <- c(1,1,1,1,1,1,1,1,1,1,2) # input number of conditions ncon <- 3 score <- c(c1,c2,c3)[sub == 1] subj <- sub[sub == 1] nsub <- length(subj) ymat <- matrix(score, nrow=nsub, ncol=ncon) ymat <- t(ymat) id <- rep(1:length(subj), ncon) cond <- gl(ncon,length(subj)) library(nlme) longa <- groupedData(score ~ cond | id) longa$cf <- factor(longa$cond, c(1:ncon)) longa$id <- factor(longa$id, c(1:length(subj))) contrasts(longa$cf) <- contr.poly(ncon) m <- contrasts(longa$cf)[,1] yc <- m %*% ymat yc <- cbind(yc[,1:length(subj)]) sec <- sd(c(yc[,1])) / sqrt(nsub) # fit repeated measures model model.cs <- gls(score ~ cf, data=longa, method=’ML’, corr=corCompSymm(form=~1 | id)) summary(model.cs) trendc <- coefficients(model.cs) # #repeat for a single case # score <- c(c1,c2,c3)[sub == 2] subj <- sub[sub == 2] id <- rep(1:length(subj), ncon) cond <- gl(ncon,length(subj)) longa <- groupedData(score ~ cond | id) longa$cf <- factor(longa$cond, c(1,2,3)) contrasts(longa$cf) <- contr.poly(ncon) m <- contrasts(longa$cf)[,1] trendp <- m %*% score tout <- (trendc[2]-trendp)/sec df <- nsub-1 pval <- dt(tout,nsub-1) #print out t, df of t and its 2-sided p-value print(tout) print(df) print(pval)