Comparing a within subjects group difference to that of a single case

Pairwise case

Suppose a group of controls and a single case do a pair of conditions (c1, c2, say) and we are interested in seeing if the relationship between the conditions in the controls is the same as that in the single case.

Since we have a single case we can treat its difference as a constant. So we end up with a one sample t-test on the control group difference minus the case difference. Ie we test if the mean difference in controls - difference in case equals 0.

There is a one-sample t-test option under analyze:means in SPSS. The two-sample (independent samples) may also be performed on the difference in SPSS. Alternatively the below example will work using R. Here c1 and c2 are the two conditions and sub denotes if the subject is a control or a case. There is some controversy over this more conservative approach which assigns the control group variance to the single subject (difference) score rather than treating it as a constant with zero variance, as in the one sample t-test (see e.g. Mycroft et al. (2002)).

These tests, therefore, assume that the slopes in the control and patient groups have the same variance. Crawford and Garthwaite present [attachment:crawford.pdf a detailed discussion of the methods available.]

c1 <- c(2,1,2,3,1,2,2,1,1,3,3,1)
c2 <- c(3,4,1,1,6,1,3,2,2,5,2,2)
sub <- c(1,1,1,1,1,1,1,1,1,1,1,2)
diff <- c1–c2
diffn <- diff[sub == 1]
diffp <- diff[sub == 2]
diffy <- diffn - diffp 
const <- gl(1,length(diffn))
id <- gl(length(diffn),1)
t.test(diffy, mu=0)
df <- length(diffn)-1
toutc <- (mean(diffn)-diffp) / sqrt(var(diffn)*((nc+1)/nc))
pv <- 2*pt(-abs(toutc), df)

More programs

• [:FAQ/singcase/multiW: Three or more conditions]
• [:FAQ/singcase/abnorm: Confidence Intervals for Abnormality]

• [http://www.abdn.ac.uk/~psy086/dept/singslope.htm Downloadable Program for comparing individual slope estimate with its standard error to Controls]. This program requires individual slopes and standard errors of the Controls and Patient as input.

Reference

Mycroft, R. H., Mitchell, D. C., & Kay, J. (2002). An evaluation of statistical procedures for comparing an individual's performance with that of a group of controls. Cognitive Neuropsychology, 19, 291-299.