What stats should I use to evaluate dichotomous data over time for a small sample? I have pilot data with 9 participants, and I'm trying to look at the change in the number of participants who meet a clinical threshold (i.e., yes, no) of symptoms across three time points. Does anyone have any idea of what statistical test I could use?
 A: My answer may be naive. Since your sample size is less, it would violate assumptions od most of the parametric tests.
You can compute the changes in the clinical threshold from first time point to second time point and then from second time point to third time point, so that you could have two new variables. Using these two variables, you can do a cross tabulation. I believe that you can do a Phi test with this cross tabulation (need to check the minimum cell value).
obs1<- rbinom(9,1,0.5)
obs2<- rbinom(9,1,0.5)
obs3<- rbinom(9,1,0.5)
mydata  <- as.data.frame(cbind(obs1, obs2, obs3))

mydata$t1t2<- mydata$obs1!=mydata$obs2
mydata$t2t3<- mydata$obs2!=mydata$obs3

ctab<-table(mydata$t1t2, mydata$t2t3)
ctab
library(rcompanion)
phi(ctab)

Output
> ctab
        FALSE TRUE
  FALSE     3    1
  TRUE      2    3

> phi(ctab)
 phi 
0.35 

If you don't want to install the library, rcompanion, 
> cv.test = function(x,y) {
  CV = sqrt(chisq.test(mydata$t1t2, mydata$t2t3, correct=FALSE)$statistic /
              (length(x) * (min(length(unique(x)),length(unique(y))) - 1)))
  print.noquote("Cramér V / Phi:")
  return(as.numeric(CV))
}

> cv.test(mydata$t1t2, mydata$t2t3)
[1] Cramér V / Phi:
[1] 0.35

If you want to have the labels Yes or No instead of TRUE or FALSE, 
mydata$t1t2<- factor(mydata$obs1!=mydata$obs2, labels = c('No', 'Yes'))
mydata$t2t3<- factor(mydata$obs2!=mydata$obs3, labels = c('No', 'Yes'))

> ctab<-table(mydata$t1t2, mydata$t2t3)
> ctab

      No Yes
  No   3   1
  Yes  2   3

