Doesn't use apply but maybe the following will work for you?
temp1<- data.frame(ID=c("Herb","Shrub"),stat=c(4,5),pvalue=c(.03,.04))
temp2<- data.frame(ID=c("Herb","Shrub",
"Tree"),stat=c(12,15,13),pvalue=c(.2,0.4,.3))
L<-list(a=temp1,b=temp2)
d.f = do.call("rbind",L)
d.f$tableName = substring(rownames(x),1,1)
HTH
Pete
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