participant <- rep(1:10, each=100)
stimuli <- rep(1:100, 10)
judgment <- rnorm(1000)
df1 <- data.frame(participant, stimuli, judgment)
df2 <- data.frame(stimuli=1:100, criterion=rnorm(100))
df <- merge(df1, df2, by='stimuli') %>% arrange(participant, stimuli)

participants_id = unique (df$participant)

MyFun = function(Data) {

HelpFun = function(x, Data) {
# x is the index for the number of participants.
# It Will be used in the lapply call bellow
participants_x = sample(participants_id, x)
filter(Data, participant %in% participants_x) %>%
  group_by(stimuli) %>%
  summarise( mean_x = mean(judgment),
             criterion = unique(criterion) ) %>%
  summarise(cor = cor(.$mean_x, .$criterion))
  }
 N <- length(unique(Data$participant))

lapply(1:N, HelpFun, Data) %>% bind_rows()
}

MyFun(df)