df <- data.frame(c(rep("s1", 5), rep("s2", 5), rep("s3", 5),rep("s4", 5)),"a1", c("i1", "i2", "i3", "i4", "i5"), c(1, 0), 1)

colnames(df) <- c("student", "assessment", "item", "score", "points.possible")

unique <- subset(df[,c("assessment", "item")], !duplicated(df[,c("assessment", "item")]))

fun1 <- function(a.id, i.id) {
  # subset original dataframe for just one assessment
  subsetdf <- df[df$assessment == a.id,]

  # generate list of students that got the item right and wrong
  correct <- subsetdf$student[subsetdf$item==i.id & subsetdf$score==1]
  wrong <- subsetdf$student[subsetdf$item==i.id & subsetdf$score==0]

  # scores by student
  scores <- aggregate(score ~ student, data=subsetdf,sum)/aggregate(points.possible ~ student, data=subsetdf, sum)

  # average scores for students that got item right/wrong
  x.1 <- sum(subsetdf$score[subsetdf$student %in% correct])/sum(subsetdf$points.possible[subsetdf$student %in% correct])
  x.0 <- sum(subsetdf$score[subsetdf$student %in% wrong])/sum(subsetdf$points.possible[subsetdf$student %in% wrong])

  # percent of students that got item right
  p <- length(correct)/(length(correct)+length(wrong))

  # final stat calculation
  r <- ((x.1-x.0)*sqrt(p*(1-p)))/sd(scores[,2])
  print(r)
}

unique$r <- mapply(fun1, unique$assessment, unique$item)