# PND FOR SINGLE-CASE RESEARCH (2016, AUGUST) 

# Citation: Tarlow, K. R., & Penland, A. (2016, August). 
#           PND for single-case research (R code). Retrieved 
#           from http://ktarlow.com/stats/

# R SYNTAX COPYRIGHT (C) 2016 KEVIN R. TARLOW & ANDREW PENLAND
# url: http://www.ktarlow.com/stats
# email: krtarlow@gmail.com

# adapted from: Tarlow, K. R., & Pendland, A. (2016). Outcome
#               assessment and inference with the Percentage
#               of Nonoverlapping Data (PND) single-case
#               statistic. Practice Innovations, 1(4), 
#               221-233.

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# 
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# the work under the following conditions:
#
# Attribution - You must attribute the work in the manner 
# specified by the author, KEVIN R. TARLOW (but not in any way 
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# of the work).
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# Noncommercial  You may not use this work for commercial 
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C <- function(n, k) {
  return(factorial(n) / (factorial(n - k) * factorial(k)))
}

pnd <- function(nA, nB, k) {
  n <- nA + nB
  p <- 0
  i <- k
  while (i < (nB + 1)) {
    M <- 1
    while (M < (n + 1)) {
      r <- 1
      while (r < (nA + 1)) {
        p <- p + C(nA, r) * (M - 1)^(nA - r) * C(nB, i) * (n - M)^i * M^(nB - i)
        r <- r + 1
      }
      M <- M + 1
    }
    i <- i + 1
  }
  p <- p / n^n
  PND <- k / nB * 100
  results <- data.frame(PND, p)
  return(results)
}