Method: Statsample::Test::UMannWhitney.u_sampling_distribution_as62

Defined in:
lib/statsample/test/umannwhitney.rb

.u_sampling_distribution_as62(n1, n2) ⇒ Object

U sampling distribution, based on Dinneen & Blakesley (1973) algorithm. This is the algorithm used on SPSS.

Parameters:

  • n1: group 1 size

  • n2: group 2 size

Reference:

  • Dinneen, L., & Blakesley, B. (1973). Algorithm AS 62: A Generator for the Sampling Distribution of the Mann- Whitney U Statistic. Journal of the Royal Statistical Society, 22(2), 269-273



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# File 'lib/statsample/test/umannwhitney.rb', line 31

def self.u_sampling_distribution_as62(n1,n2)

  freq=[]
  work=[]
  mn1=n1*n2+1
  max_u=n1*n2
  minmn=n1<n2 ? n1 : n2
  maxmn=n1>n2 ? n1 : n2
  n1=maxmn+1
  (1..n1).each{|i| freq[i]=1}
  n1+=1
  (n1..mn1).each{|i| freq[i]=0}
  work[1]=0
  xin=maxmn
  (2..minmn).each do |i|
    work[i]=0
    xin=xin+maxmn
    n1=xin+2
    l=1+xin.quo(2)
    k=i
    (1..l).each do |j|
      k=k+1
      n1=n1-1
      sum=freq[j]+work[j]
      freq[j]=sum
      work[k]=sum-freq[n1]
      freq[n1]=sum
    end
  end
  
  # Generate percentages for normal U
  dist=(1+max_u/2).to_i
  freq.shift
  total=freq.inject(0) {|a,v| a+v }
  (0...dist).collect {|i|
    if i!=max_u-i
      ues=freq[i]*2
    else
      ues=freq[i]
    end
    ues.quo(total)
  }
end