Class: Statsample::Test::WilcoxonSignedRank

Inherits:
Object
  • Object
show all
Includes:
Summarizable, Statsample::Test
Defined in:
lib/statsample/test/wilcoxonsignedrank.rb

Overview

From Wikipedia: The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student’s t-test, t-test for matched pairs, or the t-test for dependent samples when the population cannot be assumed to be normally distributed.

Instance Attribute Summary collapse

Instance Method Summary collapse

Methods included from Summarizable

#summary

Methods included from Statsample::Test

chi_square, levene, #p_using_cdf, #t_critical, t_one_sample, t_two_samples_independent, u_mannwhitney, wilcoxon_signed_rank, #z_critical

Constructor Details

#initialize(v1, v2, opts = Hash.new) ⇒ WilcoxonSignedRank

Parameters:



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 15

def initialize(v1,v2, opts=Hash.new)
@v1 = v1
@v2 = v2
  opts_default={:name=>_("Wilcoxon Signed Rank Test"),:tails=>:both}
  @opts=opts_default.merge(opts)
  opts_default.keys.each {|k|
    send("#{k}=", @opts[k])
  }
  calculate
end

Instance Attribute Details

#name ⇒ Object

Name of F analysis



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 10

def name
  @name
end

#nr ⇒ Object (readonly)

Returns the value of attribute nr.



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 12

def nr
  @nr
end

#tails=(value) ⇒ Object (writeonly)

Sets the attribute tails

Parameters:

  • value —

    the value to set the attribute tails to.



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 13

def tails=(value)
  @tails = value
end

#w ⇒ Object (readonly)

Returns the value of attribute w.



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 11

def w
  @w
end

Instance Method Details

#calculate ⇒ Object 



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 26

def calculate
df = Daru::DataFrame.new({:v1 => @v1,:v2 => @v2})
# df[:abs]=df.collect(:row) { |row|  (row[:v2] - row[:v1]).abs }
  df[:abs] = (df[:v2] - df[:v1]).abs
df[:sgn] = df.collect(:row) { |row| 
r = row[:v2] - row[:v1]
r == 0 ? 0 : r/r.abs
}
df = df.filter_rows { |row| row[:sgn] != 0}
df[:rank] = df[:abs].ranked
@nr = df.nrows

@w = df.collect(:row) { |row|
    row[:sgn] * row[:rank]
}.sum
end

#probability_exact ⇒ Object

Calculate exact probability. Don’t calculate for large Nr, please!



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 66

def probability_exact
str_format="%0#{nr}b"
combinations=2**nr
#p str_format
total_w=combinations.times.map do |i|
    comb=sprintf(str_format,i)
    w_local=comb.length.times.inject(0) do |ac,j|
      sgn=comb[j]=="0" ? -1 : 1
  ac+(j+1)*sgn
    end
end.sort

total_w.find_all do |v| 
    if @tails==:both
      v<=-w.abs or v>=w.abs
    elsif @tails==:left
      v<=w
    elsif @tails==:right
  v>=w
    end
end.count/(combinations.to_f)
end

#probability_z ⇒ Object

Assuming normal distribution of W, this calculate the probability of samples with Z equal or higher than obtained on sample



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 61

def probability_z
(1-Distribution::Normal.cdf(z))*(@tails==:both ? 2:1)
end

#report_building(generator) ⇒ Object

:nodoc:



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 43

def report_building(generator) # :nodoc:
  generator.section(:name=>@name) do |s|
    s.table(:name=>_("%s results") % @name) do |t|
      t.row([_("W Value"), "%0.3f" % @w])
      t.row([_("Z"), "%0.3f (p: %0.3f)" % [z, probability_z]])
      if(nr<=10) 
    t.row([_("Exact probability"), "p-exact: %0.3f" % [probability_exact]])
      end
    end
  end
end

#z ⇒ Object 



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# File 'lib/statsample/test/wilcoxonsignedrank.rb', line 54

def z
sigma=Math.sqrt((nr*(nr+1)*(2*nr+1))/6)
(w-0.5)/sigma
end