module Statsample::Reliability - RDoc Documentation

alfa_second_derivative(n,sx,sxy) click to toggle source

Second derivative for alfa Parameters n: Number of items sx: mean of variances sxy: mean of covariances

# File lib/statsample/reliability.rb, line 106
def alfa_second_derivative(n,sx,sxy)
  (2*(sxy**2)*(sxy-sx)).quo(((sxy*(n-1))+sx)**3)
end

alpha_first_derivative(n,sx,sxy) click to toggle source

First derivative for alfa Parameters n: Number of items sx: mean of variances sxy: mean of covariances

# File lib/statsample/reliability.rb, line 97
def alpha_first_derivative(n,sx,sxy)
  (sxy*(sx-sxy)).quo(((sxy*(n-1))+sx)**2)
end

cronbach_alpha(ods) click to toggle source

Calculate Chonbach's alpha for a given dataset. only uses tuples without missing data

# File lib/statsample/reliability.rb, line 6
def cronbach_alpha(ods)
  ds=ods.dup_only_valid
  return nil if ds.vectors.any? {|k,v| v.variance==0}
  n_items=ds.fields.size
  return nil if n_items<=1
  s2_items=ds.vectors.inject(0) {|ac,v|
  ac+v[1].variance }
  total=ds.vector_sum
  
  (n_items.quo(n_items-1)) * (1-(s2_items.quo(total.variance)))
end

cronbach_alpha_from_covariance_matrix(cov) click to toggle source

Get Cronbach's alpha from a covariance matrix

# File lib/statsample/reliability.rb, line 57
def cronbach_alpha_from_covariance_matrix(cov)
  n=cov.row_size
  raise "covariance matrix should have at least 2 variables" if n < 2
  s2=n.times.inject(0) {|ac,i| ac+cov[i,i]}
  (n.quo(n-1))*(1-(s2.quo(cov.total_sum)))
end

cronbach_alpha_from_n_s2_cov(n,s2,cov) click to toggle source

Get Cronbach alpha from n cases, s2 mean variance and cov mean covariance

# File lib/statsample/reliability.rb, line 53
def cronbach_alpha_from_n_s2_cov(n,s2,cov)
  (n.quo(n-1)) * (1-(s2.quo(s2+(n-1)*cov)))
end

cronbach_alpha_standarized(ods) click to toggle source

Calculate Chonbach's alpha for a given dataset using standarized values for every vector. Only uses tuples without missing data Return nil if one or more vectors has 0 variance

# File lib/statsample/reliability.rb, line 21
def cronbach_alpha_standarized(ods)
  
  ds=ods.dup_only_valid
  
  return nil if ds.vectors.any? {|k,v| v.variance==0}
  
  ds=ds.fields.inject({}){|a,f|
    a[f]=ods[f].standarized; 
    a
  }.to_dataset
  
  cronbach_alpha(ds)
end

n_for_desired_alpha(alpha,s2,cov) click to toggle source

Returns n necessary to obtain specific alpha given variance and covariance mean of items

# File lib/statsample/reliability.rb, line 65
def n_for_desired_alpha(alpha,s2,cov)
  # Start with a regular test : 50 items
  min=2
  max=1000
  n=50
  prev_n=0
  epsilon=0.0001
  dif=1000
  c_a=cronbach_alpha_from_n_s2_cov(n,s2,cov)
  dif=c_a - alpha
  while(dif.abs>epsilon and n!=prev_n)
    prev_n=n
    if dif<0
      min=n
      n=(n+(max-min).quo(2)).to_i
    else
      max=n
      n=(n-(max-min).quo(2)).to_i
    end
    c_a=cronbach_alpha_from_n_s2_cov(n,s2,cov)
    dif=c_a - alpha
    #puts "#{n} , #{c_a}"
    
  end
  n
end

n_for_desired_reliability(r,r_d,n=1) click to toggle source

Returns the number of items to obtain r_d desired reliability from r current reliability, achieved with n items

# File lib/statsample/reliability.rb, line 45
def n_for_desired_reliability(r,r_d,n=1)
  return nil if r.nil?
  (r_d*(1-r)).quo(r*(1-r_d))*n
end

spearman_brown_prophecy(r,n) click to toggle source

Predicted reliability of a test by replicating n times the number of items

# File lib/statsample/reliability.rb, line 36
def spearman_brown_prophecy(r,n)
  (n*r).quo(1+(n-1)*r)
end