Module: Statsample::Reliability

Defined in:
lib/statsample/reliability.rb,
lib/statsample/reliability/icc.rb,
lib/statsample/reliability/scaleanalysis.rb,
lib/statsample/reliability/skillscaleanalysis.rb,
lib/statsample/reliability/multiscaleanalysis.rb

Defined Under Namespace

Classes: ICC, ItemCharacteristicCurve, MultiScaleAnalysis, ScaleAnalysis, SkillScaleAnalysis

Class Method Summary collapse

Class Method Details

.alfa_second_derivative(n, sx, sxy) ⇒ Object

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


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# File 'lib/statsample/reliability.rb', line 103

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) ⇒ Object

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


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# File 'lib/statsample/reliability.rb', line 94

def alpha_first_derivative(n,sx,sxy)
  (sxy*(sx-sxy)).quo(((sxy*(n-1))+sx)**2)
end

.cronbach_alpha(ods) ⇒ Object

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


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# File 'lib/statsample/reliability.rb', line 6

def cronbach_alpha(ods)
  ds = ods.dup_only_valid
  n_items = ds.ncols
  return nil if n_items <= 1
  s2_items = ds.to_hash.values.inject(0) { |ac,v| 
    ac + v.variance }
  total    = ds.vector_sum
  
  (n_items.quo(n_items - 1)) * (1 - (s2_items.quo(total.variance)))
end

.cronbach_alpha_from_covariance_matrix(cov) ⇒ Object

Get Cronbach's alpha from a covariance matrix


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# File 'lib/statsample/reliability.rb', line 56

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) ⇒ Object

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


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# File 'lib/statsample/reliability.rb', line 52

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) ⇒ Object

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


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# File 'lib/statsample/reliability.rb', line 20

def cronbach_alpha_standarized(ods)
  ds = ods.dup_only_valid
  return nil if ds.any? { |v| v.variance==0}
  
  ds = Daru::DataFrame.new(
    ds.vectors.to_a.inject({}) { |a,i|
      a[i] = ods[i].standardize
      a
    }
  )
          
  cronbach_alpha(ds)
end

.n_for_desired_alpha(alpha, s2, cov) ⇒ Object

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


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# File 'lib/statsample/reliability.rb', line 64

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
  end
  n
end

.n_for_desired_reliability(r, r_d, n = 1) ⇒ Object

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


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# File 'lib/statsample/reliability.rb', line 44

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) ⇒ Object Also known as: sbp

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


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# File 'lib/statsample/reliability.rb', line 35

def spearman_brown_prophecy(r,n)
  (n*r).quo(1+(n-1)*r)
end