Class: Statistics::SpearmanRankCoefficient

Inherits:
Object
  • Object
show all
Defined in:
lib/statistics/spearman_rank_coefficient.rb

Class Method Summary collapse

Class Method Details

.coefficient(set_one, set_two) ⇒ Object

Formulas extracted from: statistics.laerd.com/statistical-guides/spearmans-rank-order-correlation-statistical-guide.php



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# File 'lib/statistics/spearman_rank_coefficient.rb', line 33

def self.coefficient(set_one, set_two)
  raise 'Both group sets must have the same number of cases.' if set_one.size != set_two.size
  return if set_one.size == 0 && set_two.size == 0

  set_one_mean, set_two_mean = set_one.mean, set_two.mean
  have_tie_ranks = (set_one + set_two).any? { |rank| rank.is_a?(Float) || rank.is_a?(Rational) }

  if have_tie_ranks
    numerator = 0
    squared_differences_set_one = 0
    squared_differences_set_two = 0

    set_one.size.times do |idx|
      local_diff_one = (set_one[idx] - set_one_mean)
      local_diff_two = (set_two[idx] - set_two_mean)

      squared_differences_set_one += local_diff_one ** 2
      squared_differences_set_two += local_diff_two ** 2

      numerator += local_diff_one * local_diff_two
    end

    denominator = Math.sqrt(squared_differences_set_one * squared_differences_set_two)

    numerator / denominator.to_r # This is rho or spearman's coefficient.
  else
    sum_squared_differences = set_one.each_with_index.reduce(0) do |memo, (rank_one, index)|
      memo += ((rank_one - set_two[index]) ** 2)
      memo
    end

    numerator = 6 * sum_squared_differences
    denominator = ((set_one.size ** 3) - set_one.size)

    1.0 - (numerator / denominator.to_r) # This is rho or spearman's coefficient.
  end
end

.rank(data:, return_ranks_only: true) ⇒ Object 



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# File 'lib/statistics/spearman_rank_coefficient.rb', line 3

def self.rank(data:, return_ranks_only: true)
  descending_order_data = data.sort { |a, b| b <=> a }
  rankings = {}

  data.each do |value|
    # If we have ties, the find_index method will only retrieve the index of the
    # first element in the list (i.e, the most close to the left of the array),
    # so when a tie is detected, we increase the temporal ranking by the number of
    # counted elements at that particular time and then we increase the counter.
    temporal_ranking = descending_order_data.find_index(value) + 1 # 0-index

    if rankings.fetch(value, false)
      rankings[value][:rank] += (temporal_ranking + rankings[value][:counter])
      rankings[value][:counter] += 1
      rankings[value][:tie_rank] = rankings[value][:rank] / rankings[value][:counter].to_r
    else
      rankings[value] = { counter: 1, rank: temporal_ranking, tie_rank: temporal_ranking }
    end
  end

  if return_ranks_only
    data.map do |value|
      rankings[value][:tie_rank]
    end
  else
    rankings
  end
end