Class: Statistics::StatisticalTest::TTest

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

Defined Under Namespace

Classes: ZeroStdError

Class Method Summary collapse

Class Method Details

.paired_test(alpha, tails, left_group, right_group) ⇒ Object

Raises:

  • (StandardError) 


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# File 'lib/statistics/statistical_test/t_test.rb', line 62

def self.paired_test(alpha, tails, left_group, right_group)
  raise StandardError, 'both samples are the same' if left_group == right_group

  # Handy snippet grabbed from https://stackoverflow.com/questions/2682411/ruby-sum-corresponding-members-of-two-or-more-arrays
  differences = [left_group, right_group].transpose.map { |value| value.reduce(:-) }

  degrees_of_freedom = differences.size - 1
  difference_std = differences.standard_deviation

  raise ZeroStdError, ZeroStdError::STD_ERROR_MSG if difference_std == 0

  down = difference_std/Math.sqrt(differences.size)

  t_score = (differences.mean - 0)/down.to_r

  t_distribution = Distribution::TStudent.new(degrees_of_freedom)
  probability = t_distribution.cumulative_function(t_score)

  p_value = if tails == :two_tail
            2 * (1 - t_distribution.cumulative_function(t_score.abs))
            else
              1 - probability
            end

  { t_score: t_score,
    probability: probability,
    p_value: p_value,
    alpha: alpha,
    null: alpha < p_value,
    alternative: p_value <= alpha,
    confidence_level: 1 - alpha }
end

.perform(alpha, tails, *args) ⇒ Object

Perform a T-Test for one or two samples. For the tails param, we need a symbol: :one_tail or :two_tail



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# File 'lib/statistics/statistical_test/t_test.rb', line 11

def self.perform(alpha, tails, *args)
  return if args.size < 2

  degrees_of_freedom = 0

  # If the comparison mean has been specified
  t_score = if args[0].is_a? Numeric
              data_mean = args[1].mean
              data_std = args[1].standard_deviation

              raise ZeroStdError, ZeroStdError::STD_ERROR_MSG if data_std == 0

              comparison_mean = args[0]
              degrees_of_freedom = args[1].size - 1

              (data_mean - comparison_mean)/(data_std / Math.sqrt(args[1].size).to_r).to_r
            else
              sample_left_mean = args[0].mean
              sample_left_variance = args[0].variance
              sample_right_variance = args[1].variance
              sample_right_mean = args[1].mean
              degrees_of_freedom = args.flatten.size - 2

              left_root = sample_left_variance/args[0].size.to_r
              right_root = sample_right_variance/args[1].size.to_r

              standard_error = Math.sqrt(left_root + right_root)

              (sample_left_mean - sample_right_mean).abs/standard_error.to_r
            end

  t_distribution = Distribution::TStudent.new(degrees_of_freedom)
  probability = t_distribution.cumulative_function(t_score)

  # Steps grabbed from https://support.minitab.com/en-us/minitab/18/help-and-how-to/statistics/basic-statistics/supporting-topics/basics/manually-calculate-a-p-value/
  # See https://github.com/estebanz01/ruby-statistics/issues/23
  p_value = if tails == :two_tail
            2 * (1 - t_distribution.cumulative_function(t_score.abs))
            else
              1 - probability
            end

  { t_score: t_score,
    probability: probability,
    p_value: p_value,
    alpha: alpha,
    null: alpha < p_value,
    alternative: p_value <= alpha,
    confidence_level: 1 - alpha }
end