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module Statistics
module StatisticalTest
class TTest
# Errors for Zero std
class ZeroStdError < StandardError
STD_ERROR_MSG = 'Standard deviation for the difference or group is zero. Please, reconsider sample contents'.freeze
end
# Perform a T-Test for one or two samples.
# For the tails param, we need a symbol: :one_tail or :two_tail
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
(data_mean - comparison_mean)/(data_std / Math.sqrt(args[1].size).to_f).to_f
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_f
right_root = sample_right_variance/args[1].size.to_f
standard_error = Math.sqrt(left_root + right_root)
(sample_left_mean - sample_right_mean).abs/standard_error.to_f
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
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_f
probability = Distribution::TStudent.new(degrees_of_freedom).cumulative_function(t_score)
p_value = 1 - probability
p_value *= 2 if tails == :two_tail
{ 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
end
end
end
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