Class: Statistics::StatisticalTest::FTest

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

Class Method Summary collapse

Class Method Details

.anova_f_score(*args) ⇒ Object

This method calculates the one-way ANOVA F-test statistic. We assume that all specified arguments are arrays. It returns an array with three elements:

[F-statistic or F-score, degrees of freedom numerator, degrees of freedom denominator].

Formulas extracted from: courses.lumenlearning.com/boundless-statistics/chapter/one-way-anova/ sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_HypothesisTesting-ANOVA/BS704_HypothesisTesting-Anova_print.html



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# File 'lib/statistics/statistical_test/f_test.rb', line 12

def self.anova_f_score(*args)
  # If only two groups have been specified as arguments, we follow the classic F-Test for
  # equality of variances, which is the ratio between the variances.
  f_score = nil
  df1 = nil
  df2 = nil

  if args.size == 2
    variances = [args[0].variance, args[1].variance]

    f_score = variances.max/variances.min.to_f
    df1 = 1 # k-1 (k = 2)
    df2 = args.flatten.size - 2 # N-k (k = 2)
  elsif args.size > 2
    total_groups = args.size
    total_elements = args.flatten.size
    overall_mean = args.flatten.mean

    sample_sizes = args.map(&:size)
    sample_means = args.map(&:mean)
    sample_stds = args.map(&:standard_deviation)

    # Variance between groups
    iterator = sample_sizes.each_with_index

    variance_between_groups = iterator.reduce(0) do |summation, (size, index)|
      inner_calculation = size * ((sample_means[index] - overall_mean) ** 2)

      summation += (inner_calculation / (total_groups - 1).to_f)
    end

    # Variance within groups
    variance_within_groups = (0...total_groups).reduce(0) do |outer_summation, group_index|
      outer_summation += args[group_index].reduce(0) do |inner_sumation, observation|
        inner_calculation = ((observation - sample_means[group_index]) ** 2)
        inner_sumation += (inner_calculation / (total_elements - total_groups).to_f)
      end
    end

    f_score = variance_between_groups/variance_within_groups.to_f
    df1 = total_groups - 1
    df2 = total_elements - total_groups
  end

  [f_score, df1, df2]
end

.one_way_anova(alpha, *args) ⇒ Object

This method expects the alpha value and the groups to calculate the one-way ANOVA test. It returns a hash with multiple information and the test result (if reject the null hypotesis or not). Keep in mind that the values for the alternative key (true/false) does not imply that the alternative hypothesis is TRUE or FALSE. It’s a minor notation advantage to decide if reject the null hypothesis or not.



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# File 'lib/statistics/statistical_test/f_test.rb', line 64

def self.one_way_anova(alpha, *args)
  f_score, df1, df2 = *self.anova_f_score(*args) # Splat array result

  return if f_score.nil? || df1.nil? || df2.nil?

  probability = Distribution::F.new(df1, df2).cumulative_function(f_score)
  p_value = 1 - probability

  # According to https://stats.stackexchange.com/questions/29158/do-you-reject-the-null-hypothesis-when-p-alpha-or-p-leq-alpha
  # We can assume that if p_value <= alpha, we can safely reject the null hypothesis, ie. accept the alternative hypothesis.
  { probability: probability,
    p_value: p_value,
    alpha: alpha,
    null: alpha < p_value,
    alternative: p_value <= alpha,
    confidence_level: 1 - alpha }
end