43 lines
1.7 KiB
Ruby
43 lines
1.7 KiB
Ruby
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module Statistics
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module StatisticalTest
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class ChiSquaredTest
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def self.chi_statistic(expected, observed)
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# If the expected is a number, we asumme that all expected observations
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# has the same probability to occur, hence we expect to see the same number
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# of expected observations per each observed value
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statistic = if expected.is_a? Numeric
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observed.reduce(0) do |memo, observed_value|
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up = (observed_value - expected) ** 2
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memo += (up/expected.to_f)
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end
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else
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expected.each_with_index.reduce(0) do |memo, (expected_value, index)|
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up = (observed[index] - expected_value) ** 2
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memo += (up/expected_value.to_f)
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end
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end
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[statistic, observed.size - 1]
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end
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def self.goodness_of_fit(alpha, expected, observed)
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chi_score, df = *self.chi_statistic(expected, observed) # Splat array result
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return if chi_score.nil? || df.nil?
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probability = Distribution::ChiSquared.new(df).cumulative_function(chi_score)
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p_value = 1 - probability
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# According to https://stats.stackexchange.com/questions/29158/do-you-reject-the-null-hypothesis-when-p-alpha-or-p-leq-alpha
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# We can assume that if p_value <= alpha, we can safely reject the null hypothesis, ie. accept the alternative hypothesis.
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{ probability: probability,
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p_value: p_value,
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alpha: alpha,
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null: alpha < p_value,
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alternative: p_value <= alpha,
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confidence_level: 1 - alpha }
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end
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end
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end
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end
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