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module Statistics
module StatisticalTest
class ChiSquaredTest
def self.chi_statistic(expected, observed)
# If the expected is a number, we asumme that all expected observations
# has the same probability to occur, hence we expect to see the same number
# of expected observations per each observed value
statistic = if expected.is_a? Numeric
observed.reduce(0) do |memo, observed_value|
up = (observed_value - expected) ** 2
memo += (up/expected.to_f)
end
else
expected.each_with_index.reduce(0) do |memo, (expected_value, index)|
up = (observed[index] - expected_value) ** 2
memo += (up/expected_value.to_f)
end
end
[statistic, observed.size - 1]
end
def self.goodness_of_fit(alpha, expected, observed)
chi_score, df = *self.chi_statistic(expected, observed) # Splat array result
return if chi_score.nil? || df.nil?
probability = Distribution::ChiSquared.new(df).cumulative_function(chi_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
end
end
end
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