From 7fbc0ce6c7a1cc89c0ccc20a948ccea7acb55ff9 Mon Sep 17 00:00:00 2001
From: Oliver Czulo <oliver.czulo@uni-leipzig.de>
Date: Sun, 7 Apr 2024 13:56:58 +0200
Subject: [PATCH] Added functions to the chi_square test library to test
 contingency tables for independence of observations

---
 .../statistical_test/chi_squared_test.rb      | 59 +++++++++++++++++++
 ruby-statistics.gemspec                       |  1 +
 .../statistical_test/chi_squared_test_spec.rb | 38 ++++++++++++
 3 files changed, 98 insertions(+)

diff --git a/lib/ruby-statistics/statistical_test/chi_squared_test.rb b/lib/ruby-statistics/statistical_test/chi_squared_test.rb
index 982d2f2..370af78 100644
--- a/lib/ruby-statistics/statistical_test/chi_squared_test.rb
+++ b/lib/ruby-statistics/statistical_test/chi_squared_test.rb
@@ -1,6 +1,9 @@
 module RubyStatistics
   module StatisticalTest
     class ChiSquaredTest
+
+      require 'matrix'
+
       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
@@ -37,6 +40,62 @@ def self.goodness_of_fit(alpha, expected, observed)
           alternative: p_value <= alpha,
           confidence_level: 1 - alpha }
       end
+
+      # The following three functions serve to calculate a test of independence for contingency
+      # tables (short: ct) of the type
+      #
+      #      A   B
+      # X   20  18
+      # Y    7  35
+      #
+      # They have been tested using 2x2 and 3x3 tables. Tables are implemented as type Matrix.
+      #
+      def self.test_of_independence(alpha, observed_matrix)
+        expected_matrix = calculate_expected_matrix(observed_matrix)
+        df = (observed_matrix.row_size - 1) * (observed_matrix.column_size - 1)
+        chi_score = chi_statistic_matrix(observed_matrix, expected_matrix)
+        probability = Distribution::ChiSquared.new(df).cumulative_function(chi_score)
+        p_value = 1.0 - probability
+    
+        {
+          chi_score: chi_score,
+          df: df,
+          probability: probability,
+          p_value: p_value,
+          alpha: alpha,
+          null: alpha < p_value,
+          alternative: p_value <= alpha,
+          confidence_level: 1 - alpha,
+          expected: expected_matrix
+        }
+      end
+      
+      # For a contingency table of observed values, calculate the expected values
+      def self.calculate_expected_matrix(observed_matrix)
+        row_sums = observed_matrix.row_vectors.map { |row| row.to_a.sum.to_r }
+        col_sums = observed_matrix.column_vectors.map { |col| col.to_a.sum.to_r }
+        total_sum = row_sums.sum
+        
+        # create a mutable array from the Matrix of observed values
+        # so we have a 'template' for our Matrx of expected values
+        expected = observed_matrix.to_a
+        # calculate the expected values
+        observed_matrix.each_with_index do |i, row, col|
+          expected[row][col] = (row_sums[row] * col_sums[col]) / total_sum
+        end
+        Matrix.rows(expected)
+      end
+
+      def self.chi_statistic_matrix(observed_matrix, expected_matrix)
+        sum = 0.0
+        observed_matrix.each_with_index do |i, row, col|
+            sum += (observed_matrix[row, col] - expected_matrix[row, col])**2 / expected_matrix[row, col]
+        end
+        sum
+      end
+
+      private_class_method :chi_statistic_matrix
+
     end
   end
 end
diff --git a/ruby-statistics.gemspec b/ruby-statistics.gemspec
index ff4d555..83bccfd 100644
--- a/ruby-statistics.gemspec
+++ b/ruby-statistics.gemspec
@@ -32,4 +32,5 @@ Gem::Specification.new do |spec|
   spec.add_development_dependency "grb", '~> 0.4.1', '>= 0.4.1'
   spec.add_development_dependency 'byebug', '>= 9.1.0'
   spec.add_development_dependency 'pry'
+  spec.add_development_dependency 'matrix'
 end
diff --git a/spec/ruby-statistics/statistical_test/chi_squared_test_spec.rb b/spec/ruby-statistics/statistical_test/chi_squared_test_spec.rb
index a8ad853..534dfbd 100644
--- a/spec/ruby-statistics/statistical_test/chi_squared_test_spec.rb
+++ b/spec/ruby-statistics/statistical_test/chi_squared_test_spec.rb
@@ -1,4 +1,5 @@
 require 'spec_helper'
+require 'matrix'
 
 describe RubyStatistics::StatisticalTest::ChiSquaredTest do
   describe '.chi_statistic' do
@@ -82,4 +83,41 @@
       expect(result[:alternative]).to be false
     end
   end
+
+  describe '.calculate_expected_matrix' do
+    
+    it 'calculate expected values for a 2*3 contingency table of observed values' do
+      
+      observed = Matrix[[388,51692],[119,45633],[271,40040]]
+      result = described_class.calculate_expected_matrix(observed)
+
+      expect(result.map(&:to_i)).to eq(Matrix[[(40518240/138143), (7153969200/138143)], [(35595056/138143), (6284723480/138143)], [(31361958/138143), (5537320515/138143)]])
+
+    end
+
+  end
+
+  describe '.test_of_independence' do
+
+    it 'calculate test of independence for a 2*3 contingency table' do
+
+      observed = Matrix[[388,51692],[119,45633],[271,40040]]
+      alpha = 0.05
+      result = {}
+
+      expect do
+        result = described_class.test_of_independence(alpha, observed)
+      end.not_to raise_error
+
+      expect(result[:chi_score].round(4)).to eq(114.3600)
+      expect(result[:p_value]).to eq(0.0)
+      expect(result[:df]).to eq(2)
+      expect(result[:null]).to be false
+      expect(result[:alternative]).to be true
+
+    end
+
+  end
+
+
 end