analyze correlation between homicide and atheism

analysis.rb

#!/usr/bin/env ruby -Ku

# take countries by atheism                 http://en.wikipedia.org/wiki/Demographics_of_atheism
# compare to countries by homicide rate     http://en.wikipedia.org/wiki/List_of_countries_by_intentional_homicide_rate

# calculations and analysis down below

countries = {
  "Sweden"=>{:atheism=>85, :crime=>1.17},
  "Denmark"=>{:atheism=>80, :crime=>1.11},
  "Norway"=>{:atheism=>72, :crime=>0.78},
  "Japan"=>{:atheism=>65, :crime=>0.64},
  "Czech Republic"=>{:atheism=>61, :crime=>1.34},
  "Finland"=>{:atheism=>60, :crime=>2.75},
  "France"=>{:atheism=>54, :crime=>1.64},
  "South Korea"=>{:atheism=>52, :crime=>2.18},
  "Estonia"=>{:atheism=>49, :crime=>9.4},
  "Germany"=>{:atheism=>49, :crime=>1.06},
  "Russia"=>{:atheism=>48, :crime=>27.0},
  "Hungary"=>{:atheism=>46, :crime=>2.09},
  "Netherlands"=>{:atheism=>44, :crime=>1.17},
  "United Kingdom"=>{:atheism=>44, :crime=>1.75},
  "Belgium"=>{:atheism=>43, :crime=>2.05},
  "Bulgaria"=>{:atheism=>40, :crime=>3.09},
  "Slovenia"=>{:atheism=>38, :crime=>1.45},
  "Israel"=>{:atheism=>37, :crime=>2.62},
  "Canada"=>{:atheism=>30, :crime=>1.95},
  "Latvia"=>{:atheism=>29, :crime=>8.58},
  "Slovakia"=>{:atheism=>28, :crime=>2.27},
  "Switzerland"=>{:atheism=>27, :crime=>1.07},
  "Austria"=>{:atheism=>26, :crime=>0.72},
  "Australia"=>{:atheism=>25, :crime=>1.28},
  "Spain"=>{:atheism=>24, :crime=>1.23},
  "Iceland"=>{:atheism=>23, :crime=>1.03},
  "New Zealand"=>{:atheism=>22, :crime=>2.0},
  "Ukraine"=>{:atheism=>20, :crime=>7.42},
  "Belarus"=>{:atheism=>17, :crime=>8.31},
  "Greece"=>{:atheism=>16, :crime=>0.99},
  "Italy"=>{:atheism=>15, :crime=>1.23},
  "Armenia"=>{:atheism=>14, :crime=>2.48},
  "China"=>{:atheism=>14, :crime=>2.36},
  "Lithuania"=>{:atheism=>13, :crime=>9.38},
  "Singapore"=>{:atheism=>13, :crime=>0.49},
  "Uruguay"=>{:atheism=>12, :crime=>5.64},
  "Kazakhstan"=>{:atheism=>12, :crime=>12.1},
  "Mongolia"=>{:atheism=>9, :crime=>12.81},
  "Portugal"=>{:atheism=>9, :crime=>1.37},
  "United States"=>{:atheism=>9, :crime=>5.5},
  "Albania"=>{:atheism=>8, :crime=>5.68},
  "Argentina"=>{:atheism=>8, :crime=>6.3},
  "Kyrgyzstan"=>{:atheism=>7, :crime=>8.01},
  "Dominican Republic"=>{:atheism=>7, :crime=>25.25},
  "Croatia"=>{:atheism=>7, :crime=>1.83}
}


# calculate coefficient of correlation in accordance with http://mathbits.com/mathbits/tisection/statistics2/correlation.htm
# let x = atheism in or around 2004 (with the bar set at weak/negative atheism, ie not convinced there are gods as opposed to convinced there are no gods)
# let y = crime (intentional homicide rate per 100,000 inhabitants in 2004)
n   = countries.size                                                                                          # => 45
Σx  = countries.inject(0) { |sum,(country,attributes)| sum + attributes[:atheism] }                           # => 1411
Σy  = countries.inject(0) { |sum,(country,attributes)| sum + attributes[:crime]   }                           # => 200.57
Σxy = countries.inject(0) { |sum,(country,attributes)| sum + attributes[:crime] * attributes[:atheism]   }    # => 4930.82
Σx² = countries.inject(0) { |sum,(country,attributes)| sum + attributes[:atheism]**2 }                        # => 64181
Σ²x = countries.inject(0) { |sum,(country,attributes)| sum + attributes[:atheism] }**2                        # => 1990921
Σy² = countries.inject(0) { |sum,(country,attributes)| sum + attributes[:crime]**2 }                          # => 2340.8835
Σ²y = countries.inject(0) { |sum,(country,attributes)| sum + attributes[:crime] }**2                          # => 40228.3249

include Math
numerator     = n*Σxy - Σx*Σy                             # => -61117.3700000001
denominator   = sqrt(n*Σx² - Σ²x)  *  sqrt(n*Σy² - Σ²y)   # => 241701.344644796
r             = numerator / denominator                   # => -0.252863177446605
puts r


# since r is negative, we know they are negatively correlated
# value of 0.25 is half of 0.5, therefore the correlation is weak

# So the conclusion is that atheism implies lower homicide rates, though not very strongly.


# Uncertainty in this analysis:
# * There are many ways this could be measured, I googled "countries by crime" and found homicide rates, 
#     but you could also look at violence, arrests, standard of living, etc.
# * data is from 2004, so 6 or 7 years old.
# * homicide rates are from wikipedia, I did not check their sources (though they did cite them)
# * this really correlates weak/negative atheism, for example, Bhuddists are included in this category, 
#     there is also a comment on the site I got the data from that says refusal to disclose gets lumped in with nonbelief
# * there are approximately 195 countries in the world, but I only have data for 45 of them, that is a significant deficiency
# * in some cases, homicide rates for 2004 did not exist, I selected the next closest year
# * I may have made a mistake, feel free to check my work
# * These countries have data on atheism but not homicide: ["Vietnam", "Taiwan", "North Korea", "Cuba"]
#     though Taiwan's status as a country is questionable.
#     also, atheism data listed Britain, I changed that to United Kingdom

data.rb

#!/usr/bin/env ruby -Ku


# this file was used to scrape the data, see other file for calculations, analysis, conclusion



# as of 2004
atheism = <<-ATHEISM
Sweden 	8,986,000 	46 – 85% 	4,133,560 – 7,638,100
Vietnam 	82,690,000 	81% 	66,978,900
Denmark 	5,413,000 	43 – 80% 	2,327,590 – 4,330,400
Norway 	4,575,000 	31 – 72% 	1,418,250 – 3,294,000
Japan 	127,333,000 	64 – 65% 	81,493,120 – 82,766,450
Czech Republic 	10,246,100 	54 – 61% 	5,328,940 – 6,250,121
Finland 	5,215,000 	28 – 60% 	1,460,200 – 3,129,000
France 	60,424,000 	43 – 54% 	25,982,320 – 32,628,960
South Korea 	48,598,000 	30 – 52% 	14,579,400 – 25,270,960
Estonia 	1,342,000 	49% 	657,580
Germany 	82,425,000 	41 – 49% 	33,794,250 – 40,388,250
Russia 	143,782,000 	24 – 48% 	34,507,680 – 69,015,360
Hungary 	10,032,000 	32 – 46% 	3,210,240 – 4,614,720
Netherlands 	16,318,000 	39 – 44% 	6,364,020 – 7,179,920
United Kingdom 	60,271,000 	31 – 44% 	18,684,010 – 26,519,240
Belgium 	10,348,000 	42 – 43% 	4,346,160 – 4,449,640
Bulgaria 	7,518,000 	34 – 40% 	2,556,120 – 3,007,200
Slovenia 	2,011,000 	35 – 38% 	703,850 – 764,180
Israel 	6,199,000 	15 – 37% 	929,850 – 2,293,630
Canada 	32,508,000 	19 – 30% 	6,176,520 – 9,752,400
Latvia 	2,306,000 	20 – 29% 	461,200 – 668,740
Slovakia 	5,424,000 	10 – 28% 	542,400 – 1,518,720
Switzerland 	7,451,000 	17 – 27% 	1,266,670 – 2,011,770
Austria 	8,175,000 	18 – 26% 	1,471,500 – 2,125,500
Australia 	19,913,000 	24 – 25% 	4,779,120 – 4,978,250
Taiwan 	22,750,000 	24% 	5,460,000
Spain 	40,281,000 	15 – 24% 	6,042,150 – 9,667,440
Iceland 	294,000 	16 – 23% 	47,040 – 67,620
New Zealand 	3,994,000 	20 – 22% 	798,800 – 878,680
Ukraine 	47,732,000 	20% 	9,546,400
Belarus 	10,311,000 	17% 	1,752,870
Greece 	10,648,000 	16% 	1,703,680
North Korea 	22,698,000 	15%* 	3,404,700
Italy 	58,057,000 	6 – 15% 	3,483,420 – 8,708,550
Armenia 	2,991,000 	14% 	418,740
China 	1,298,848,000 	8 – 14%* 	103,907,840 – 181,838,720
Lithuania 	3,608,000 	13% 	469,040
Singapore 	4,354,000 	13% 	566,020
Uruguay 	3,399,000 	12% 	407,880
Kazakhstan 	15,144,000 	11 – 12% 	1,665,840 – 1,817,280
Mongolia 	2,751,000 	9% 	247,590
Portugal 	10,524,000 	4 – 9% 	420,960 – 947,160
United States 	293,028,000 	3 – 9% 	8,790,840 – 26,822,520
Albania 	3,545,000 	8% 	283,600
Argentina 	39,145,000 	4 – 8% 	1,565,800 – 3,131,600
Kyrgyzstan 	5,081,000 	7% 	355,670
Dominican Republic 	8,834,000 	7% 	618,380
Cuba 	11,309,000 	7%* 	791,630
Croatia 	4,497,000 	7% 	314,790
ATHEISM


# country, source, 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, most recent
violence = <<-VIOLENCE
El Salvador 	[6][7][8][9] 	37 	35 	31 	33 	41 	55 	55 	49 	52 	71 	71
Honduras 	[10][11][12][13] 	50 	54 	56 	34 	32 	35 	43 	50 	58 	67 	67
Jamaica 	[14][15] 	34 	44 	40 	36 	54 	58 	49 	58 		58 	58
Guatemala 	[8][9][16] 	26 	25 	31 	35 	36 	42 	45 	45 	49 	52 	52
Venezuela 	[17][18][19] 	33 	32 	38 	44 	37 	37 	45 	48 	52 	49 	49
Trinidad and Tobago 	[20] 	10 	13 	15 	20 	22 	33 	31 	33 	46 	43 	43
Colombia 	[21][22][23][24][25] 	63 	65 	66 	53 	44 	39 	40 	39 	36 	35 	35
South Africa 	[26][27] 	50 	48 	48 	43 	40 	40 	41 	39 	37 	34 	34
Belize 	[28][29] 	16.3 	24.9 	33.1 	24.9 	28.7 	30.0 	33.0 	30.8 	33.4 		33.4
Brazil 	[30][31][32] 	26.7 	27.8 	28.4 	28.9 	27.4 	26.6 	25.7 	25.2 			25.2
Dominican Republic 	[33] 	13.09 	12.49 	14.51 	18.73 	25.25 	26.41 	23.56 				23.57
Puerto Rico 	[34][35][36][37][38][39][40][41][42][43] 	18 	19 	20 	20 	20 	20 	19 	19 	20 	23 	23
Ecuador 	[44][45][46] 				15.07 	18.33 	18.07 	16.24 	16.90 	19 		19
Mexico 	[47][48][49][50] 	14.11 	13.94 	13.04 	10 	11 	11 	11 	10 	12 	15 	15
Russia 	[51][52] 	28 	30 	31 	29 	27 	25 	20 	17.9 	16.5 	14.9 	14.9
Swaziland 	[45][47] 	88.61 			13.05 	13.63 						13.63
Panama 	[48][53] 	10.1 	10.56 	9.56 	10.8 	9.7 	11.2 	11.3 	12.9 			12.9
Paraguay 	[44][47] 	12.05 					15.02 	12.33 				12.33
Madagascar 	[54] 					12 						12
Nicaragua 	[55][56] 	9 	10 	11 	12 	11 	12 	12 				12
Mongolia 	[44][45] 				13.51 	12.81 	12.01 	11.94 				11.94
Kazakhstan 	[44] 						12.1 	11.5 				11.5
Suriname 	[45] 				15.10 	10.30 						10.30
Papua New Guinea 	[47] 	9.06 										9.06
Kyrgyzstan 	[44][45][47] 	8.40 			8.15 	8.01 	9.44 	8.48 				8.48
Zimbabwe 	[45][47] 	7.24 			7.99 	8.44 						8.44
Lithuania 	[44][45][47][48] 	10.01 	10.14 	8.45 	9.96 	9.38 	10.77 	8.13 				8.13
Thailand 	[44][47] 	8.47 					8.16 	7.92 				7.92
Zambia 	[47] 	7.89 										7.89
Costa Rica 	[45][48][57] 	6.34 	6.64 	6.44 	6.99 	6.23 	7.81 	7.68 				7.68
Belarus 	[44][45][47][48] 	10.13 	9.72 	9.96 	8.91 	8.31 	8.53 	7.53 				7.53
Barbados 	[47] 	7.49 										7.49
Seychelles 	[47] 	7.39 										7.39
Uganda 	[45] 				7.95 	7.37 						7.37
Georgia 	[44][45][47] 	4.76 			6.62 	6.22 	9.01 	7.29 				7.29
Estonia 	[58][59] 	10.42 	10.02 	10.43 	13.86 	9.40 	11.58 	8.85 	8.19 	7.76 	7.09 	7.09
Ukraine 	[45][47][60] 	8.93 			8.51 	7.42 	7.04 					7.04
Turkey (excluding attempts) 	[58] 	9.96 	8.60 	8.26 	7.61 	7.05 	6.94 					6.94
Pakistan 	[47][61] 	6.86										6.86
Sri Lanka 	[45] 				6.42 	6.69 						6.69
Namibia 	[48] 		6.33 	6.35 								6.35
Kenya 	[44] 					6.50 	5.72 					5.72
Albania 	[48] 		6.64 	5.68 								5.68
Peru 	[45][48] 		4.91 	4.25 	4.85 	5.54 						5.54
Argentina 	[47][48][62][63] 	7.17 	8.43 	9.47 	7.9 	6.3 	5.8 	5.27 	5.26 	5.80 	5.45 	5.45
United States 	[64] 	5.5 	5.6 	5.6 	5.7 	5.5 	5.6 	5.7 	5.6 	5.4 	5.0 	5.0
Latvia (including attempts) 	[65] 	9.19 	9.00 	8.76 	9.44 	8.58 	5.51 	6.45 	5.13 	5.24 	4.82 	4.82
Moldova 	[44][45][47][48] 	8.13 	8.36 	7.99 	7.94 	6.71 	5.83 	4.80 				4.80
Uruguay 	[45][47][48] 	4.61 	6.31 	6.46 	5.30 	5.64 	4.3 					4.3
Montenegro 	[44] 						3.62 	4.16 				4.16
Côte d'Ivoire 	[47] 	4.07 										4.07
Mauritius 	[45][47] 	2.19 			2.95 	2.51 	2.98 	4.00 				4.00
Yemen 	[47] 	3.98 										3.98
Palestine 	[44][45] 				2.70 	4.04 	3.85 					3.85
Philippines 	[44][45][47][48] 	7.59 	7.47 	8.20 	4.97 	4.31 	3.83 	3.82 				3.82
Iran 	[45] 				2.64 	2.93 						2.93
Bolivia 	[48] 		3.74 	2.82 								2.82
India 	[44] 						2.88 	2.82 				2.82
Dominica 	[47] 	2.74 										2.74
Bangladesh 	[44] 						2.24 	2.64 				2.64
Bulgaria (excluding attempts) 	[45][47][58] 	4.07 	3.90 	3.25 	3.17 	3.09 	2.54 					2.54
Romania (excluding attempts) 	[45][48][58] 	2.50 	2.66 	2.52 	2.52 	2.37 	2.09 	2.76 	2.51 			2.51
Armenia 	[44][45][47] 	3.34 			2.50 	2.48 	1.82 	2.49 				2.49
Azerbaijan 	[45][47][48] 	2.81 	2.69 	2.59 	2.20 	2.41 						2.41
China 	[66] 							2.36 				2.36
Malaysia 	[44][47] 	2.36 					1.94 	2.31 				2.31
South Korea 	[44][45][47] 	2.02 			2.19 	2.18 						2.18
Finland (excluding attempts) 	[45][47][48][60] 	2.86 	3.01 	2.54 	1.97 	2.75 	2.17 					2.17
Macedonia (excluding attempts) 	[44][58] 	2.52 	2.71 	2.94 	3.46 	2.41 	2.16 	2.01 				2.01
New Zealand 	[47][48][60] 	1.17 	1.16 	1.29 			2.00 					2.00
Slovakia (excluding attempts) 	[58] 	2.65 	2.40 	2.38 	2.71 	2.27 	1.97 					1.97
Israel 	[45][67] 				3.01 	2.62 		2.68 	1.87 			1.87
Bosnia and Herzegovina 	[44] 						1.79 	1.86 				1.86
Nepal 	[44][48] 		2.56 	3.42 			2.08 	1.84 				1.84
Canada 	[45][47][48][68][69][70]	1.59 	1.67 	1.67 	1.74 	1.95 	2.05 	1.86 	1.80 	1.83 		1.83
Jordan 	[44] 						1.21 	1.75 				1.75
Chile 	[45][47][71] 		1.9 	1.9 	1.8 	1.7 	1.9 	1.9 	1.9 	1.6 	1.7 	1.7
Cyprus (excluding attempts) 	[44][45][48][58] 	1.16 	1.00 	0.43 	2.10 	2.05 	2.14 	1.66 				1.66
Croatia (excluding attempts) 	[44][45][48][58] 	2.47 	1.86 	1.79 	1.53 	1.83 	1.49 	1.62 				1.62
France (excluding attempts) 	[45][47][58][60] 	1.79 	1.76 	1.87 	1.64 	1.64 	1.60 					1.60
Bermuda 	[45] 				3.14 	1.56 						1.56
Belgium (excluding attempts) 	[58] 	2.00 	2.35 	2.23 	1.83 	2.05 	1.65 	1.81 	1.85 	1.49 		1.49
Serbia 	[44] 						1.44 	1.46 				1.46
Hungary (excluding attempts) 	[45][47][48][60] 	2.05 	2.49 	2.00 	2.33 	2.09 	1.64 		1.47 		1.38 	1.38
Czech Republic (excluding attempts) 	[44][45][47][48][58] 	1.69 	1.45 	1.36 	1.56 	1.34 	1.02 	1.33 				1.33
Poland (excluding attempts) 	[44][45][48][58] 	2.21 	2.01 	1.87 	1.72 	1.64 	1.45 	1.28 				1.28
Maldives 	[45][48] 		2.50 	2.79 	1.28 							1.28
United Kingdom (excluding attempts) 	[58][72] 	1.70 	1.78 	2.06 	1.76 	1.75 	1.49 				1.28 	1.28
Portugal (excluding attempts) 	[58] 	1.14 	1.02 	1.15 	1.43 	1.37 	1.26 					1.26
Tunisia 	[47][48] 	1.18 	1.26 	1.22 								1.22
Australia 	[45][45][47][47][60][73][74] 	1.57 			1.53 	1.28 	1.45 	1.42 	1.2 	1.2 		1.2
Spain (excluding attempts) 	[58][75] 	1.38 	1.43 	1.38 	1.41 	1.23 	1.20 	1.20 				1.20
Syria 	[45] 				1.04 	1.14 						1.14
Ireland (excluding attempts) 	[58][76] 	1.48 	1.51 	1.51 	1.31 	1.11 	1.46 	1.59 	1.84 	1.01 	1.12 	1.12
Senegal 	[77][78] 	0.33 				1.1 						1.1
Italy (excluding attempts) 	[44][45][47][48] 	1.29 	1.23 	1.12 	1.24 	1.23 	1.04 	1.06 				1.06
Indonesia 	[47] 	1.05 										1.05
Denmark (excluding attempts) 	[58][79] 	1.48 	1.16 	1.08 	1.52 	1.11 	1.29 		0.84 	0.97 	1.01 	1.01
Switzerland (excluding attempts) 	[58] 	0.96 	1.19 	1.19 	1.00 	1.07 	1.01 					1.01
Slovenia (excluding attempts) 	[58] 	1.81 	0.75 	1.45 	1.05 	1.45 	1.00 					1.00
Malta (excluding attempts) 	[58] 	1.05 	1.28 	1.27 	0.00 	1.75 	0.99 					0.99
Kuwait 	[48] 		1.71 	0.99 								0.99
Greece (excluding attempts) 	[44][47][58] 	1.45 	1.27 	0.98 	1.11 	0.99 	1.14 	0.98 				0.98
Bahrain 	[44][45] 				0.43 	0.98 	0.55 	0.95 				0.95
Sweden (excluding attempts) 	[58] 	1.00 	0.95 	1.04 	0.91 	1.17 	0.92 					0.92
United Arab Emirates 	[45] 				1.12 	0.63 	1.36 	0.92 				0.92
Saudi Arabia 	[47][48] 	0.51 	0.87 	0.92 								0.92
Netherlands (excluding attempts) 	[80] 	1.13 	1.26 	1.21 	1.25 	1.17 	1.07 	0.78 	0.87 	0.91 	0.92 	0.92
Luxembourg (excluding attempts) 	[58] 	0.92 	1.37 	0.90 	0.70 	0.44 	0.87 					0.87
Germany (excluding attempts) 	[44][45][47][48][81] 	1.25 	1.14 	1.17 	1.06 	1.06 	1.06 	0.98 	0.92 	0.88 	0.86 	0.86
Qatar 	[45][47] 	0.17 			0.55 	0.77 						0.77
Austria (excluding attempts) 	[44][58] 	1.02 	0.87 	0.81 	0.62 	0.72 	0.65 	0.73 				0.73
Algeria 	[44][45] 				2.04 	1.39 	0.62 	0.64 				0.64
Norway (excluding attempts) 	[44][58] 	1.07 	0.82 	1.02 	1.12 	0.78 	0.71 	0.72 	0.64 	0.69 	0.60 	0.60
Oman 	[48] 		0.52 	0.59 								0.59
Lebanon 	[44] 						2.34 	0.57 				0.57
Morocco 	[44][45][48] 		0.44 	0.48 	0.50 	0.47 	0.52 	0.53 				0.53
Brunei 	[44][45] 				0.56 	1.37 	0.00 	0.50 				0.50
Hong Kong 	[45][47][60] 	0.56 			0.73 	0.63 	0.49 					0.49
Japan 	[44][47][60] 	0.50 	0.53 	0.59 			0.64 	0.44 				0.44
Singapore 	[44][45][47][60] 	0.92 			0.57 	0.49 	0.48 	0.39 			0.38 	0.38
Iceland (excluding attempts) 	[58] 	1.79 	0.35 	1.40 	0.00 	1.03 	1.02 	0.31 	0.63 	0.31 		0.31
Liechtenstein (excluding attempts) 	[58] 	0.00 	0.00 	0.00 	0.00 	2.92 	0.00 					0.00
VIOLENCE

countries = Hash.new
atheism.split("\n").each do |line|
  country = line[/^[^\d]*/].strip
  percent = line[/[0-9.]*%/].to_i
  countries[country] = Hash[ :atheism , percent ]
end

to_delete = Array.new
countries.each do |country,attributes|
  unless line = violence[/^.*#{country}.*$/i]
    to_delete << country
    next
  end
  results = line.gsub(/\(.*?\)/,'').gsub(/\[.*?\]/,'').split("\t")
  results.shift
  results.shift
  p results
  raise "incorrect number of columns #{results.inspect}" unless results.size == 11
  _2000 , _2001 , _2002 , _2003 , _2004 , _2005 , _2006 , _2007 , _2008 , _2009 , recent = results
  attributes[:crime] = [_2004,_2005,_2003,_2006,_2002,_2007,_2001,_2008,_2000,_2009,recent].find { |rate| !rate.empty? }.to_f
  puts "#{country} = #{attributes.inspect}"
end

puts
puts "DELETING: #{to_delete.inspect}"
puts

countries.delete_if { |country,attributes| to_delete.include? country } 

require 'pp'
pp countries