CHAPTER 6:

Chapter 6 discusses the fascinating theory called 'Benford's Law'. To see if Benford's Law has merit, I experimented with the following data. You can find the results in the following spreadsheets.

Benford's Law Experiments

Please find your own data set to experiment on. (Feel free to use my spreadsheets as a model.)

Share your thoughts regarding this method of fraud detection. Did your experiment match Benford's predictions?

Please attach your sample data and results.

(By the way, this website tests Benford's Law on many datasets: http://testingbenfordslaw.com/)

C1 fic First Digit A B D E F G H 1 J K L M N Area (sq mi) First Digit Digit Occurences Actual Percentage 33% Benford's Law Prediction 2 1 77 30% 1 41 18% 18% 2 3 9 29 28 12% 12% 7 4 12% 10% 8% 7% 1 5 11 5% 4 6 12 5% 3 7 12 6% 1 8 9 5% 4% 6% 5% 1 9 15 5% 100% 1 Total: 234 100% 6 2 3 35% 3 251,770 11,100 919,595 77 181 481,400 35 171 1,073,500 11,484 69 2,969,907 32,383 33,400 293 55,598 170 80,200 11,787 8,867 43,484 21 14,824 424,164 19,767 225,000 3,287,612 23 30% 2 5 25% 1 Country 1 2 Afghanistan 3 Albania 4 Algeria 5 American Samoa 6 Andorra 7 Angola 8 Anguilla 9 Antigua and Barbuda 10 Argentina 11 Armenia 12 Aruba 13 Australia 14 Austria 15 Azerbaijan 16 Bahrain 17 Bangladesh 18 Barbados 19 Belarus 20 Belgium 21 Belize 22 Benin 23 Bermuda 24 Bhutan 25 Bolivia 26 Bosnia and Herzegovina 27 Botswana 28 Brazil 29 British Indian Ocean Territory 30 British Virgin Islands 31 Brunei 32 Bulgaria 33 Burkina Faso 34 Burma 35 Burundi 36 Cambodia 37 Cameroon 38 Canada 8 20% Actual Percentage 1 15% 8 Benford's Law Prediction 4 10% 2 1 5% It 4 0% 1 1 2 3 4 5 6 7 8 9 2 3 2 58 5 2 4 1 2 2,226 42,811 105,393 261,228 10,747 69,898 183,569 3,855,100 1 6 1 3 Sheet1 Sheet2 Sheet3 Ready HE C1 X fx First Digit A C D E F 3 1 1 2 4 2 4 8 9 1 1 2 4 1 3 1 9 B 3,855,100 1,557 102 240,535 496,000 291,933 440,831 863 91 19,700 124,504 21,851 42,427 171 3,572 30,450 905,355 16,639 9,000 290 18,792 5,743 98,985 387,000 8,124 10,831 45,400 17,462 426,400 4,700 538 271 7,055 130,666 247,219 1,500 2,875 103,347 26,900 2 38 Canada 39 Cape Verde 40 Cayman Islands 41 Central African Republic 42 Chad 43 Chile 44 Colombia 45 Comoros 46 Cook Islands 47 Costa Rica 48 Cte d'Ivoire 49 Croatia 50 Cuba 51 Curaao 52 Cyprus 53 Czech Republic 54 Democratic Republic of the Congo 55 Denmark 56 Djibouti 57 Dominica 58 Dominican Republic 59 East Timor 60 Ecuador 61 Egypt 62 El Salvador 63 Equatorial Guinea 64 Eritrea 65 Estonia 66 Ethiopia 67 Falkland Islands 68 Faroe Islands 69 Federated States of Micronesia 70 Fiji 71 Finland 72 France 73 French Polynesia 74 French Southern and Antarctic Lands 75 Gabon 76 Georgia Sheet1 Sheet2 Sheet3 1 | 8 1 4 1 4 4 5 2 7 1 2 1 2 1 2 + c1 X fic First Digit B D E F 2 1 9 2 5 8 1 26,900 137,882 92,098 2 50,949 836,330 133 212 42,042 30 94,926 13,948 83,000 10,710 43,433 2 4 3 9 1 8 1 4 426 4 3 4 1 76 Georgia 77 Germany 78 Ghana 79 Gibraltar 80 Greece 81 Greenland 82 Grenada 83 Guam 84 Guatemala 85 Guernsey 86 Guinea 87 Guinea-Bissau 88 Guyana 89 Haiti 90 Honduras 91 Hong Kong 92 Hungary 93 Iceland 94 India 95 Indonesia 96 Iran 97 Iraq 98 Ireland 99 Isle of Man 100 Israel 101 Italy 102 Jamaica 103 Japan 104 Jersey 105 Jordan 106 Kazakhstan 107 Kenya 108 Kiribati 109 Kuwait 110 Kyrgyzstan 111 Laos 112 Latvia 113 Lebanon 114 Lesotho 7 6 1 2 2 8 1 4 35,918 40,000 1,269,219 737,815 636,372 168,049 27,133 221 8,522 116,346 4,244 145,920 45 34,495 1,052,100 224,081 280 6,880 77,202 91,400 24,926 4,036 11,720 1 4 3 1 2 2 6 7 9 2 4 1 Sheet1 Sheet2 Sheet3 C1 X fic First Digit B C D E TI F 1 4 6 11,720 43,000 679,360 62 25,200 998 6 2 9 12 1 9 2. 4 1 1 4 1 7 3 7 7 1 A 114 Lesotho 115 Liberia 116 Libya 117 Liechtenstein 118 Lithuania 119 Luxembourg 120 Macau 121 Macedonia 122 Madagascar 123 Malawi 124 Malaysia 125 Maldives 126 Mali 127 Malta 128 Marshall Islands 129 Mauritania 130 Mauritius 131 Mexico 132 Moldova 133 Monaco 134 Mongolia 135 Montenegro 136 Montserrat 137 Morocco 138 Mozambique 139 Namibia 140 Nauru 141 Nepal 142 Netherlands 143 New Caledonia 144 New Zealand 145 Nicaragua 146 Niger 147 Nigeria 148 Niue 149 Norfolk Island 150 North Korea 151 Northern Mariana Islands 152 Norway 0 6 9,928 226,658 45,747 127,724 120 478,841 122 70 395,960 760 758,449 13,068 1 603,900 5,333 39 172,410 309,500 318,252 8 56,827 14,422 7,172 104,428 50,337 489,000 356,669 100 5 3 1 3 3 8 5 1 7 1 5 4 3 1 14 1 4 46,540 179 125,013 1 1 Sheet1 Sheet2 Sheet3 Ready C1 fr First Digit B D E 1 1 3 1 2 2 1 1 3 4 1 125,013 119,500 307,374 177 2,320 29,119 178,700 157,048 3,722,029 496,225 115,800 18 120,728 35,560 3,420 4,473 13,972 132,000 92,043 6,601,668 10,169 9 119 1 1 3 3 4 1 1 A 152 Norway 153 Oman 154 Pakistan 155 Palau 156 Palestinian territories 157 Panama 158 Papua New Guinea 159 Paraguay 160 People's Republic of China 161 Peru 162 Philippines 163 Pitcairn Islands 164 Poland 165 Portugal 166 Puerto Rico 167 Qatar 168 Republic of China (Taiwan) 169 Republic of the Congo 170 Romania 171 Russia 172 Rwanda 173 Saint Barthlemy 174 Saint Helena, Ascension and Tristan da Cunha 175 Saint Kitts and Nevis 176 Saint Lucia 177 Saint Martin 178 Saint Pierre and Miquelon 179 Saint Vincent and the Grenadines 180 Samoa 181 San Marino 182 So Tom and Prncipe 183 Saudi Arabia 184 Senegal 185 Serbia 186 Seychelles 187 Sierra Leone 188 Singapore 189 Sint Maarten 190 Slovakia 9 6 1 9 1 101 1 208 2 22 2 9 1 1 2 3 93 150 1,097 24 372 830,000 75,955 34,116 175 27,700 270 8 7 3 1 2 2 13 1 18,933 1 Sheet1 Sheet2 Sheet3 + C1 X First Digit A B C D E F G 1 7 1 2 4 1 3 2 1 2 7 6 18,933 7,827 11,157 246,201 471,445 1,507 38,544 239,285 195,365 25,330 718,723 63,250 24,101 6,704 173,860 15,937 71,500 55,300 364,900 198,120 5,383 4,361 21,925 5 2 6 1 1 7 5 190 Slovakia 191 Slovenia 192 Solomon Islands 193 Somalia 194 South Africa 195 South Georgia and the South Sandwich Islands 196 South Korea 197 South Sudan 198 Spain 199 Sri Lanka 200 Sudan 201 Suriname 202 Svalbard and Jan Mayen 203 Swaziland 204 Sweden 205 Switzerland 206 Syria 207 Tajikistan 208 Tanzania 209 Thailand 210 The Bahamas 211 The Gambia 212 Togo 213 Tokelau 214 Tonga 215 Trinidad and Tobago 216 Tunisia 217 Turkey 218 Turkmenistan 219 Turks and Caicos Islands 220 Tuvalu 221 Uganda 222 Ukraine 223 United Arab Emirates 224 United Kingdom 225 United States 226 United States Virgin Islands 227 Uruguay 228 Uzbekistan 3 1 5 4 2 4 288 2 1 6 3 1 3 1 9 1,980 63,170 302,535 188,500 366 10 93,260 233,000 32,300 93,800 3,717,813 134 68,037 172,700 2 3 9 3 1 6 1 Sheet1 Sheet2 Sheet3 + Ready C1 First Digit A D E 5 4 2 4 2 1 6 3 1 3 1 9 2 B 5,383 4,361 21,925 5 288 1,980 63,170 302,535 188,500 366 10 93,260 233,000 32,300 93,800 3,717,813 134 68,037 172,700 4,706 0 352,140 127,882 55 103,000 203,850 290,585 150,872 3 9 3 1 6 210 The Bahamas 211 The Gambia 212 Togo 213 Tokelau 214 Tonga 215 Trinidad and Tobago 216 Tunisia 217 Turkey 218 Turkmenistan 219 Turks and Caicos Islands 220 Tuvalu 221 Uganda 222 Ukraine 223 United Arab Emirates 224 United Kingdom 225 United States 226 United States Virgin Islands 227 Uruguay 228 Uzbekistan 229 Vanuatu 230 Vatican City 231 Venezuela 232 Vietnam 233 Wallis and Futuna 234 Western Sahara 235 Yemen 236 Zambia 237 Zimbabwe 238 239 240 241 242 243 244 245 246 247 248 1 4 0 3 1 5 1 2 2 1 Sheet1 Sheet2 Sheet3