SOC 60 Quantitative Analysis I Creating Pictures
Introducing Statistics Descriptive vs. inferential statistics Preparing Data for Analysis Gather data Enter data Data matrix Clean data
Lie Factor Lie factor = Size of effect shown/size of effect in data What is the actual growth from 18 to 27.5 mpg? (27.5-18)/18=.53 A growth of 53% Represented by a growth of 0.6 inches to 5.3 inches 5.3-0.6/0.6=7.83 A growth of 783% A Lie Factor of 7.83/.53=14.8
Attitudes about abortion on demand in the US. Bar Charts
Attitudes about abortion on demand in the US.
Ages of respondents on a bar chart
Age of respondents on a histogram Histogram
Describing ONE Variable What is the typical value? Central Tendency Measures Mode Median Mean How Typical is the typical value? Measures of Variation Range InterQuartile Range IQR Variance/Standard Deviation
Describing Relationships Between TWO Variables Tables Independent Variable Column/Dependent Variable Row Percentage Difference For dichotomies Cramer s V Gamma For nominal variables For ordinal variables difference of two column percentages in the same row 0 V 1 1 γ +1
GNP per capita 1998, Albania 810 Algeria 1550 Angola 340 Antigua and Barbuda 8300 Argentina 8970 Armenia 480 Australia 20300 Austria 26850 Azerbaijan 490 Bahrain 7660 Bangladesh 350 Barbados 7890 Belarus 2200 Belgium 25380 Belize 2610 Benin 380 Bermuda 34000 Bolivia 1000 Botswana 3600 Brazil 4570 Brunei 24000 Bulgaria 1230 Burkina Faso 240 Burundi 140 Cambodia 280 Cameroon 610 Canada 20020 Cape Verde 1060 Cayman Islands 31000 Central African Rep. 300 Chad 230 Chile 4810 China 750 Colombia 2600 Comoros 370 Congo Dem. Rep. 110 Congo Rep. 690 Costa Rica 2780 Côte d'ivoire 700 Croatia 4520 Czech Republic 5040 Denmark 33260 Dominica 3010 Dominican Republic 1770 Ecuador 1530 Egypt 1290 El Salvador 1850 Equatorial Guinea 1500 Eritrea 200 Estonia 3390 Ethiopia 100 Fiji 2110 Finland 24110 France 24940 Gabon 3950 Gambia The 340 Georgia 930 Germany 25850 Atlas method (US Ghana 390 Greece 11650 Grenada 3170 Guatemala 1640 Guinea 540 Guinea-Bissau 160 Guyana 770 Haiti 410 Honduras 730 Hong Kong China 23670 Hungary 4510 Iceland 28010 India 430 Indonesia 680 Iran 1770 Ireland 18340 Israel 15940 Italy 20250 Jamaica 1680 Japan 32380 Jordan 1520 Kazakhstan 1310 Kenya 330 Kiribati 1180 Korea Rep. 7970 Kyrgyz Republic 350 Lao PDR 330 Latvia 2430 Lebanon 3560 Lesotho 570 Liechtenstein 50000 Lithuania 2440 Luxembourg 43570 Macedonia FYR 1290 Madagascar 260 Malawi 200 Malaysia 3600 Maldives 1230 Mali 250 Malta 9440 Marshall Islands 1540 Mauritania 410 Mauritius 3700 Mexico 3970 Micronesia Fed. Sts. 1800 Moldova 410 Monaco 25000 Mongolia 400 Morocco 1250 Mozambique 210 Namibia 1940 Nepal 210 Netherlands 24760 New Zealand 14700 Nicaragua 390 Niger 190 Nigeria 300 Norway 34330 Pakistan 480 Panama 3080 Papua New Guinea 890 Paraguay 1760 Peru 2460 Philippines 1050 Poland 3900 Portugal 10690 Romania 1390 Russian Federation 2300 Rwanda 230 Samoa 1020 São Tomé & Principe 280 Senega l 530 Seychelles 6450 Sierra Leone 140 Singapore 30060 Slovak Republic 3700 Slovenia 9760 Solomon Islands 750 South Africa 2880 Spain 14080 Sri Lanka 810 St. Kitts and Nevis 6130 St. Lucia 3410 St. Vincent&Gr 2420 Sudan 290 Suriname 1660 Swaziland 1400 Sweden 25620 Switzerland 40080 Syrian Arab Republic 1020 Tajikistan 350 Tanzania 210 Thailand 2200 Togo 330 Tonga 1690 Trinidad and Tobago 4430 Tunisia 2050 Turkey 3160 Uganda 320 Ukraine 850 United Arab Emirates 18220 United Kingdom 21400 United States 29340 Uruguay 6180 Uzbekistan 870 Vanuatu 1270 Venezuela 3500 Vietnam 330 Yemen Rep. 300 Zambia 330 Zimbabwe 610 http://www.worldbank.org/data /databytopic/databytopic.html #MACROECONOMICS AND GROWTH
1.Liechtenstein 50000 2.Luxembourg 43570 3.Switzerland 40080 4.Norway 34330 5.Bermuda 34000 6.Denmark 33260 7.Japan 32380 8.Cayman Islands 31000 9.Singapore 30060 10.United States 29340 11.Iceland 28010 12.Austria 26850 13.Germany 25850 14.Sweden 25620 15.Belgium 25380 16.Monaco 25000 17.France 24940 18.Netherlands 24760 19.Finland 24110 20.Brunei 24000 21.Hong Kong China 23670 22.United Kingdom 21400 23.Australia 20300 24.Italy 20250 25.Canada 20020 26.Ireland 18340 27.Un. Arab Emirates 18220 28.Israel 15940 29.New Zealand 14700 30.Spain 14080 31.Greece 11650 32.Portugal 10690 33.Slovenia 9760 34.Malta 9440 35.Argentina 8970 36.Antigua&Barbuda 8300 37.Korea Rep. 7970 38.Barbados 7890 39.Bahrain 7660 40.Seychelles 6450 41.Uruguay 6180 42.St.Kitts&Nevis 6130 43.Czech Republic 5040 44.Chile 4810 45.Brazil 4570 46.Croatia 4520 47.Hungary 4510 48.Trinidad&Tobago 4430 49.Mexico 3970 50.Gabon 3950 51.Poland 3900 52.Mauritius 3700 53.Slovak Republic 3700 54.Botswana 3600 55.Malaysia 3600 56.Lebanon 3560 57.Venezuela 3500 58.St. Lucia 3410 59.Estonia 3390 60.Grenada 3170 61.Turkey 3160 62.Panama 3080 63.Dominica 3010 64.South Africa 2880 65.Costa Rica 2780 66.Belize 2610 67.Colombia 2600 68.Peru 2460 69.Lithuania 2440 70.Latvia 2430 71.St.Vincent&Gr 2420 72.Russian Fed. 2300 73.Belarus 2200 74.Thailand 2200 75.Fiji 2110 76.Tunisia 2050 77.Namibia 1940 78.El Salvador 1850 79.Micronesia 1800 80.Dominican Rep. 1770 81.Iran 1770 82.Paraguay 1760 83.Tonga 1690 84.Jamaica 1680 85.Suriname 1660 86.Guatemala 1640 87.Algeria 1550 88.Marshall Islands 1540 89.Ecuador 1530 90.Jordan 1520 91.Eq. Guinea 1500 92.Swaziland 1400 93.Romania 1390 94.Kazakhstan 1310 95.Egypt 1290 96.Macedonia FYR 1290 97.Vanuatu 1270 98.Morocco 1250 99.Bulgaria 1230 100.Maldives 1230 101.Kiribati 1180 102.Cape Verde 1060 103.Philippines 1050 104.Samoa 1020 105.Syrian Arab Rep. 1020 106.Bolivia 1000 107.Georgia 930 108.Papua N. Guinea 890 109.Uzbekistan 870 110.Ukraine 850 111.Albania 810 112.Sri Lanka 810 113.Guyana 770 114.China 750 115.Solomon Islands 750 116.Honduras 730 117.Côte d'ivoire 700 118.Congo Rep. 690 119.Indonesia 680 120.Cameroon 610 121.Zimbabwe 610 122.Lesotho 570 123.Guinea 540 124.Senegal 530 125.Azerbaijan 490 126.Armenia 480 127.Pakistan 480 128.India 430 129.Haiti 410 130.Mauritania 410 131.Moldova 410 132.Mongolia 400 133.Ghana 390 134.Nicaragua 390 135.Benin 380 136.Comoros 370 137.Bangladesh 350 138.Kyrgyzistan 350 139.Tajikistan 350 140.Angola 340 141.Gambia The 340 142.Kenya 330 143.Lao PDR 330 144.Togo 330 145.Vietnam 330 146.Zambia 330 147.Uganda 320 148.C. African Rep. 300 149.Nigeria 300 150.Yemen Rep. 300 151.Sudan 290 152.Cambodia 280 153.São Tomé & Pr. 280 154.Madagascar 260 155.Mali 250 156.Burkina Faso 240 157.Chad 230 158.Rwanda 230 159.Mozambique 210 160.Nepal 210 161.Tanzania 210 162.Eritrea 200 163.Malawi 200 164.Niger 190 165.Guinea-Bissau 160 166.Burundi 140 167.Sierra Leone 140 168.Congo Dem. Rep. 110 169.Ethiopia 100
50000.0 45000.0 40000.0 35000.0 30000.0 25000.0 20000.0 15000.0 10000.0 0.0 5000.0 80 60 40 20 0 GNPCAP98
GNPCAP98 Frequency Percent Valid Percent Cumulative Percen Valid 100 1.6.6.6 110 1.6.6 1.2 140 2 1.2 1.2 2.4 160 1.6.6 3.0 190 1.6.6 3.6 200 2 1.2 1.2 4.7 210 3 1.8 1.8 6.5 230 2 1.2 1.2 7.7 240 1.6.6 8.3 250 1.6.6 8.9 260 1.6.6 9.5 280 2 1.2 1.2 10.7 290 1.6.6 11.2 300 3 1.8 1.8 13.0 320 1.6.6 13.6 330 5 3.0 3.0 16.6 340 2 1.2 1.2 17.8
Central Tendency Measures What is the typical value? Mode Median 50 th percentile Mean (Average) ΣX i /N
Examples Number of children people have: 0,0,0,0,0,1,1,2,2,2,3,3,4,5,7 0 5 1 2 2 3 3 2 Frequency Distribution 4 1 5 1 7 1 N= 15 Mode 0 Median 2 Mean 0+0+0+0+0+1+1+2+2+2+3+3+4+5+7=30 30/15=2
Which central tendency measure to use when? Mode Median Mean Nominal Yes No No Ordinal Yes Yes No Interval and Ratio Yes Yes Yes
Measures of Variability How typical is the typical value? Range Maximum-Minimum Interquartile Range Difference between the 25 th and 75 th percentile Variance Average Squared Deviation from the Mean Σ[Xi-Mean(Xi)] 2 /N Corrected variance Σ[Xi-Mean(Xi)] 2 /(N-1)
Measures of Variability (cont.) Standard Deviation Square root of variance ( Xi Xi / N) s = N 1 2
Example N=15 Mean=2 # kids(x i ) [X i -Mean(X i )] [X i -Mean(X i )] 2 0 0-2=-2 (-2) 2 =4 0 0-2=-2 (-2) 2 =4 0 0-2=-2 (-2) 2 =4 0 0-2=-2 (-2) 2 =4 Variance: 62/15=4.1333 0 0-2=-2 (-2) 2 =4 1 1-2=-1 (-1) 2 =1 1 1-2=-1 (-1) 2 =1 2 2-2=0 (0) 2 =0 2 2-2=0 (0) 2 =0 Corrected Variance 62/14=4.4286 2 2-2=0 (0) 2 =0 3 3-2=+1 (1) 2 =1 3 3-2=+1 (1) 2 =1 4 4-2=+2 (2) 2 =4 5 5-2=+3 (3) 2 =9 7 7-2=+5 (5) 2 =25 Total 62
Measures of Variability (cont.) Standard Deviation σ Square root of variance Z-score or Standard Score Z=(Score-Mean)/Standard Deviation Tells you how many standard deviations away you are from the mean. Chebycheff s theorem If a Z score k>1 the probability of being this far or farther away from the mean is not more than 1/k 2 P( Z >=k) < =1/k 2 Eg.: If k= 4 P<1/16 or P<.0694
Which variability measure to use when? Range Interquartile Range Nominal No No No Variance/ Stand.Dev. Ordinal Yes Yes No Interval/ Ratio Yes Yes Yes