Simpson's Paradox
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Weight-Drug Example
↓ SCROLL DOWN further to see the numbers for the Double Simpson's Paradox and also the NBA example. ↓
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(also the same numbers for the gender discrimination and Trump voting examples)
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Cured
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#%#
List of things we need to check:
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Non-overweight6500Drug50%3250
1)
The percentages are correct.
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1500No drug70%1050
2)
Non-overweight drug-takers (6,500) + overweight drug-takers (200) = Total drug-takers (6,700)
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Overweight200Drug5%10
3)
Cured non-overweight drug-takers (3,250) + cured overweight drug-takers (10) = Total cured drug-takers (3,260)
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1800No drug7%126
4)
Non-overweight non-drug-takers (1,500) + overweight non-drug-takers (1,800) = Total non-drug-takers (3,300)
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Total6700Drug48.7%3260
5)
Cured non-overweight non-drug-takers (1,050) + cured overweight non-drug-takers (126) = Total cured non-drug-takers (1,176)
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3300No drug35.6%1176
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I recycle the exact same numbers from this first drug example later on in the gender discrimination and Trump vote examples.
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So if these numbers are correct; those should be, too.
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Gender Discrimination Example (Double Simpsons's Paradox)
↓ SCROLL DOWN further to see the NBA example. ↓
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Admitted
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#%#
The department and total numbers (last 6 rows) are the exact same as before.
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Blonde Math700Men92.9%650
So we don't need to check those.
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1300Women75.4%980
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Non-blonde
Math
5800Men44.8%2,600
List of things we need to check:
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200Women35.0%70
1)
The percentages are correct.
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Blonde English195Men4.6%9
2)
Blonde Math men (700) + non-blonde Math men (5,800) = Total Math men (6,500)
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305Women2.0%6
3)
Blonde Math men admits (650) + non-blonde Math men admits (2,600) = Total Math men admits (3,250)
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Non-blonde
English
5Men20%1
4)
Blonde Math women (1,300) + non-blonde Math women (200) = Total Math women (1,500)
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1495Women8.0%120
5)
Blonde Math women admits (980) + non-blonde Math women admits (70) = Total Math women admits (1,050)
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Math6500Men50%3,250
6)
Blonde English men (190) + non-blonde English men (5) = Total English men (200)
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1500Women70%1,050
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Blonde English men admits (9) + non-blonde English men admits (1) = Total English men admits (10)
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English200Men5%10
8)
Blonde English women (305) + non-blonde English women (1,495) = Total English women (1,800)
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1800Women7%126
9)
Blonde English women admits (6) + non-blonde English women admits (1270) = Total English women admits (126)
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Total6700Men48.7%3,260
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3300Women35.6%1,176
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NBA Free Throws Example
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Made
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Attempted
%#
Source: Basketball-Reference.com
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2015187Williams87.2%163
Williams stats.
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171Durant85.4%146
Durant stats.
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201642Williams90.5%38
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498Durant89.8%447
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Total229Williams87.8%201
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669Durant88.6%593
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