심슨의 역설

그 심슨 아닙니다. Edward Simpson 입니다.

Transcript

1. बट੄ ৉ࢸ ؘ੉ఠঠ֥੗ 2019 2019-10-19 షਃੌ য়റ 3द 40࠙ ~ য়റ 4द 20࠙ ਮࢶ޷ (੉ ੗ܐח ৻ࠗ ҕѐਊ ੑפ׮. ߊ಴ܳ ٛ૑ ঋਵन ٜ࠙ਸ ਤ೧ झೖழ ֢౟ ੌࠗܳ ठۄ੉٘ী ੿ܻ೧ ֬ওणפ׮.)
2. ؘ੉ఠঠ֥੗ 2018 ߊ಴
3. ਮࢶ޷ ೐ܻےࢲ ؘ੉ఠ ࠙ࢳо ؘ੉ఠ ࠙ࢳ ъࢎ അ ؘ੒Ѧૉ 3ӝ 
 ؘ੉ఠ ࠙ࢳ ౵౟ ъࢎ അ DS School ؘ੉ఠࢎ੉঱झ ੑޙ߈ ઑҮ ੹ ௢౿ Business Analyst ysunmi0427@gmail.com linkedin.com/in/yoonsunmi
4. ੉ बट ইפীਃ Edward H. Simpson ੉ীਃ.
5. ߊ಴੄ ݾ੸ - बट੄ ৉ࢸਸ ಴, ߭ఠ, 2ରਗ ࢑੼ب ١ ׮নೠ ߑߨਵ۽ ࣗѐೠ׮. - ഥࢎ۽ جইо ؘ੉ఠ ࠙ࢳਸ ೡ ٸ݃׮ ‘഑द ৈӝীب बट੉!’ ೞҊ ؘ ੉ఠܳ ଂѐࠁѱ ݅ٚ׮. (࠙ݺ൤ ੓׮) Treatment A
6. बट੄ ৉ࢸ੉ ޤભ?
7. (ߊ಴ ળ࠺ ੹) ղо ࢤпೠ बट੄ ৉ࢸ ੉޷૑ ୹୊
 Understanding Simpson’s Paradox And Its Impact On Data Analytics
8. (ߊ಴ ળ࠺ द੘) ૓૞ बट੄ ৉ࢸ Pearl, Judea. "Comment: understanding Simpson’s paradox." The American Statistician 68.1 (2014): 8-13.
9. बट੄ ৉ࢸ Simpson’s paradox is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined. 
 - wikipedia बट੄ ಁ۞ةझח ৈ۞ ࠗ࠙ Ӓܛ੄ ੗ܐܳ ೤೮ਸ ٸ੄ Ѿҗ৬ пп ࠗ࠙Ӓ ܛ੄ Ѿҗо ׮ܲ ٸܳ ݈ೠ׮. ࠗ࠙ਸ ױࣽ൤ ೤ଢ଼חؘ Ӓ Ѿҗо ࠗ࠙੄ Ѿҗ ৬ ׳ۄ૑ח Ѿҗо ߊࢤೞח Ѫ਷ ੌ߈੸ੋ ࢚धਵ۽ח औѱ ੉೧о غ૑ ঋ ਵ޲۽ Paradoxۄ ೠ׮. 
 - ࢚धਸ ٍ૘ח ా҅ Simpson’s paradox
10. рױೠ ৘दܳ ݻ ѐ ٜযࠇद׮
11. न੢Ѿࢳ ஖ܐߨ ࠺Ү ஖ܐߨ A ஖ܐߨ B ੘਷ Ѿࢳ Ӓܛ 1 93% (81/87) Ӓܛ 2 87% (234/270) ௾ Ѿࢳ Ӓܛ 3 73% (192/263) Ӓܛ 4 69% (55/80) ੘਷ Ѿࢳ + ௾ Ѿࢳ 78% (273/350) 83% (289/350) ੘਷ Ѿࢳীח ઱۽ ஖ܐߨ Bܳ ୊ߑ ಴ܳ ખ ੍য ࠁ੗ݶ, न੢Ѿࢳী ஖ܐߨ Aҗ Bо ੓Ҋ Ѿࢳ਷ ੘਷ Ѿࢳҗ, ௾ Ѿࢳ੉ ੓णפ׮. ੘਷ Ѿࢳ੄ ҃਋ ઱۽ ஖ܐߨ Bܳ ୊ߑೞҊ, ௾ Ѿࢳ੄ ҃਋ীח ஖ܐߨ Aܳ दبೞח Ѫਵ۽ ࠁ੉Ҋਃ. ੹୓ ؘ੉ఠܳ Ѿࢳ੄ ௼ӝ৬ दبೠ ஖ܐߨী ٮۄ ௼ѱ 4ѐ Ӓܛਵ۽ ଂѐ֬ওणפ׮.
12. Batting averages Derek Jeter David Justice 1995 Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) 1996 Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) 1995+1996 .31 (195/630) .27 (149/551) ژ ׮ܲ ৘दܳ ࠅөਃ? খী ࠌ؍ न੢Ѿࢳ ஖ܐߨ ಴৬ ࠺त೤פ׮. ڙэ੉ ੹୓ ؘ੉ఠܳ 4ѐ Ӓܛਵ۽ ա־঻Ҋਃ. 1995֙, 1996֙ ппਸ ࠌਸ ٸীח David Justice ࢶࣻ੄ ࢿ੸੉ (ডр) ֫૑݅, 1995֙җ 1996֙ਸ ೤ଢ଼ਸ ٸীח Derek Jeter ੄ ࢿ੸੉ જইࠁ੉֎ਃ. ب؀୓ ੉ ؘ੉ఠ উীࢲ ޖट ੌ੉ ੓যաҊ ੓ח Ѧөਃ?
13. ઑӘ ؊ ੗ࣁೞѱ ࢓ಝࠇद׮
14. न੢Ѿࢳ ஖ܐߨ ࠺Ү ஖ܐߨ A ஖ܐߨ B ੘਷ Ѿࢳ Ӓܛ 1 93% (81/87) Ӓܛ 2 87% (234/270) ௾ Ѿࢳ Ӓܛ 3 73% (192/263) Ӓܛ 4 69% (55/80) ੘਷ Ѿࢳ + ௾ Ѿࢳ 78% (273/350) 83% (289/350) 81 87 > 234 270 192 263 > 55 80 (81 + 192) (87 + 263) < (234 + 55) (270 + 80) ׮द न੢Ѿࢳ ஖ܐߨ ಴۽ جই৳֎ਃ. ੘਷ Ѿࢳ, ௾ Ѿࢳ ݽف ஖ܐߨ Aо ࢿҕܫ੉ ֫਷ؘ, ੹୓ ؘ੉ఠܳ ࠁפө ஖ܐߨ Bо ࢿҕܫ੉ ֫਷ Ѫ୊ۢ ࠁ੉חѱ ੉࢚ೞ׮ח ফӝܳ ೮঻ભ.
15. न੢Ѿࢳ ஖ܐߨ ࠺Ү ؘ੉ఠ੄ ੉ݶ ஖ܐߨ A ஖ܐߨ B ੘਷ Ѿࢳ Ӓܛ 1 93% (81/87) Ӓܛ 2 87% (234/270) ௾ Ѿࢳ Ӓܛ 3 73% (192/263) Ӓܛ 4 69% (55/80) ੘਷ Ѿࢳ + ௾ Ѿࢳ 78% (273/350) 83% (289/350) 81 87 > 234 270 192 263 > 55 80 (81 + 192) (87 + 263) < (234 + 55) (270 + 80) The totals are dominated by Group 2 and 3. ਋ܻо ࠁח ࢿҕܫ % ੉ݶী Ӓ ஖ܐܳ ݻ ݺ੄ ࢎۈٜীѱ ੸ਊ೮ח૑ ژೠ ੹୓ ஖ܐ ࢿҕܫী ৔ೱਸ ޷஖ӝ ٸޙੑפ׮. ࠁदݶ ੘਷ Ѿࢳ੄ ҃਋ীח ஖ܐߨ Bܳ ஖ܐߨ A ࠁ׮ ഻ঁ ݆੉ दب೮ભ. ஖ܐߨ Aח 87ݺਸ ؀࢚ਵ۽ ೮חؘ, ஖ܐߨ Bח ޖ۰ 270ݺਸ ؀࢚ਵ۽ ೤פ׮. ৈ۞о૑ ੉ਬо ੓ѷ૑݅, ஖ܐߨ Bо ࢚؀੸ਵ۽ рױೞѢա, ஖ܐೞח ؘ ٘ח ࠺ਊ੉ ੸ӝ ٸޙী ੘਷ Ѿࢳ ੿بח B۽ ೧ب ௾ ޖܻо হ׮ח ੄ܐ૓੄ ౸ױ੉ ੓঻ਸ ࣻ ੓ѷભ
16. ੗, Ӓۧ׮ݶ ௰ૉܳ ղѷणפ׮. Ѩࢎܳ ా೧ Ѿࢳ੄ ௼ӝܳ ঌ ࣻ ੓ח ࢚ടীࢲ
17. न੢Ѿࢳ ஖ܐߨ ࠺Ү ؘ੉ఠ੄ ੉ݶ ஖ܐߨ A ஖ܐߨ B ੘਷ Ѿࢳ Ӓܛ 1 93% (81/87) Ӓܛ 2 87% (234/270) ௾ Ѿࢳ Ӓܛ 3 73% (192/263) Ӓܛ 4 69% (55/80) ੘਷ Ѿࢳ + ௾ Ѿࢳ 78% (273/350) 83% (289/3 50) Ѩࢎܳ ߉ইࠌ؊פ ജ੗о ੘਷ Ѿࢳਸ о૑Ҋ ੓׮Ҋ ೧ࠇद׮. ஖ܐߨ Aܳ ॄঠೡөਃ, ஖ܐߨ Bܳ ॄঠೡөਃ?
18. Ӓۧ׮ݶ ௾ Ѿࢳਸ о૑Ҋ ੓׮Ҋ ೞݶਃ? न੢Ѿࢳ ஖ܐߨ ࠺Ү ؘ੉ఠ੄ ੉ݶ ஖ܐߨ A ஖ܐߨ B ੘਷ Ѿࢳ Ӓܛ 1 93% (81/87) Ӓܛ 2 87% (234/270) ௾ Ѿࢳ Ӓܛ 3 73% (192/263) Ӓܛ 4 69% (55/80) ੘਷ Ѿࢳ + ௾ Ѿࢳ 78% (273/350) 83% (289/350)
19. Ӓۧ׮ݶ, Ѿࢳ੄ ௼ӝܳ ঌ ࣻ হਸ ٸח?
20. न੢Ѿࢳ ஖ܐߨ ࠺Ү ؘ੉ఠ੄ ੉ݶ ஖ܐߨ A ஖ܐߨ B ੘਷ Ѿࢳ Ӓܛ 1 93% (81/87) Ӓܛ 2 87% (234/270) ௾ Ѿࢳ Ӓܛ 3 73% (192/263) Ӓܛ 4 69% (55/80) ੘਷ Ѿࢳ + ௾ Ѿࢳ 78% (273/350) 83% (289/350) Ѿࢳ੄ ௼ӝܳ Ѩࢎೞӝ ਤ೧ ੉۠ ੷۠ Ѩࢎٜਸ ೧ࠌחؘ, ب੷൤ Ӓ ௼ӝܳ ঌইյ ࣻ হ঻׮Ҋ о੿೧ࠇद׮.
21. न੢Ѿࢳ ஖ܐߨ ࠺Ү ؘ੉ఠ੄ ੉ݶ ஖ܐߨ A ஖ܐߨ B ੘਷ Ѿࢳ Ӓܛ 1 93% (81/87) Ӓܛ 2 87% (234/270) ௾ Ѿࢳ Ӓܛ 3 73% (192/263) Ӓܛ 4 69% (55/80) ੘਷ Ѿࢳ + ௾ Ѿࢳ 78% (273/350) 83% (289/350) ੹୓੸ਵ۽ જ਷ ஖ܐ ࢿҕܫਸ ࠁ੉ח ஖ܐߨ B?
22. न੢Ѿࢳ ஖ܐߨ ࠺Ү ؘ੉ఠ੄ ੉ݶ ஖ܐߨ A ஖ܐߨ B ੘਷ Ѿࢳ Ӓܛ 1 93% (81/87) Ӓܛ 2 87% (234/270) ௾ Ѿࢳ Ӓܛ 3 73% (192/263) Ӓܛ 4 69% (55/80) ੘਷ Ѿࢳ + ௾ Ѿࢳ 78% (273/350) 83% (289/350) ੘਷ Ѿࢳ, ௾ Ѿࢳ ݽف ֫਷ ஖ܐ ࢿҕܫਸ ࠁ੉ח ஖ܐߨ A?
23. ੗, ঠҳ ࢶࣻ੄ ఋਯ ؘ੉ఠب ࢓ಝࠅөਃ. न੢Ѿࢳ ஖ܐߨ ؘ੉ఠܳ ࠁ׮о ц੗ӝ ޖट ঠҳջ! ೡ ࣻب ੓ѷ૑݅, बट੄ ৉ࢸ ҙ੼ਵ۽ ࠅ ٸח ղղ ࠺तೠ ޙઁੑפ׮.
24. Batting averages Derek Jeter David Justice 1995 Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) 1996 Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) 1995+1996 .31 (195/630) .27 (149/551) 12 48 < 104 411 183 582 < 45 140 (12 + 183) (48 + 582) > (104 + 45) (411 + 140) ׮द ੉ ಴۽ جই৳֎ਃ. 1995֙ীب ؘ੉࠺٘ ੷झ౭झ੄ ఋਯ੉ ֫ওҊ, 1996֙ীب ؘ੉࠺٘ ੷झ౭झ੄ ఋਯ੉ ֫ওחؘ 1995֙җ 1996֙ ؘ੉ఠܳ ೤೧֬ਵפ ؘܼ ૑ఠ੄ ఋਯ੉ ֫ই ࠁ੉֎ਃ? न੢ Ѿࢳ ஖ܐߨ ޙઁ৬ ࠺तೠ ҳࢳਸ ߊѼೞ࣑աਃ?
25. Batting averages ؘ੉ఠ੄ ੉ݶ Batting averages Derek Jeter David Justice 1995 Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) 1996 Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) 1995+1996 .310 (195/630) .270 (149/551) 12 48 < 104 411 183 582 < 45 140 (12 + 183) (48 + 582) > (104 + 45) (411 + 140) The totals are dominated by Group 2 and 3. न੢ Ѿࢳ ஖ܐߨ ࢎ۹৬ э੉, ಴ݶਵ۽ ࠁৈ૑ח ࢿҕೠ ఋਯ ੉ݶী п ࢶٜࣻ੉ ݻ ߣ੉ա ఋࢳী ৢۋח૑ ؘ੉ఠܳ ਬबೞѱ ࢓ಝࠌযঠ ੉ ੉࢚ೠ അ࢚ਸ ੉೧ೡ ࣻ ੓ѱ ؾפ׮.
26. Batting averages ؘ੉ఠ੄ ੉ݶ Batting averages Derek Jeter David Justice 1995 Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) 1996 Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) 1995+1996 .310 (195/630) .270 (149/551) 12 48 < 104 411 183 582 < 45 140 (12 + 183) (48 + 582) > (104 + 45) (411 + 140) The totals are dominated by Group 2 and 3. ؘ੉࠺٘ ੷झ౭झח 1995֙ী ഝߊೠ ഝزਸ ೮Ҋ, ؘܼ ૑ఠח 1995֙ীח ഝز੉ ੷ઑೞ׮о 1996֙ী ఋࢳী ݆੉ য়ܰભ. ੹୓ ؘ੉ఠܳ Ӓܛ 2৬ Ӓܛ 3੉ ՑҊ р׮ח Ѫਸ ঌ ࣻ ੓णפ׮. п ࢶࣻ੄ 1995, 1996֙ ೤࢑ ఋਯ਷ п ࢶࣻо о੢ ഝߊೞѱ ഝز೮؍ োب੄ ఋਯ ଃਵ۽ Ց۰т ࣻ ߆ী হ׮חѢ৘ਃ.
27. ੉ܳ 2ରਗ ߭ఠ ҕрਵ۽ب ಴അ೧ ࠅ ࣻ ੓णפ׮
28. Batting averages
 Vector Interpretation बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) By matplotlib pyplot ࢶࣻ߹۽ Ӓ۰ࠇद׮ (ੜ উࠁ੉֎ਃ… ഛ؀ ೧ ࠇद׮)
29. Batting averages
 Vector Interpretation By matplotlib pyplot बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) 1995 ఋਯ 1996 ఋਯ
30. Batting averages
 Vector Interpretation By matplotlib pyplot बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) 1996 ఋਯ 1995 ఋਯ 1995+1996 ఋਯ
31. Batting averages
 Vector Interpretation By matplotlib pyplot बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) 1995 ఋਯ 1996 ఋਯ
32. ؘܼ ૑ఠ ࢶࣻח 1995֙, 1996֙ ఋਯ੄ ର੉, Ӓ۞פө ߭ఠ ӝ਎ӝ੄ ର੉о ߹۽ উ աࢲ दпച ೞݶ ੉ۧѱ ݧ੉ উա؊ۄҳਃ. दпച ೞח ࢎۈ ੑ੢ীࢲ જ਷ ৘दח ইפ૑݅, Ӓ݅ఀ ࢶࣻо ӝࠂ੉ হ੉ ੜೞח ࢶࣻۄח Ѧ ࠁৈ઱ח Ѣѷભ? Batting averages
 Vector Interpretation बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) 1995 ఋਯ 1996 ఋਯ 1995+1996 ఋਯ
33. Batting averages
 Vector Interpretation बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) By matplotlib pyplot ੉ߣূ োب߹۽ Ӓ۰ࠇद׮ (ৈ੹൤ ੜ উࠁ੉֎ਃ… ׮द ೠ ߣ ഛ؀ ೧ ࠇद׮)
34. Batting averages
 Vector Interpretation By matplotlib pyplot बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) Derek Jeter David Justice 12 48 = 0.25 104 411 ≃ 0.253 ӝ਎ӝী ର੉о աחѱ ੜ উࠁ੉ભ… ࢎप ੜೞח ࢶࣻՙܻ ఋਯਸ ࠺Ү೧ࠌ੗, ‘ষ୒’ ੜೞח ࢶࣻо իջ, ‘૓૞’ ੜೞח ࢶࣻо իջ ޙઁۄࢲ Success/Trial ӝ਎ӝо ௼ѱ ର੉о զ ࣻо হ؊ۄҳਃ. ӵ׳ওਸ ٸח ੉޷ ן঻ӝ ٸޙী Ӓր ੉Ѧ۽ ૓೯೧ࠁѷणפ׮. 1995֙ীח David Justice о ఋਯ੉ ઑӘ ؊ ի֎ਃ.
35. Batting averages
 Vector Interpretation By matplotlib pyplot बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) Derek Jeter David Justice 183 582 ≃ 0.314 45 140 ≃ 0.321 1996֙ীب (Ӕࣗೠ ର੉۽) David Justice о ఋਯ੉ ઑӘ ؊ જणפ׮.
36. ߭ఠ दпചܳ ೮ਸ ٸী, Trial੉ ݆ও؍ ೧੄ ఋਯ੉ ف ೧ܳ ೤࢑ೠ Ѿҗী ௾ ৔ೱਸ ޷஘׮ח Ѫਸ ׀ਵ۽ ഛੋೡ ࣻ ੓যਃ. п ࢶࣻ੄ 1995, 1996֙ ೤࢑ ఋਯ਷ п ࢶࣻо о੢ ഝߊೞѱ ഝز೮؍ োب੄ ఋਯ ଃਵ۽ Ց۰т ࣻ ߆ী হח Ѫਸ ૒ҙ੸ਵ ۽ ੉೧ೞחؘ ب਑੉ ؾפ׮. Batting averages
 Vector Interpretation बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) Derek Jeter David Justice (12 + 183) (48 + 582) ≃ 0.310 (104 + 45) (411 + 140) ≃ 0.270
37. ޙઁܳ ઑӘ݅ ࠂ੟ೞѱ ٜ݅য ࠅөਃ?
38. Batting averages Batting averages Derek Jeter David Justice 1995 Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) 1996 Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) 1995+1996 .31 (195/630) .27 (149/551)
39. Batting averages Derek Jeter David Justice ࢚߈ӝ Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) ೞ߈ӝ Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) ୨೤ .31 (195/630) .27 (149/551) ޙઁܳ ডр݅ ߄Լࠇद׮. ӝઓ੄ 1995, 1996֙ਸ ࢚߈ӝ, ೞ߈ӝ۽
40. Batting averages ӣ୍߽ ӣ੼೐ ࢚߈ӝ Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) ೞ߈ӝ Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) ୨೤ .31 (195/630) .27 (149/551) Derek Jeter৬ David Justice ࢶٜࣻਸ ӣ୍߽җ ӣ੼೐۽ ׮ٜ ੉ ࣁ҅ҙ ۽٬੉ ՘ա࣑աਃ?
41. Batting averages ৢ೧੄ ࢶ࢚ࣻ਷ ־ҳীѱ?
42. Batting averages Batting averages ӣ୍߽ ӣ੼೐ ࢚߈ӝ Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) ೞ߈ӝ Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) ୨೤ .31 (195/630) .27 (149/551) ࢚߈ӝ, ೞ߈ӝ ݽف ୭Ҋ੄ ఋਯਸ ӝ۾ೠ ӣ੼೐ ࢶࣻ?
43. Batting averages ӣ୍߽ ӣ੼೐ ࢚߈ӝ Ӓܛ 1 .25 (12/48) Ӓܛ 2 .253 (104/411) ೞ߈ӝ Ӓܛ 3 .314 (183/582) Ӓܛ 4 .321 (45/140) ୨೤ .31 (195/630) .27 (149/551) ࢚߈ӝ, ೞ߈ӝܳ ઙ೤೧ ࠌਸ ٸ ୭Ҋ੄ ఋਯਸ ӝ۾ೠ ӣ୍߽ ࢶࣻ?
44. Batting averages
 Vector Interpretation By matplotlib pyplot बट੄ ৉ࢸ਷ 2ରਗ ߭ఠ ҕрীب ಴അؼ ࣻ ੓׮. ࢿҕܫ (i.e., ࢿҕ/दب)ח ߭ఠ ۽ ಴അೠ׮. p q ⃗ A = (q, p) ӣ୍߽ ӣ੼೐ (12 + 183) (48 + 582) ≃ 0.310 (104 + 45) (411 + 140) ≃ 0.270
45. য۵ભ, ֎ য۵णפ׮.
46. ೞ૑݅ അসীࢲ ࠙ࢳਸ ೞदח ٜ࠙ীѱ ੉ ޙઁо Ӓۧѱ ݄ ੉೧о উ ؼ ੿ب۽ য۵૑ח ঋਸѢۄҊ ࢤп೤פ׮. ৵ջೞݶ, ਋ܻ ੋೞ਋झ ࠙ࢳо۽ ੌೞݶ ૑಴࠙ࢳਸ ݆੉ ೞભ. ੷ب ଵ~ ݆੉ ೮঻חؘਃ. Ӓ۞ݶ ݒߣ Ҋ޹ೞѱ غח ޙઁо ݒੌݒੌ ૑಴о աоחؘ, ੉Ѧ ੌ઱ੌ ೤࢑ਸ ٜ݅য ׳ۄҊ ೞݶ ੉޷ ҅࢑ػ ؘੌܻ ૑಴ܳ ಣӐ೧ࢲ աоঠ ೞחѤ૑, ইפݶ ؘ੉ఠܳ ੌ઱ੌ஖ܳ ׮ ݽইࢲ ಣӐਸ ࢜۽ ҅࢑೧ঠ ೞח૑ભ. ࠙ݺ Ӓ فѐ੄ ं੗о ׮ܰѢٚਃ. ࠺तೠ ਗܻੑפ׮. ݒੌݒੌ੄ ૑಴ܳ ಣӐೞݶ Ӓ ݒੌ੄ ࢿҗо ಣӐ੉ غয աоח Ѫ੉Ҋਃ. ੌ઱ੌ஖ ؘ੉ఠܳ ׮ ೤࢑೧ࢲ ಣӐਸ ׮द ҳೞѱ غݶ ੌ઱ੌ ઺ী о੢ ݒ୹੉ ݆ও؍ զ, ௿ܼ੉ ݆ও؍ զ, ੹ജ੉ ݆ও؍ զ, ߓ࣠੉ ਬդ൤ ݆ও؍ զ੉ ੹୓੄ ಣӐਸ ੗ӝଃਵ۽ Ցযߡ݀פ׮. খীࢲ 4ѐ Ӓܛ઺ী, о੢ दبо ݆ও؍ Ӓܛٜ੉ ੹୓੄ Ѿҗܳ ՑҊ աоח Ѫ୊ۢਃ. ੉ѱ য۰ਕࠁ੉૑݅ ࢎप ਋ܻо ݒੌ ಽҊ੓ח ޙઁੑפ׮.
47. ف ߸ࣻ੄ ࢚ҙҙ҅ܳ ੉ঠӝ ೡ ٸীب बट੄ ৉ࢸਸ ઙઙ ҙ଴ೡ ࣻ ੓णפ׮.
48. बट੄ ৉ࢸ਷ ഥӈ҅ࣻ੄ ࠗഐө૑ ߄Լߡܻӝب ೞભ
49. ؘ੉ఠܳ ߄ۄࠁח ҙ੼੄ ߸ച
50. ৘ܳ ٜয,
 ੉۠ ׏झܳ ݅լ׮Ҋ ೤द׮ “؀೟ࢤ ৢ೧ ࣻמ ಽযࠁפ ೟੼җ ࣻמࢿ੸ ইޖ ҙ۲ হয… 
 द೷ ೠ҅ ૑੸ೞҊ ૓੿ೠ ҕࠗ ݽ࢝೧”
51. बट੄ ৉ࢸਸ ݽܰח ࢎۈ਷ ੉ۧѱ ߈਽ೡ ѩפ׮. “য়ഐ ా੤ۄ! ੑद ઺ब੄ Үਭী ૘઺ೡѱ ইפۄ, ࢎۈ੉ ࢿ੢ೡ ࣻ ੓ח ૓੿ೠ Үਭ੉ ೙ਃೠ ٸ׮”
52. ੉ઁ बट੄ ৉ࢸਸ ইח ৈ۞ٜ࠙਷ ੉ۧѱ ߈਽ೡ ࣻ ੓णפ׮. “഑द Ӓې೐о ੉ۧѱ ࢤӟѢ ইפঠ?” x୷ਸ ࣻמࢿ੸, y୷ਸ ೟੼੉ۄҊ ࠇद׮. ؀୽ ࢚؀੸ੋ ч੉ۄҊ ࠊ઱दݶ غѷणפ׮. पઁ ؘ੉ఠח ইפҊ, ઁ ࢚࢚ীࢲ աৡ ؘ੉ఠ੉Ҋਃ. п ੼ٜ਷ Ӓ۞פө ࣻמࢿ੸җ ೟੼੄ ઑ೤੉ѷભ. ৘ܳ ٜয (400, 2.5)׮ Ӓ۞ݶ ࣻמ੼ࣻ 400੼ਵ۽ ੑ೟೮חؘ ೟੼ ಣӐ਷ 2.5ੋ ѐੋ੉ѷભ. ࣻמ ࢿ੸җ ೟੼рী ߹ ࢚ҙҙ҅о হ׮Ҋ ೮ਵפө ࢶഋ ഥӈ ૒ࢶਸ ೖ౴೧ ࠌਸ ٸী ੷ۧѱ ࣻಣী оө਍ ૒ࢶ੉ աৢѩפ׮.
53. ੉ઁ बट੄ ৉ࢸਸ ইח ৈ۞ٜ࠙਷ ੉ۧѱ ߈਽ೡ ࣻ ੓णפ׮. “഑द Ӓې೐о ੉ۧѱ ࢤӟѢ ইפঠ?” খ੄ Ӓܿҗ э਷ ನੋ౟ী ੼ٜ੉ ନഃ੓ח ੿ഛ൤ э਷ ࢑ನبੑפ׮. ׳ۄ૓ѱ ೞա ੓׮ݶ, п ೟җ߹۽ ࢝ӭਸ ઑӘ ׮ ܰѱ ச೧ࠌযਃ. э਷ ೟Ү؊ۄب ೟җ߹۽ ੑ೟੼ ࣻо ઑӘঀ ׮ܰભ. ৘ܳ ٜযࢲ ޤ ੄؀ա ೠ੄؀ח э਷ ೟Ү؊ۄب ੑ ೟ ੼ࣻо ݒ਋ ֫Ҋ, ߈ݶী ࢚؀੸ਵ۽ ੑ೟੼ࣻ о ખ ծ਷ ೟җب ੓ભ. Ӓېࢲ ই݃ ࣻמ੼ࣻҗ ೟ ੼р੄ ࢑ನبח ੉۠धਵ۽ Ӓ۰૕ѩפ׮
54. ੉ઁ बट੄ ৉ࢸਸ ইח ৈ۞ٜ࠙਷ ੉ۧѱ ߈਽ೡ ࣻ ੓णפ׮. “഑द Ӓې೐о ੉ۧѱ ࢤӟѢ ইפঠ?” ౵ۆ࢝ Ӓܛ੄ ޖѱ઺ब п Ӓܛ߹۽ x୷, ૊ ࣻמ੼ࣻ੄ ಣӐ਷ ׮ܰભ. ౵ۆ࢝ Ӓܛ੄ x୷ ಣӐ਷ x Ӓܛ੄ ੿ഛ൤ ޖѱ ઺बী ନਸ ࣻ ੓ਸѢ৘ਃ. п Ӓܛ੄ ࣻמ੼ࣻ ಣӐ੉ ׮ܰ׮חѤ, п ೟җ ߹۽ ੑ೟੼ࣻ, ૊ ࣻמ੼ࣻ, ী ޥо ର੉о ઓ੤ ೠ׮ח Ѣѷભ. Ӓѱ ా҅੸ਵ۽ ਬ੄޷ೞѱ ׮ܰ ջח ੉ঠӝח ੌױ ৈӝীࢲ ࢤۚೞҊਃ. ੉ۧѱ ੹୓੄ ؘ੉ఠܳ п Ӓܛ߹۽ աׂ ࣻ ੓ ׮Ҋ о੿ೞҊ ഥӈ ૒ࢶਸ ׮द Ӓ۰ࠅөਃ?
55. ੉ઁ बट੄ ৉ࢸਸ ইח ৈ۞ٜ࠙਷ ੉ۧѱ ߈਽ೡ ࣻ ੓णפ׮. “഑द Ӓې೐о ੉ۧѱ ࢤӟѢ ইפঠ?” ੹୓ ؘ੉ఠীࢲח ࠁ੉૑ ঋও؍ ਋࢚ೱ ౟۪౟о ࠁ ੉ભ. ೟җܳ ޖदೞҊ ੹୓ ؘ੉ఠܳ 2ରਗ ಣݶী ࡸ۷ਸ ٸী ੹ഃ ࢚ҙҙ҅о হয ࠁ੉؍ ف ߸ࣻ, ࣻמ੼ࣻ ৬ ೟੼੉, ؘ੉ఠܳ ଂѐҊ ࠁওਸ ٸ ੉ۧѱ ݺഛೠ ࢚ҙҙ҅ܳ ࠁੌ ࣻب ੓׮ח ѩפ׮. п ೟җ߹۽ ੑ೟੼ࣻח ׮ؘܲ, ೟੼਷ ೟җ উীࢲ ࢚؀ಣоܳ ೞפө ੉۠ ੌ੉ ࢤӡ ࣻ ੓חѢભ.
56. ੉ઁ बट੄ ৉ࢸਸ ইח ৈ۞ٜ࠙਷ ੉ۧѱ ߈਽ೡ ࣻ ੓णפ׮. “഑द Ӓې೐о ੉ۧѱ ࢤӟѢ ইפঠ?” “೟җ߹ ੑ೟ ੼ࣻо ׮ܰӝ ٸޙী ੌ੿ ࣻמ੼ࣻ ߧਤ ߹۽ ೟җо ա׊য ૗ п ೟җ߹۽ ࣻמ ੼ࣻ(x)৬ ೟੼(y) р੄ ҙ҅ܳ ഥӈࢶਵ۽ Ӓ۰ࠁפ x੄ ҅ࣻо ন੄ чਸ о૓׮ ࣁࠗ Ӓܛ ߹(೟җ ߹)۽ ࠌਸ ٸ ف ߸ࣻ੄ ҙ҅৬ ੹୓੄ ҙ҅о ׮ܲ ੹ഋ੸ੋ Simpson’s paradox” о ੓ਸ ࣻ ੓׮!
57. ૑Әө૑ “؀೟ࢤ ৢ೧ ࣻמ ಽযࠁפ ೟੼җ ࣻמࢿ੸ ইޖ ҙ۲ হয… द೷ ೠ҅ ૑ ੸ೞҊ ૓੿ೠ ҕࠗ ݽ࢝೧” ۄח ӝࢎ ઁݾਸ ࠌਸ ٸী ೡ ࣻ ੓ח о੢ ؘ੉ఠ ࠙ࢳоझ۞਍ ࠺ಣਸ ೧ࠌणפ׮.
58. “ت੉ ࢎۈਸ ೯ࠂೞѱ ݅٘חѱ ইפۄ ࢎۈ੉ ࢎۈਸ ೯ࠂೞѱ ݅٘חѢ׮.” ޤ ੉۠ ݺ঱ ٜযࠁ࣑ਸѢ৘ ਃ. хزب ߉ইࠁҊ. ਤ Ӓې೐ীࢲ x୷਷ 1ੋ׼ GDP, y୷਷ ࢕੄ ݅઒بੑ פ׮. ೩ૉৡ ݠन۞׬੉ۄח, ੉ ଼ ҕध ӥ೸ীࢲ о ઉ৳חؘ ୷ ۄ߰ਸ ੜ ޅ ॳ࣑؊ۄҳਃ. ӒܻҊ п ੼ٜ਷ Ҵо߹ ಣӐ੉ীਃ. ಣӐ੉ۄח ױয ܳ ٜਵפө ٯ ঌۈ੉ ெ૑૑ ঋաਃ? ӒܻҊ ୋ ࠊࢲח ؀ױೠ ਋࢚ೱ ౟۪٘о ੓য ࠁ੉૑ ݅, y ୷੉ 0ࠗఠ 10ө૑о ইפۄ ࢎप 5ࠗఠ 7.5ө ૑ ੜ۰੓যਃ. 0ࠗఠ 10ө૑ झாੌ۽ ಟ୛֬Ҋ ࠌਸ ٸী ੉ ࢑ನبח ഻ঁ ৮݅೧૘פ׮. ୹୊: ೩ૉৡ ݠन۞׬
 Chapter 01. ೠ׀ী ࠁח ݠन۞׬ ت੉ ࢎۈਸ ೯ࠂೞѱ ݅٘חо?
59. ؘ੉ఠ ࠙ࢳਸ ೞӝ ੹ী ੉ ফӝܳ ٜ঻ਸ ٸীח ‘Ӓ ې! ೯ࠂ਷ تਸ ઱Ҋ ࢓ ࣻ হ૑’ ژח ‘ޤ ت੉ ೯ࠂী ޷޷ೠ ৔ೱਸ ޷஖ӟ ೞѷ૑݅, Ӓۧѱ ௾ ಂఠח ইפ ૑’ ೮ѷ૑݅, ૑Ә਷ ખ ׮ܵפ׮. ӒܻҊ पઁ۽ تਸ ߥযࠁפө ҭ੢൤ ೯ࠂೞ؊ۄҊ ਃ? ୹୊: ೩ૉৡ ݠन۞׬
 Chapter 01. ೠ׀ী ࠁח ݠन۞׬ ت੉ ࢎۈਸ ೯ࠂೞѱ ݅٘חо?
60. ੷ӝ ନ൦ ੷ ੼੉ 2015֙੄ ೠҴੑפ׮. ੿ഛ൤ ח, ೠҴ੄ 1ੋ׼ GDPܳ x۽ ೞҊ, ೠҴীࢲ ࢠ೒ ۽ ࣻ૘ೠ ࢎۈٜ੉ ਽׹ೠ life satisfaction੄ ಣ Ӑчਸ y۽ ೞח ઝ಴੼੉ભ. ੉ ؘ੉ఠо ‘ت੉ ࢎۈਸ ೯ࠂೞѱ ݅٘חо?’ܳ ؀ ׹ೡ ੗Ѻ੉ ੓աਃ? ೯ࠂਸ וՙח ઱୓ח Ҵоо ইפۄ ѐੋੑפ׮. ӒܻҊ Ҵ޹ٜ ೞա ೞաܳ ੼ਵ۽ Ӓ۷ਸ ٸী, ੷ ӝী ࠁ੉ח ౵ۆ࢝ ੼ਸ ޖѱ઺बਵ۽ ೞח Ӓ য ڃ ࢑ನبب Ӓܾ ࣻ ੓ભ. ӒѪ੉ ਋࢚ೱೞח ౟۪ ٘ܳ о઎ਸ૑, ਋ೞೱೡ૑, ইפݶ ಁఢ੉ হ੉ ൝ যઉ ੓ਸ૑ח ইޖب ݽܰחѢભ. Ӓ੷ ੷ ੼੉, য ڃ ݽন੄ ࢑ನب੄ ޖѱ઺ब੉ۄח Ѫ݅ ঌ ࣻ ੓ ਸ ࡺੑפ׮. ୹୊: ೩ૉৡ ݠन۞׬
 Chapter 01. ೠ׀ী ࠁח ݠन۞׬ ت੉ ࢎۈਸ ೯ࠂೞѱ ݅٘חо? ೠҴ
61. ੉ۧѱ Ӓܛ੄ ಣӐਵ۽ ޡڨӒ۰֬਷ ؘ੉ఠܳ о૑ Ҋ ‘ت੉ ࢎۈਸ ೯ࠂೞѱ ݅٘חо?’ۄח ઁݾਸ ױ Ѥ ցޖ ա੉࠳ೞѱ ࢤпೠѢભ. (ৌब൤ Ӳ૑݅, ੹ ੷ ଼ જই೤פ׮.) খ੄ ৘द৬ ݃ଲо૑۽ बट੄ ৉ࢸ੉ ੓ਸ ࣻ ੓׮ ח ѩפ׮. ѐੋ੄ ೯ࠂҗ ࣗٙ ؘ੉ఠܳ ઑࢎ೧ࠁ૑ ঋח ੉࢚ ૐݺਸ ೡ ࣽ হѷ૑݅, Ӓٜ੉ ࣁਕ֬਷ о ࢸ੉ ౣ۷ਸ ࣻ ੓׮! ח Ѧ ݈ೞח Ѫਵ۽ ࠺౸਷ ୽ ࠙ೞભ. ୹୊: ೩ૉৡ ݠन۞׬
 Chapter 01. ೠ׀ী ࠁח ݠन۞׬ ت੉ ࢎۈਸ ೯ࠂೞѱ ݅٘חо? ೠҴ
62. ݃ޖܻ
63. ੉ઁ बट੄ ৉ࢸ੉ ޥ૑ х੉ ੟൤दաਃ?
64. ই૒ ੜ ݽܰदѷ׮ҳਃ.
65. ҡଳणפ׮.
 ৈ۞ٜ࠙ਸ ਤ೧ प۱੓ח ೐ܻےࢲо ৈӝী ੓ભ.
66. ysunmi0427@gmail.com https://www.linkedin.com/in/yoonsunmi
67. ۨಌ۠झ - Pearl, Judea. “Comment: understanding Simpson’s paradox.” The American Statistician 68.1 (2014): 8-13. - “Simpson’s paradox” Wikipedia - উ࢚ഋ “࢚धਸ ٍ૘ח ా҅ - Simpson’s paradox” Seoul Business Letter - Berman, S. DalleMule, L. Greene, M., Lucker, J. "Simpson’s Paradox: A Cautionary Tale in Advanced Analytics" The Statistics Dictionary (2012) - “Is this Simpson's Paradox on the Titanic data set?" Stack exchange Cross Validated
68. Thanks to
 Chiwan Park, ؘ੒Ѧૉ3ӝ хࢎ೤פ׮