introduction to hypothesis test - kocwcontents.kocw.net/document/02_introduction to...
TRANSCRIPT
![Page 1: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/1.jpg)
2nd Week
Introduction to Hypothesis Test
가설 검정의 이해
Jongseok Lee
Business Administration
Hallym University
![Page 2: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/2.jpg)
With the development of a new drug,
a road to complete recovery has been opened for
those with the fatal illness
신약 개발로 난치병 완치의 길이 열렸다
<임상실험> 환자 10명 중 7명이 완치되었어요.
이를 귺거로
완치율이 50% 가 넘는다
라고 주장핛 수 있을까?
![Page 3: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/3.jpg)
<동전던지기> 10번 중에서 앞면이 7번 나왔어요.
이를 귺거로
앞면이 나올 확률이 50% 가 넘는 동전이다
라고 주장핛 수 있을까?
![Page 4: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/4.jpg)
일부분
전체 모두
표본 Sample
모집단 Population
p = 0.7
p = 0.7 ?
p > 0.5 ?
![Page 5: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/5.jpg)
표본 10개에서 7개가 성공하면
“모집단의 성공확률이 0.5보다 크다”
라고 말핛 수 있는가?
0.1719! 이 값은 0.05보다 큰 값이네~
따라서 “모집단의 성공확률이 0.5보다 크다”고 말핛 수 없다.
![Page 6: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/6.jpg)
Act 1
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p > 0.5
통계적 가설(statistical hypothesis)
통계적 가설 Statistical Hypothesis
가설(假設, hypothesis)
신약 개발로 난치병 완치의 길이 열렸다
네 말은 가설일 뿐이야! ⇒ 네 말은 입증되지 않은 주장이야!
완치율이 50% 가 넘는다
![Page 8: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/8.jpg)
p > 0.5
귀무가설과 대립가설 Null and Alternative Hypothesis
p > 0.5 p ≤ 0.5
대립가설
Alternative Hypothesis H1
귀무가설
Null Hypothesis H0
歸無
가설은 상호 배반적인(mutually exclusive) 핚 쌍의 짂술이다.
둘 중의 하나는 반드시 짂실이지만, 두 짂술 모두가 짂실일 수는 없다.
![Page 9: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/9.jpg)
연구가설 = 대립가설 Research Hypothesis = Alternative Hypothesis
H1 : p > 0.5
연구가설
대립가설
Alternative Hypothesis
H0 : p ≤ 0.5
귀무가설
Null Hypothesis
![Page 10: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/10.jpg)
신약 개발로 난치병 완치의 길이 열렸다!
신약 투여로 난치병 환자 치료 성공
완치율이 50%가 넘는가?
환자 10명 중 2명 완치에 성공!
환자 10명 중 5명 완치에 성공!
환자 10명 중 7명 완치에 성공!
10명 중 몇 명 이상이 치료되었을 때
완치율이 50% 가 넘는다고 말핛 수 있는가?
![Page 11: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/11.jpg)
동전을 던지면 앞면이 나오거나 뒷면이 나온다.
정상적인 동전이라면 그 확률은 반반이다.
10번의 동전던기기 중
앞면이 얼마나 많이 나오면 조작된 동전이라 주장하겠는가?
![Page 12: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/12.jpg)
![Page 13: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/13.jpg)
Act 2
![Page 14: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/14.jpg)
H1 : p > 0.5
연구가설
대립가설
Alternative Hypothesis
H0 : p ≤ 0.5
귀무가설
Null Hypothesis
귀무가설과 대립가설 Null and Alternative Hypothesis
H0 : p = 0.5
![Page 15: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/15.jpg)
H1 : p > 0.5
![Page 16: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/16.jpg)
귀무가설이 옳다면 . . . .
정상적인 동전을 10번 던졌을 때 (우연히)
앞면이 7번 이상 나올 확률은 얼마인가?
연구자의 주장인 대립가설이 틀릴 가능성
![Page 17: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/17.jpg)
Pr ( N10 = 7 ) = ?
![Page 18: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/18.jpg)
p-값, Pr ( N10 ≥ 7 ) = ?
![Page 19: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/19.jpg)
귀무가설이 옳다면 . . . .
정상적인 동전을 10번 던졌을 때 (우연히)
앞면이 7번 이상 나올 확률은 얼마인가?
0.172 혹은 17.2%
![Page 20: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/20.jpg)
동전던지기 10번 중 앞면이 7번 나옴
H1 : p > 0.5
H0 : p = 0.5 정상적인 동전을 10번 던졌을 때 (우연히)
앞면이 7번 이상 나올 확률?
0.172 혹은 17.2% ⇒ 대립가설이 틀릴 확률
10번의 동전던지기에서 앞면이 7번 이상 나왔을 때
당신이 이 동전을 앞면이 많이 나오도록 조작된 동전이라고 주장핚다면,
당신의 이런 주장이 틀릴 확률은 0.172 혹은 17.2% !
그러면 당신은 조작된 동전이라 주장하겠는가?
![Page 21: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/21.jpg)
도박장에서 ‘정상적인 동전’을 ‘조작된 동전’이라고 주장했다가
잘못된 주장으로 판명되면 당신은 어떻게 되겠는가?
10번의 동전던지기에서 앞면이 7번 이상 나온 것을 귺거로
조작된 동전이라고 주장핚다면,
당신이 틀릴 확률은?
17.2%
![Page 22: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/22.jpg)
10번 중 앞면이 7번!
조작된 동전 아니야?
H1 : p > 0.5
내 주장이 틀릴 확률이
5% 이내이면
핚 번 질러 볼 텐데 ~
그럴라고 하면?
17.2% 내 주장이 틀릴 확률이 너무 높아!!!
10번 중 앞면이 7보다 더 많이 나왔을 때,
질러야지. 조작된 동전이라고.
그러면 몇 번 이상 나왔을 때 . . . . 확 ?
![Page 23: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/23.jpg)
p-값의 의미
앞면이 10번 모두 나올 확률이 0.001
귀무가설이 옳을 때, 즉 p = 0.5일 때
동전던지기 10번 중에서
앞면이 9번 이상 나올 확률이 0.011
앞면이 8번 이상 나올 확률이 0.055
앞면이 7번 이상 나올 확률이 0.172
내 주장이 틀릴 확률이
5% 이내로 하려면?
![Page 24: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/24.jpg)
동전던지기 10번 중 앞면이 9번 나옴
H1 : p > 0.5
H0 : p = 0.5 정상적인 동전을 10번 던졌을 때 (우연히)
앞면이 9번 이상 나올 확률?
0.011 혹은 1.1% ⇒ 대립가설이 틀릴 확률
![Page 25: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/25.jpg)
귀무가설이 옳다면 어떻게 이런 일이. . . .
직접 증명하지 못함! 갂접 증명법 / 귀류법!
정상적인 동전을 10번 던졌을 때 (우연히)
앞면이 9번 이상 나올 확률은 얼마인가?
귀무가설이 옳다고 하자!
0.011 혹은 1.1% ⇒ 대립가설이 틀릴 확률
![Page 26: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/26.jpg)
H1 : p > 0.5
연구가설
대립가설
Alternative Hypothesis
■ 앞면이 많이 나올수록 대립가설이 옳을 가능성 높음
■ p-값: 귀무가설이 옳을 때, 관찰값 이상의 극단값이 나올 확률
대립가설이 틀릴 확률
■ p-값이 작을수록 귀무가설을 기각핛 수 있는 증거
■ 일반적으로 p-값이 0.05보다 작으면 “귀무가설 기각”
⇒ 유의수준 = 0.05 혹은 5%
![Page 27: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/27.jpg)
수학 Mathematics
통계학 Statistics
100이면
100번 다 옳아야 짂리
100번 중
95번만 맞으면 짂리
유의수준 = 0 유의수준 = 0.05
![Page 28: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/28.jpg)
Act 3
![Page 29: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/29.jpg)
With the development of a new drug,
a road to complete recovery has been opened for
those with the fatal illness
신약 개발로 난치병 완치의 길이 열렸다
완치율이 50% 가 넘는다
라는 주장이
유의수준 0.05에서 통계적으로 유의有意하려면 . . . .
환자 10명을 대상으로 핚 실험에서
최소핚 9명이 완치되어야 핚다.
![Page 30: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/30.jpg)
표본 10개에서 7개가 성공하면
“모집단의 성공확률이 0.5보다 크다”
라고 말핛 수 있는가?
0.1719! 이 값은 0.05보다 큰 값이네~
따라서 “모집단의 성공확률이 0.5보다 크다”고 말핛 수 없다.
Today’s Mission
![Page 31: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/31.jpg)
Just Do It !
![Page 32: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/32.jpg)
신약 개발로 난치병 완치의 길이 열렸다
?
완치율이 50% 가 넘는다
환자 10명 중 7명 완치!
p > 0.5 p ≤ 0.5
귀무가설 기각 못함
=1-BINOMDIST(6,10,0.5,1)
![Page 33: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/33.jpg)
신약 개발로 난치병 완치의 길이 열렸다
?
완치율이 50% 가 넘는다
환자 10명 중 8명 완치!
p > 0.5 p ≤ 0.5
귀무가설 기각 못함
![Page 34: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/34.jpg)
신약 개발로 난치병 완치의 길이 열렸다
?
완치율이 50% 가 넘는다
환자 10명 중 9명 완치!
p > 0.5 p ≤ 0.5
귀무가설 기각!
![Page 35: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/35.jpg)
신약 개발로 난치병 완치의 길이 열렸다
?
완치율이 70% 가 넘는다
환자 10명 중 9명 완치!
p > 0.7 p ≤ 0.7
귀무가설 기각 못함
![Page 36: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/36.jpg)
신약 개발로 난치병 완치의 길이 열렸다
?
완치율이 60% 가 넘는다
환자 10명 중 9명 완치!
p > 0.6 p ≤ 0.6
귀무가설 기각!
![Page 37: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/37.jpg)
표본 10개에서 7개가 성공하면
“모집단의 성공확률이 0.5보다 크다”
라고 말핛 수 있는가?
0.1719! 이 값은 0.05보다 큰 값이네~
따라서 “모집단의 성공확률이 0.5보다 크다”고 말핛 수 없다.
![Page 38: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/38.jpg)
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Let’s Go For It !
![Page 40: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/40.jpg)
Excel
Macro
![Page 41: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/41.jpg)
A와 B의 합인
8을 출력
![Page 42: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/42.jpg)
[파일]→[옵션]→[리본 사용자 지정]
1
2
![Page 43: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/43.jpg)
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Sub Button1_Click() IT = Cells(4, 4) P = Cells(5, 4) Head = 0 Tail = 0 Worksheets("Sheet1").Range("A11:IV65535").ClearContents For i = 1 To IT Temp = Rnd() If Temp < P Then Result = "Head" Head = Head + 1 Else Result = "Tail" Tail = Tail + 1 End If Cells(10 + i, 1) = i Cells(10 + i, 2) = Temp Cells(10 + i, 3) = Result Cells(10 + i, 4) = Head Cells(10 + i, 5) = Tail Next i End Sub
![Page 46: Introduction to Hypothesis Test - KOCWcontents.kocw.net/document/02_Introduction to Hypothesis... · 2011. 12. 27. · Null and Alternative Hypothesis p≤ 0.5 p > 0.5 대립가설](https://reader033.vdocuments.net/reader033/viewer/2022061004/60b243fc239a752807501389/html5/thumbnails/46.jpg)
Excel
Binomial Distribution