Statistic(1) - Hypothesis Test(1)

<Learned Stuff>

Key Points

• Hypothesis Test
  • 가설검정 이해

 

• 기술 통계치 (Descriptive Statistics) v.s. 추리 통계치 (Inferential Statistics)
  • 기존 데이터 분석 v.s. 모집단 분석

 

개념

• Stduent T-test
  • Null Hypothesis v.s. Alternative Hypothesis
  • One Sample T-test / Two Sample T-test
  • Two-side test / One-side test

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<New Stuff>

[Student T-test]

[Two-side test]

1. One Sample t-test

# H0 : sample_mean == specific_value (D=0)
# H1 : sample_mean != specific_value (D>0 or D<0)

# D = sample_mean - specific_value

t-value = (sample_mean - specific_value) / (sample_std/sqrt(sample_size))

# ==> 평균은 0 , 표준편차가 1 인 데이터로 scaling! ==> p-value는 컴퓨터 계산으로 나옴

 

2. Two Sample t-test

# H0 : sample_mean1 == sample_mean2 (D=0)
# H1 : sample_mean1 != sample_mean2 (D>0 or D<0)

# D = sample_mean1 - sample_mean2

t-value = (sample_mean1 - sample_mean2) / (sample1_std/sqrt(sample_size1) + sample2_std/sqrt(sample_size2)

# ==> 평균은 0 , 표준편차가 1 인 데이터로 scaling! ==> p-value는 컴퓨터 계산으로 나옴

 

[One-side test]

H0 : sample_mean1 == sample_mean2 (D=0)
H1 : sample_mean1 > sample_mean2 (D>0)

right-hand-side

H0 : sample_mean1 == sample_mean2 (D=0)
H1 : sample_mean1 < sample_mean2 (D<0)

 

[Conclusion]

• Confidence level : 95% 가정
  • p-value >= 0.05 : accept Null Hypothesis
  • p-value < 0.05 : accept Alternative Hypothesis