Power analyses

power analyses는 주로 필요한 표본의 갯수를 구하기 위해 사용한다.

 

이를 위해서는 power, significant level(or alpha), effect size를 알아야함.

 

Power:

• The probability of rejecting the null hypothesis when it is false.
• It is also the basis of procedures for estimating the sample size needed to detect an effect of a particular magnitude
• Power gives a method of discriminating between competing tests of the same hypothesis, the test with the higher power being preferred.

Significance level:

• The level of probability at which it is agreed that the null hypothesis will be rejected.
• Conventionally set at 0.05.

Effect size:

• Most commonly the difference between the control group and experimental group population means of a response variable divided by the assumed common population standard deviation.
• Estimated by the difference of the sample means in the two groups divided by a pooled estimate of the assumed common standard deviation.

power과 needed data point와의 관계는 지수함수의 꼴을 나타냄.
power가 올라갈수록 needed data point가 기하급수적으로 늘어남. 다른 변수는 고정이라 가정.


significance level이 오를수록 needed data point의 관계는  1이하의 분수꼴의 지수함수 형태로 나타남.
significance level이 오를수록 needed data point는 기하급수적으로 감소함.

significance level이 굉장히 작으면 필요로 하는 data point가 굉장히 많음.

Effect size와 needed data point와의 관계는 'ㄴ'자 형태를 띄고 있음.
일정수준의 Effect size를 가지면 필요한 data point는 거의 변함이 없음.