R data analysis examples
功效分析
power analysis for one-sample t-test單樣本t檢驗
例1.一批電燈泡，標准壽命850小時，標准偏差50，40小時的差值是巨大的，此研究設定效應值d=
(850-810)/50,希望有90%的可能檢測到，即功效值為0.9，還希望有95%的把握不誤報顯著差異，
問需要多少支電燈泡。
H0=850，HA=810
library('pwr')
pwr.t.test(d=(850-810)/50,power=0.9,sig.level=0.05,type="one.sample",alternative = 'two.sided')
One-sample t test power calculation
n = 18.44623
d = 0.8
sig.level = 0.05
power = 0.9
alternative = two.sided
結果說明需要19支燈泡去拒絕H0，並保證在HA下有達到0.9的功效
然后，如果我們只取10支電燈泡，會達到什么程度的功效水平呢？
pwr.t.test(d=(850-810)/50,n=10,sig.level=0.05,type="one.sample",alternative = 'two.sided')
One-sample t test power calculation
n = 10
d = 0.8
sig.level = 0.05
power = 0.6162328
alternative = two.sided
結果功效只有0.616。那麽如果選15支呢？
pwr.t.test(d=(850-810)/50,n=15,sig.level=0.05,type="one.sample",alternative = 'two.sided')
One-sample t test power calculation
n = 15
d = 0.8
sig.level = 0.05
power = 0.8213105
alternative = two.sided
power=0.821，你將有18%的可能錯過你要尋找的效應值
取樣20支，
pwr.t.test(d=(850-810)/50,n=20,sig.level=0.05,type="one.sample",alternative = 'two.sided')
One-sample t test power calculation
n = 20
d = 0.8
sig.level = 0.05
power = 0.9238988
alternative = two.sided
功效為0.924 大於n=19時的功效0.9
結論，取樣n增大，相應功效power也會增大
下面改變標准差
pwr.t.test(d=(850-810)/30,power=0.8,sig.level=0.05,type="one.sample",alternative = 'two.sided')
One-sample t test power calculation
One-sample t test power calculation
n = 6.581121
d = 1.333333
sig.level = 0.05
power = 0.8
alternative = two.sided
所需的取樣量減少
下面我們再討論一下the effect size
pwr.t.test(d=(50-10)/50,power=0.9,sig.level=0.05,type="one.sample",alternative="two.sided")
One-sample t test power calculation
n = 18.44623
d = 0.8
sig.level = 0.05
power = 0.9
alternative = two.sided
n=18.44623
pwr.t.test(d=(1-.2),power=0.9,sig.level=0.05,type="one.sample",alternative="two.sided")
One-sample t test power calculation
n = 18.44623
d = 0.8
sig.level = 0.05
power = 0.9
alternative = two.sided
n=18.44623
可以看到 結果這3個實驗的結果n 相等。但是去決定 the true effect size並不簡單。一個
正確的the effect size的估值是成功的功效分析的關鍵。