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  • R笔记 单样本t检验 功效分析

    R data analysis examples
    功效分析
    power analysis for one-sample t-test单样本t检验

    例1.一批电灯泡,标准寿命850小时,标准偏差50,40小时的差值是巨大的,此研究设定效应值d=
    (850-810)/50,希望有90%的可能检测到,即功效值为0.9,还希望有95%的把握不误报显著差异,
    问需要多少支电灯泡。
    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
    
    

    结果说明需要19支灯泡去拒绝H0,并保证在HA下有达到0.9的功效

    然后,如果我们只取10支电灯泡,会达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
    
    

    结果功效只有0.616。那麽如果选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,你将有18%的可能错过你要寻找的效应值
    取样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
    

    功效为0.924 大于n=19时的功效0.9
    结论,取样n增大,相应功效power也会增大

    下面改变标准差

    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
    

    所需的取样量减少

    下面我们再讨论一下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 结果这3个实验的结果n 相等。但是去决定 the true effect size并不简单。一个
    正确的the effect size的估值是成功的功效分析的关键。

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  • 原文地址:https://www.cnblogs.com/li-volleyball/p/5645617.html
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