作业帮多重比较的几种校正方法求答案
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多重比较的几种校正方法求答案
举个例子：如要在同一数据集上检验两个独立的假设,显著水平设为常见的0.05.此时用于检验该两个假设应使用更严格的 0.025.即0.05* (1/2).该方法是由Carlo Emilio Bonferroni发展的,因此称Bonferroni校正. 这样做的理由是基于这样一个事实：在同一数据集上进行多个假设的检验,每20个假设中就有一个可能纯粹由于概率,而达到0.05的显著水平.
维基百科原文： Bonferroni correction: Bonferroni correction states that if an experimenter is testing n independent hypotheses on a set of data, then the statistical significance level that should be used for each hypothesis separately is 1/n times what it would be if only one hypothesis were tested.
For example, to test two independent hypotheses on the same data at 0.05 significance level, instead of using a p value threshold of 0.05, one would use a stricter threshold of 0.025.
The Bonferroni correction is a safeguard against multiple tests of statistical significance on the same data, where 1 out of every 20 hypothesis-tests will appear to be significant at the α = 0.05 level purely due to chance. It was developed by Carlo Emilio Bonferroni.
A less restrictive criterion is the rough false discovery rate giving (3/4)0.05 = 0.0375 for n = 2 and (21/40)0.05 = 0.02625 for n = 20.
Benjamini and Hochberg在1995年第一次提出了FDR(False Discovery Rate)的概念,其出发点就是基于Bonferroni的保守性,并给出了控制FDR的方法（这算是FDR控制方法的祖师爷了）.不过他们的方法也有其保守性.所以随后人们开始研究更加powerful的方法,现有的方法有Storey的, Broberg的,Dalmasso的,Guan的,Strimmer的等等等等.Benjamini的方法是将FDR控制在一个level以下,而之后所有的方法都在试图精确地估计FDR.所以后来的这些方法都要powerful一些.不过他们所付出的代价就是robustness.据说Storey方法是最流行的FDR control procedure(For details see Storey's paper published ON PNAS ,2003).
维基百科原文： Bonferroni correction: Bonferroni correction states that if an experimenter is testing n independent hypotheses on a set of data, then the statistical significance level that should be used for each hypothesis separately is 1/n times what it would be if only one hypothesis were tested.
For example, to test two independent hypotheses on the same data at 0.05 significance level, instead of using a p value threshold of 0.05, one would use a stricter threshold of 0.025.
The Bonferroni correction is a safeguard against multiple tests of statistical significance on the same data, where 1 out of every 20 hypothesis-tests will appear to be significant at the α = 0.05 level purely due to chance. It was developed by Carlo Emilio Bonferroni.
A less restrictive criterion is the rough false discovery rate giving (3/4)0.05 = 0.0375 for n = 2 and (21/40)0.05 = 0.02625 for n = 20.
Benjamini and Hochberg在1995年第一次提出了FDR(False Discovery Rate)的概念,其出发点就是基于Bonferroni的保守性,并给出了控制FDR的方法（这算是FDR控制方法的祖师爷了）.不过他们的方法也有其保守性.所以随后人们开始研究更加powerful的方法,现有的方法有Storey的, Broberg的,Dalmasso的,Guan的,Strimmer的等等等等.Benjamini的方法是将FDR控制在一个level以下,而之后所有的方法都在试图精确地估计FDR.所以后来的这些方法都要powerful一些.不过他们所付出的代价就是robustness.据说Storey方法是最流行的FDR control procedure(For details see Storey's paper published ON PNAS ,2003).