统计学中的概念

平均值:表示为

期望：表示为E(X)

方差：表示为V(X)

标准差：

中心极限定理：设随机变量X1，X2，......Xn，......独立同分布，并且具有有限的数学期望和方差：E(Xi)=μ，D(Xi)=σ20(k=1,2....)，则对任意x，分布函数

满足

切比雪夫不等式：设随机变量X具有数学期望，方差

则对任意正数ε，不等式

成立。

费希尔确切概率检验：设n为样本例数，Xo为现有样本某事件发生数，p=Xo/n,π为总体率，a，b，c，d为四格表中的4个频数，当b+c≤40，且a和d较小时，用确切概率法，令n=b+c，X=b，用样本率与总体率比较的方法检验。相应的假设检验为Ho:π=0.5 H1:π≠0.05

一种直接计算概率的假设检验方法，

检验应用条件不满足时，可直接计算概率

邦费罗尼校正：

作者：Sichao Song

链接：https://www.zhihu.com/question/56062084/answer/148462953

来源：知乎

著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。

Statistical hypothesis testingis based on rejecting thenull hypothesisif the likelihood of the observed data under the null hypotheses is low. If multiple comparisons are done or multiple hypotheses are tested, the chance of a rare event increases, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.e., making aType I error) increases.

The Bonferroni correction compensates for that increase by testing each individual hypothesis at a significance level of α/m, where α is the desired overall alpha level and m is the number of hypotheses. For example, if a trial is testing m=20 hypotheses with a desired α=0.05, then the Bonferroni correction would test each individual hypothesis at α=0.05/20=0.0025.

Bonferroni correction比较保守，容易错误的接受零假设。用的更多的是Holm's-Bonferroni，比前者要更容易发现显著差异。