平均值:表示為

期望：表示為E(X)

方差：表示為V(X)

標(biāo)準(zhǔn)差：

中心極限定理：設(shè)隨機變量X1，X2，......Xn，......獨立同分布，并且具有有限的數(shù)學(xué)期望和方差：E(Xi)=μ，D(Xi)=σ20(k=1,2....)，則對任意x，分布函數(shù)

滿足

切比雪夫不等式：設(shè)隨機變量X具有數(shù)學(xué)期望，方差

則對任意正數(shù)ε，不等式

成立。

費希爾確切概率檢驗：設(shè)n為樣本例數(shù)，Xo為現(xiàn)有樣本某事件發(fā)生數(shù)，p=Xo/n,π為總體率，a，b，c，d為四格表中的4個頻數(shù)，當(dāng)b+c≤40，且a和d較小時，用確切概率法，令n=b+c，X=b，用樣本率與總體率比較的方法檢驗。相應(yīng)的假設(shè)檢驗為Ho:π=0.5 H1:π≠0.05

一種直接計算概率的假設(shè)檢驗方法，

檢驗應(yīng)用條件不滿足時，可直接計算概率

邦費羅尼校正：

作者：Sichao Song

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

來源：知乎

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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比較保守，容易錯誤的接受零假設(shè)。用的更多的是Holm's-Bonferroni，比前者要更容易發(fā)現(xiàn)顯著差異。