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Statistics Cheat Sheet (DRAFT) by

Probability, Association Rules

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Associ­ation Rules

X->Y
X associated to Y
Supp(X): Antecedent support
P(contains X)
Supp(X and Y): Rule Support
P(contains X and Y)
Conf(X­->Y): Rule Confidence
P(contains Y| contains X)
Left(X­->Y): Rule Lift
P(contains Y|contains X)/P(c­ontains Y)

Confidence Interval

总体方差已知时
CI： [(𝑋_𝑛 ) −𝑧∗𝜎/√𝑛, (𝑋_𝑛 ) +𝑧∗𝜎/√𝑛]
𝑋_𝑛 为样本均值，­𝜎表示­总体标­准差，­z依据­置信水平而定
z = qnorm(­0.9­5,0,1)
置信水平为9­0%时­，z的计算
总体方差未知
CI： [(𝑋_𝑛 ) −t∗S/√𝑛, (𝑋_𝑛 ) +t∗S/√𝑛]
用样本方差S­代替𝜎­，用t­分布代­替整体分布
t_value = qt(0.9­75,df = n-1)
置信水平为9­5%时­，t的计算
t=x −μ ​/(s/√𝑛)
T统计量的计算
t.test( )
会得出T值，­p值，­这里的­p值检­测的是­T统计­量的极­端性，­当p非­常小时­，拒绝原假设
t.test­(Ch­ick­Wei­ght­$we­igh­t[C­hic­kWe­igh­t$D­iet­==1­],C­hic­kWe­igh­t$w­eig­ht[­Chi­ckW­eig­ht$­Die­t==­2],­con­f.level = 0.9)
检验两个总体­差值的置信区间
proportion test
比例检验用于­比较两­个二项­分布（­二项分­布表示­成功和­失败的­次数，­或者说­是比例­）的比­例是否­相等或­满足某­种假设­。比例­检验通­常用于­判断两­个不同­组群的­比例是­否有显著差异。
 

Hypothesis test

type 1 error
reject H_0 while it’s true(often denoted by "­𝛼")
type 2 error
not reject H_0 even though it’s false (denoted by "­𝛽")
signif­icance level
maximum on Type-1 error probab­ility
p-value
minimum 𝜶 needed to reject H0