如何在 R 中识别 Kolmogorov-Smirnov 检验与卡方拟合优度检验之间的差异？

卡方拟合优度检验用于检验标称变量的分布是否相同，以及其他分布匹配，而另一方面，Kolmogorov-Smirnov 检验仅用于检验连续数据的拟合优度。区别不在于编程工具，而在于统计学概念。

示例

现场演示

> x<-rnorm(20)
> x

输出

[1] 0.078716115 -0.682154062 0.655436957 -1.169616157 -0.688543382
[6] 0.646087104 0.472429834 2.277750805 0.963105637 0.414918478
[11] 0.575005958 -1.286604138 -1.026756390 2.692769261 -0.835433410
[16] 0.007544065 0.925296720 1.058978610 0.906392907 0.973050503

示例

> ks.test(x,pnorm)

One-sample Kolmogorov-Smirnov test

data: x
D = 0.2609, p-value = 0.1089
alternative hypothesis: two-sided

Chi-Square test:

> chisq.test(x,p=rep(1/20,20))
Error in chisq.test(x, p = rep(1/20, 20)) :
all entries of 'x' must be nonnegative and finite

对于离散分布 −

示例

现场演示

> y<-rpois(200,5)
> y

输出

[1] 6 8 7 3 5 7 6 5 2 6 4 4 3 6 6 6 6 11 7 5 4 8 6 1 3
[26] 10 4 4 9 5 2 6 4 1 5 4 4 5 1 7 8 7 3 6 6 6 2 8 7 6
[51] 7 5 5 4 6 5 3 5 3 4 4 9 3 3 3 8 3 3 2 5 4 6 6 8 4
[76] 6 12 6 1 5 5 5 0 7 4 7 7 3 2 5 5 2 5 5 4 6 4 3 4 4
[101] 4 6 5 1 2 4 4 4 8 5 8 6 3 4 5 2 3 3 3 6 7 4 4 5 3
[126] 5 5 5 8 2 5 8 1 2 3 5 9 4 3 5 6 3 6 3 6 3 7 4 4 1
[151] 3 5 0 7 2 9 6 10 2 6 4 5 1 7 2 8 7 4 2 5 4 2 4 5 6
[176] 3 9 3 9 5 9 7 3 1 3 9 5 6 3 10 7 5 5 6 7 4 2 5 5 1

示例

> chisq.test(y,p=rep(1/200,200))

Chi-squared test for given probabilities

data: y
X-squared = 203.61, df = 199, p-value = 0.3964

Warning message:
In chisq.test(y, p = rep(1/200, 200)) :
Chi-squared approximation may be incorrect

示例

现场演示

> a<-sample(0:9,100,replace=TRUE)
> a

输出

[1] 4 6 1 8 1 7 3 9 8 5 4 0 7 2 2 4 6 2 1 2 1 9 1 3 1 9 2 9 1 8 4 0 4 7 1 7 1
[38] 0 1 5 9 6 5 4 6 6 9 6 1 0 8 9 4 8 2 8 1 6 9 1 0 4 6 8 8 1 1 0 3 2 6 7 2 1
[75] 7 9 9 8 2 6 4 7 3 4 0 9 5 5 9 4 5 7 8 7 3 0 1 4 8 5

示例

> ks.test(a,pnorm)

One-sample Kolmogorov-Smirnov test

data: a
D = 0.76134, p-value < 2.2e-16
alternative hypothesis: two-sided

Warning message:
In ks.test(a, pnorm) :
ties should not be present for the Kolmogorov-Smirnov test
> chisq.test(a,p=rep(1/100,100))

Chi-squared test for given probabilities

data: a
X-squared = 198.88, df = 99, p-value = 1.096e-08

Warning message:
In chisq.test(a, p = rep(1/100, 100)) :
Chi-squared approximation may be incorrect

更新时间：2021-01-04

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