如何识别R中的Kolmogorov Smirnov检验和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名义变量的分布是否相同以及是否与其他分布匹配相同；另一方面，KolmogorovSmirnov检验仅用于检验连续性的拟合度数据。区别不在于编程工具，而是统计概念。
示例
> x<-rnorm(20) > x输出结果
[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
具有离散分布-
示例
> y<-rpois(200,5) > y输出结果
[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
> a<-sample(0:9,100,replace=TRUE) > a输出结果
[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