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统计学中的t检验和方差分析等方法的应用条件是样本都来自正态总体或近似正态总体,只有符合这个条件,才能用这些方法来检验各样本所属的总体参数的差异显著性。文本向大家介绍在R语言中检验正态性的几种方法:
1、Kolmogorov-Smirnov检验
K-S检验检验单一样本是否来自某一特定分布。比如检验一组数据是否为正态分布。它的检验方法是以样本数据的累积频数分布与特定理论分布比较,若两者间的差距很小,则推论该样本取自某特定分布族。K-S检验的原假设和备择假设为:
H0:样本所来自的总体分布服从某特定分布
H1:样本所来自的总体分布不服从某特定分布
如果要检验数据是否满足正态分布,只需要将这个特定分布设定为“正态分布”即可。用R语言进行K-S检验的代码如下:
set.seed(10);x <- rnorm(100000) ks.test(x,"pnorm")
## One-sample Kolmogorov-Smirnov test ## ## data: x ## D = 0.003649, p-value
= 0.1394 ## alternative hypothesis: two-sided
根据结果p-value > 0.05 ,接受原假设,即认为数据满足正态分布。
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大样本、已知总体均数和标准差,选择非参数检验-单样本KS检验号。
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单样本K-S检验要求检验分布是连续的,而连续分布出现相同值的概率为0.如果是出现相同的,