柯尔莫可洛夫-斯⽶洛夫检验（Kolmogorov–Smirnovtest，K-Stest）
柯尔莫哥洛夫-斯⽶尔诺夫检验（Колмогоров-Смирнов检验）基于累计分布函数，⽤以检验两个经验分布是否不同或⼀个经验分布与另⼀个理想分布是否不同。
在进⾏cumulative probability统计(如下图)的时候，你怎么知道组之间是否有显著性差异？有⼈⾸先想到单因素⽅差分析或双尾检验（2 tailed TEST）。其实这些是不准确的，最好采⽤Kolmogorov-Smirnov test（柯尔莫诺夫-斯⽶尔诺夫检验）来分析变量是否符合某种分布或⽐较两组之间有⽆显著性差异。
Kolmogorov-Smirnov test原理：寻最⼤距离（Distance），所以常简称为D法。适⽤于⼤样本。 KS test checks if two independent distributions are similar or different, by generating cumulative probability plots for two distributions and finding the distance along the y-axis for a given x values between the two curves. From all the distances calculated for each x value, the maximum distance is searched.
如何分析结果呢？This maximum distance or maximum difference is then plugged into KS probability function to calculate the probability value.  The lower the probability value is the less likely the two distributions are similar.  Conversely, the higher or more close to 1 the value is the more similar the two distributions are.极端情况：如果P值为１的话，说明两给数据基本相同，如果P值⽆限接近０，说明两组数据差异性极⼤。
有⼀个⽹站可以进⾏在线的统计，你只需要输⼊数据就可以了。地址如下：
当然还有更多的软件⽀持这个统计，如SPSS,SAS,MiniAnalysis,Clampfit10
根据软件统计出来后给出的结果决定有没有显著性差异，如果D max值>D 0.05。则认为有显著性差异。D 0.05的经验算法：1.36/SQRT(N) 其中SQRT为平⽅要，N为样本数。D 0.0１经验算法1.64/SQRT(N) 。当然最准确的办法还是去查KS检定表。不过⼤多数软件如CLAMPFIT,MINIANALYSIS统计出来的结果都是直接有P值。根据这个值（alpha=0.05）就可以断定有没有差异了。
在统计学中，柯尔莫可洛夫-斯⽶洛夫检验基于累计分布函数，⽤以检验两个经验分布是否不同或⼀个经验分布与另⼀个理想分布是否不同。
在进⾏累计概率（cumulative probability）统计的时候，你怎么知道组之间是否有显著性差异？有⼈⾸先想到单因素⽅差分析或双尾检验（2 tailedTEST）。其实这些是不准确的，最好采⽤Kolmogorov-Smirnov test（柯尔莫诺夫-斯⽶尔诺夫检验）来分析变量是否符合某种分布或⽐较两组之间有⽆显著性差异。
分类：
1、Single sample Kolmogorov-Smirnov goodness-of-fit hypothesis test.
采⽤柯尔莫诺夫-斯⽶尔诺夫检验来分析变量是否符合某种分布，可以检验的分布有正态分布、均匀分布、Poission分布和指数分布。指令如下：
>> H = KSTEST(X,CDF,ALPHA,TAIL) % X为待检测样本，CDF可选：如果空缺，则默认为检测标准正态分布；
如果填写两列的矩阵，第⼀列是x的可能的值，第⼆列是相应的假设累计概率分布函数的值G(x)。ALPHA是显著性⽔平（默认0.05）。TAIL是表⽰检验的类型（默认unequal，不平衡）。还有larger，s
maller可以选择。
如果，H=1 则否定⽆效假设； H=0，不否定⽆效假设（在alpha⽔平上）
例如，
x = -2:1:4
x =
-2  -1  0  1  2  3  4
[h,p,k,c] = kstest(x,[],0.05,0)
h =
p =
( ) 0.13632
k =
0.41277
c =
0.48342
The test fails to reject the null hypothesis that the values come from a standard normal distribution.
2、Two-sample Kolmogorov-Smirnov test
检验两个数据向量之间的分布的。
>>[h,p,ks2stat] = kstest2(x1,x2,alpha,tail)
% x1,x2都为向量，ALPHA是显著性⽔平（默认0.05）。TAIL是表⽰检验的类型（默认unequal，不平衡）。
例如，x = -1:1:5
y = randn(20,1);
[h,p,k] = kstest2(x,y)
h =
p =
0.0774
k =
0.5214
wiki翻译起来太⿇烦，还有可能曲解本意，最好看原版解释。
In , the – test (K–S test) is a form of  used as a  of equality of one-dimensional  used to compare a  with a reference probability distribution (one-sample K–S test), or to compare two samples (two-sample K–S test). The Kolmogorov–Smirnov statistic quantifies a  between the of the sample and the  of the reference distribution, or between the empirical distribution functions of two samples. The  of this statistic is calculated under the null hypothesis that the samples are drawn from the same distribution (in the two-sample case) or that the sample is drawn from the reference distribution (in the one-sample case). In each case, the distributions considered under the null hypothesis are continuous distributions but are otherwise unrestricted.
The two-sample KS test is one of the most useful and general nonparametric methods for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples.
The Kolmogorov–Smirnov test can be modified to serve as a  test. In the special case of testing for  of the distribution, samples are standardized and compared with a standard normal distribution. This is equivalent to setting the mean and variance of the reference distribution equal to the sample estimates, and it is known that using the sample to modify the null hypothesis reduces the  of a test. Correcting for this bias leads to the. However, even Lilliefors' modification is less powerful than the  or  for testing normality.

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