[R] P-values Kolmogorov–Smirnov test

[Rui Barradas]

Hello,

I don't have the algorithms at hand but the KS statistic calculation is 
more complicated than your max/abs difference.

Anyway, why not use ks.test? it's not that difficult:


set.seed(1234)
#reference distribution
d_1 <- sort(rpois(1000, 500))
p_1 <- d_1/sum(d_1)
m_1 <- data.frame(d_1, p_1)

#data frame to store the values of the simulation
d_stat <- data.frame(1:1000, NA, NA)
names(d_stat) <- c("sample_size", "ks_distance", "p_value")

#simulation
for (i in 1:1000) {
   #sample from the reference distribution
   m_2 <-m_1[(sample(nrow(m_1), size=i, prob=p_1, replace=F)),]
   d_2 <- m_2$d_1

   ht <- ks.test(d_1, d_2)
   #kolmogorov-smirnov distance
   d_stat[i, 2] <- ht$statistic
   d_stat[i, 3] <- ht$p.value
}

hist(d_stat[, 2])
hist(d_stat[, 3])


Note that d_2 is not sorted, but the results are equal in the sense of 
function identical(), meaning they are *exactly* the same. Why shouldn't 
they?

Hope this helps,

Rui Barradas


Às 17:06 de 05/09/19, Boo G. escreveu:
> Hello,
> 
> I am trying to perform a Kolmogorov–Smirnov test to assess the difference between a distribution and samples drawn proportionally to size of different sizes. I managed to compute the Kolmogorov–Smirnov distance but I am lost with the p-value. I have looked into the ks.test function unsuccessfully. Can anyone help me with computing p-values for a two-tailed test?
> 
> Below a simplified version of my code.
> 
> Thanks in advance.
> Gianluca
> 
> 
> library(spatstat)
> 
> #reference distribution
> d_1 <- sort(rpois(1000, 500))
> p_1 <- d_1/sum(d_1)
> m_1 <- data.frame(d_1, p_1)
> 
> #data frame to store the values of the siumation
> d_stat <- data.frame(1:1000, NA, NA)
> names(d_stat) <- c("sample_size", "ks_distance", "p_value")
> 
> #simulation
> for (i in 1:1000) {
>    #sample from the reference distribution
>    m_2 <-m_1[(sample(nrow(m_1), size=i, prob=p_1, replace=F)),]
>    m_2 <-m_2[order(m_2$d_1),]
>    d_2 <- m_2$d_1
>    p_2 <- m_2$p_1
> 
>    #weighted ecdf for the reference distribution and the sample
>    f_d_1 <- ewcdf(d_1, normalise=F)
>    f_d_2 <- ewcdf(d_2, 1/p_2, normalise=F, adjust=1/length(d_2))
> 
>    #kolmogorov-smirnov distance
>    d_stat[i,2] <- max(abs(f_d_1(d_2) - f_d_2(d_2)))
> }
> 
> 
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