Hello again. I have tied this before but I see two problems:
1) According to the documentation I could read (including the ks.test code), the ks statistic would be max(abs(x - y)) and if you plot this for very low sample sizes you can actually see that this make sense. The results of ks.test(x, y) yields very different values. 2) Also in this case the p-values don’t make much sense, according to my previous interpretation. Again, I could be wrong in my interpretation. On 5 Sep 2019, at 20:46, Rui Barradas <ruipbarra...@sapo.pt<mailto:ruipbarra...@sapo.pt>> wrote: Hello, I'm sorry, but apparently I missed the point of your problem. Please do not take my previous answer seriously. But you can use ks.test, just in a different way than what I wrote previously. Corrected code: #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$p_1 #weighted ecdf for the reference distribution and the sample f_d_1 <- ewcdf(d_1, normalise=F) f_d_2 <- ewcdf(d_2, 1/p_2, normalise=F, adjust=1/length(d_2)) #kolmogorov-smirnov distance x <- f_d_1(d_2) y <- f_d_2(d_2) ht <- ks.test(x, y) d_stat[i, 2] <- ht$statistic d_stat[i, 3] <- ht$p.value } Hope this helps, Rui Barradas Às 19:29 de 05/09/19, Rui Barradas escreveu: Hello, I don't have the algorithms at hand but the KS statistic calculation is more complicated than your max/abs difference. Anyway, why not use ks.test? it's not that difficult: set.seed(1234) #reference distribution d_1 <- sort(rpois(1000, 500)) p_1 <- d_1/sum(d_1) m_1 <- data.frame(d_1, p_1) #data frame to store the values of the simulation d_stat <- data.frame(1:1000, NA, NA) names(d_stat) <- c("sample_size", "ks_distance", "p_value") #simulation for (i in 1:1000) { #sample from the reference distribution m_2 <-m_1[(sample(nrow(m_1), size=i, prob=p_1, replace=F)),] d_2 <- m_2$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))) } [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org<mailto:R-help@r-project.org> mailing list -- To UNSUBSCRIBE and more, see https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstat.ethz.ch%2Fmailman%2Flistinfo%2Fr-help&data=01%7C01%7Cgianluca.boo%40soton.ac.uk%7C4b4a253a1edc4960297f08d732316627%7C4a5378f929f44d3ebe89669d03ada9d8%7C0&sdata=ZntDJlPtp%2Bu%2FeO7xNZLbUQgLwpvS1M%2FUVNwovp%2FZPmA%3D&reserved=0 PLEASE do read the posting guide https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.R-project.org%2Fposting-guide.html&data=01%7C01%7Cgianluca.boo%40soton.ac.uk%7C4b4a253a1edc4960297f08d732316627%7C4a5378f929f44d3ebe89669d03ada9d8%7C0&sdata=YKZNBeGme6V9QGyV2%2F150H6rZnLy9bX7xly%2BQEf6O14%3D&reserved=0 and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org<mailto:R-help@r-project.org> mailing list -- To UNSUBSCRIBE and more, see https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstat.ethz.ch%2Fmailman%2Flistinfo%2Fr-help&data=01%7C01%7Cgianluca.boo%40soton.ac.uk%7C4b4a253a1edc4960297f08d732316627%7C4a5378f929f44d3ebe89669d03ada9d8%7C0&sdata=ZntDJlPtp%2Bu%2FeO7xNZLbUQgLwpvS1M%2FUVNwovp%2FZPmA%3D&reserved=0 PLEASE do read the posting guide https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.R-project.org%2Fposting-guide.html&data=01%7C01%7Cgianluca.boo%40soton.ac.uk%7C4b4a253a1edc4960297f08d732316627%7C4a5378f929f44d3ebe89669d03ada9d8%7C0&sdata=YKZNBeGme6V9QGyV2%2F150H6rZnLy9bX7xly%2BQEf6O14%3D&reserved=0 and provide commented, minimal, self-contained, reproducible code. 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