I know this must be a wrong method, but I cannot help to ask: Can I only use the p-value from KS test, saying if p-value is greater than \beta, then two samples are from the same distribution. If the definition of p-value is the probability that the null hypothesis is true, then why there's little people uses p-value as a "true" probability. e.g. normally, people will not multiply or add p-values to get the probability that two independent null hypothesis are both true or one of them is true. I had this question for very long time.
-Monnand On Tue Jan 13 2015 at 2:47:30 PM Andrews, Chris <chri...@med.umich.edu> wrote: > This sounds more like quality control than hypothesis testing. Rather > than statistical significance, you want to determine what is an acceptable > difference (an 'equivalence margin', if you will). And that is a question > about the application, not a statistical one. > ________________________________________ > From: Monnand [monn...@gmail.com] > Sent: Monday, January 12, 2015 10:14 PM > To: Andrews, Chris > Cc: r-help@r-project.org > Subject: Re: [R] two-sample KS test: data becomes significantly different > after normalization > > Thank you, Chris! > > I think it is exactly the problem you mentioned. I did consider > 1000-point data is a large one at first. > > I down-sampled the data from 1000 points to 100 points and ran KS test > again. It worked as expected. Is there any typical method to compare > two large samples? I also tried KL diverge, but it only gives me some > number but does not tell me how large the distance is should be > considered as significantly different. > > Regards, > -Monnand > > On Mon, Jan 12, 2015 at 9:32 AM, Andrews, Chris <chri...@med.umich.edu> > wrote: > > > > The main issue is that the original distributions are the same, you > shift the two samples *by different amounts* (about 0.01 SD), and you have > a large (n=1000) sample size. Thus the new distributions are not the same. > > > > This is a problem with testing for equality of distributions. With > large samples, even a small deviation is significant. > > > > Chris > > > > -----Original Message----- > > From: Monnand [mailto:monn...@gmail.com] > > Sent: Sunday, January 11, 2015 10:13 PM > > To: r-help@r-project.org > > Subject: [R] two-sample KS test: data becomes significantly different > after normalization > > > > Hi all, > > > > This question is sort of related to R (I'm not sure if I used an R > function > > correctly), but also related to stats in general. I'm sorry if this is > > considered as off-topic. > > > > I'm currently working on a data set with two sets of samples. The csv > file > > of the data could be found here: http://pastebin.com/200v10py > > > > I would like to use KS test to see if these two sets of samples are from > > different distributions. > > > > I ran the following R script: > > > > # read data from the file > >> data = read.csv('data.csv') > >> ks.test(data[[1]], data[[2]]) > > Two-sample Kolmogorov-Smirnov test > > > > data: data[[1]] and data[[2]] > > D = 0.025, p-value = 0.9132 > > alternative hypothesis: two-sided > > The KS test shows that these two samples are very similar. (In fact, they > > should come from same distribution.) > > > > However, due to some reasons, instead of the raw values, the actual data > > that I will get will be normalized (zero mean, unit variance). So I tried > > to normalize the raw data I have and run the KS test again: > > > >> ks.test(scale(data[[1]]), scale(data[[2]])) > > Two-sample Kolmogorov-Smirnov test > > > > data: scale(data[[1]]) and scale(data[[2]]) > > D = 0.3273, p-value < 2.2e-16 > > alternative hypothesis: two-sided > > The p-value becomes almost zero after normalization indicating these two > > samples are significantly different (from different distributions). > > > > My question is: How the normalization could make two similar samples > > becomes different from each other? I can see that if two samples are > > different, then normalization could make them similar. However, if two > sets > > of data are similar, then intuitively, applying same operation onto them > > should make them still similar, at least not different from each other > too > > much. > > > > I did some further analysis about the data. I also tried to normalize the > > data into [0,1] range (using the formula (x-min(x))/(max(x)-min(x))), but > > same thing happened. At first, I thought it might be outliers caused this > > problem (I can see that an outlier may cause this problem if I normalize > > the data into [0,1] range.) I deleted all data whose abs value is larger > > than 4 standard deviation. But it still didn't help. > > > > Plus, I even plotted the eCDFs, they *really* look the same to me even > > after normalization. Anything wrong with my usage of the R function? > > > > Since the data contains ties, I also tried ks.boot ( > > http://sekhon.berkeley.edu/matching/ks.boot.html ), but I got the same > > result. > > > > Could anyone help me to explain why it happened? Also, any suggestion > about > > the hypothesis testing on normalized data? (The data I have right now is > > simulated data. In real world, I cannot get raw data, but only normalized > > one.) > > > > Regards, > > -Monnand > > > > [[alternative HTML version deleted]] > > > > > > ********************************************************** > > Electronic Mail is not secure, may not be read every day, and should not > be used for urgent or sensitive issues > ********************************************************** > Electronic Mail is not secure, may not be read every day, and should not > be used for urgent or sensitive issues > > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
