Re: [R] two-sample KS test: data becomes significantly different after normalization
Thank you, Chris and Martin!
On Wed Jan 14 2015 at 7:31:12 AM Andrews, Chris chri...@med.umich.edu
wrote:
Your definition of p-value is not correct. See, for example,
http://en.wikipedia.org/wiki/P-value#Misunderstandings
-Original Message-
From: Monnand [mailto:monn...@gmail.com]
Sent: Wednesday, January 14, 2015 2:17 AM
To: Andrews, Chris
Cc: r-help@r-project.org
Subject: Re: [R] two-sample KS test: data becomes significantly different
after normalization
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
Re: [R] two-sample KS test: data becomes significantly different after normalization
Monnand monn...@gmail.com
on Wed, 14 Jan 2015 07:17:02 + writes:
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,
Ouch, ouch, ouch, ouch
The worst misuse/misunderstanding of statistics now even on R-help ...
--- please get help from a statistician !!
-- and erase that sentence from your mind (unless you are pro
and want to keep it for anectdotal or didactical purposes...)
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
Re: [R] two-sample KS test: data becomes significantly different after normalization
Your definition of p-value is not correct. See, for example,
http://en.wikipedia.org/wiki/P-value#Misunderstandings
-Original Message-
From: Monnand [mailto:monn...@gmail.com]
Sent: Wednesday, January 14, 2015 2:17 AM
To: Andrews, Chris
Cc: r-help@r-project.org
Subject: Re: [R] two-sample KS test: data becomes significantly different after
normalization
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
Re: [R] two-sample KS test: data becomes significantly different after normalization
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
Re: [R] two-sample KS test: data becomes significantly different after normalization
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
__
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
Re: [R] two-sample KS test: data becomes significantly different after normalization
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
__
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.
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
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[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]]
__
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.
