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Science Forum Index » Statistics - Math Forum » Two-Sample Chi-Squared test?
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| Yaroslav Bulatov |
 Posted: Thu Apr 24, 2008 10:24 pm |
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Guest
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Is there an analogue of two-sample t-test for categorical data? In
other words, I'm given a sample of a multinomial random variable X and
of a multinomial random variable Y and want to test if X and Y are the
same |
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| Bruce Weaver |
| Posted: Fri Apr 25, 2008 6:22 am |
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Yaroslav Bulatov wrote:
Quote: Is there an analogue of two-sample t-test for categorical data? In
other words, I'm given a sample of a multinomial random variable X and
of a multinomial random variable Y and want to test if X and Y are the
same
Look up chi-square test of association (aka test of independence).
The null hypothesis states that there is no association between
X and Y.
--
Bruce Weaver
bweaver@lakeheadu.ca
www.angelfire.com/wv/bwhomedir
"When all else fails, RTFM." |
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| Yaroslav Bulatov |
| Posted: Fri Apr 25, 2008 6:32 am |
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On Apr 25, 8:26 am, Paul Rubin <ru...@msu.edu> wrote:
Quote: Yaroslav Bulatov wrote:
Is there an analogue of two-sample t-test for categorical data? In
other words, I'm given a sample of a multinomial random variable X and
of a multinomial random variable Y and want to test if X and Y are the
same
Try the two sample Kolmogorov-Smirnov test:http://en.wikipedia.org/wiki/Kolmogorov-Smirnov.
/Paul
Kolmogorov Smirnoff seems to require an ordering on the sample space
of the random variable, whereas chi-squared test of association needs
paired samples, so neither seems to fit |
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| Jack Tomsky |
| Posted: Fri Apr 25, 2008 10:24 am |
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Quote: On Apr 25, 8:26 am, Paul Rubin <ru...@msu.edu> wrote:
Yaroslav Bulatov wrote:
Is there an analogue of two-sample t-test for
categorical data? In
other words, I'm given a sample of a multinomial
random variable X and
of a multinomial random variable Y and want to
test if X and Y are the
same
Try the two sample Kolmogorov-Smirnov
test:http://en.wikipedia.org/wiki/Kolmogorov-Smirnov.
/Paul
Kolmogorov Smirnoff seems to require an ordering on
the sample space
of the random variable, whereas chi-squared test of
association needs
paired samples, so neither seems to fit
Incidentally, the chi-square goodness of fit test can be inverted (analogous to the inversion of the Scheffe and Tukey ANOVA tests) to obtain multiple comparisons in the form of simultaneous confidence intervals on linear combinations of the p1i - p2i. You can find the details in Tomsky (1994), “Simultaneous confidence bounds for binary experiments”, 1994 SIAM Conference on Discrete Mathematics.
Jack |
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| Paul Rubin |
| Posted: Fri Apr 25, 2008 10:26 am |
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Guest
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Yaroslav Bulatov wrote:
Quote: Is there an analogue of two-sample t-test for categorical data? In
other words, I'm given a sample of a multinomial random variable X and
of a multinomial random variable Y and want to test if X and Y are the
same
Try the two sample Kolmogorov-Smirnov test:
http://en.wikipedia.org/wiki/Kolmogorov-Smirnov.
/Paul |
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| Richard Ulrich |
| Posted: Fri Apr 25, 2008 10:52 pm |
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On Fri, 25 Apr 2008 09:32:12 -0700 (PDT), Yaroslav Bulatov
<yaroslavvb@gmail.com> wrote:
Quote: On Apr 25, 8:26 am, Paul Rubin <ru...@msu.edu> wrote:
Yaroslav Bulatov wrote:
Is there an analogue of two-sample t-test for categorical data? In
other words, I'm given a sample of a multinomial random variable X and
of a multinomial random variable Y and want to test if X and Y are the
same
Try the two sample Kolmogorov-Smirnov test:http://en.wikipedia.org/wiki/Kolmogorov-Smirnov.
/Paul
Kolmogorov Smirnoff seems to require an ordering on the sample space
of the random variable, whereas chi-squared test of association needs
paired samples, so neither seems to fit
So, what you want is a good test to compare
counts of apples and oranges and watermelons
versus counts of dogs and cats?
What field do you work in?
--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html |
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| Yaroslav Bulatov |
| Posted: Wed Apr 30, 2008 11:25 am |
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On Apr 25, 8:52 pm, Richard Ulrich <Rich.Ulr...@comcast.net> wrote:
Quote: On Fri, 25 Apr 2008 09:32:12 -0700 (PDT), Yaroslav Bulatov
yarosla...@gmail.com> wrote:
On Apr 25, 8:26 am, Paul Rubin <ru...@msu.edu> wrote:
Yaroslav Bulatov wrote:
Is there an analogue of two-sample t-test for categorical data? In
other words, I'm given a sample of a multinomial random variable X and
of a multinomial random variable Y and want to test if X and Y are the
same
Try the two sample Kolmogorov-Smirnov test:http://en.wikipedia.org/wiki/Kolmogorov-Smirnov.
/Paul
Kolmogorov Smirnoff seems to require an ordering on the sample space
of the random variable, whereas chi-squared test of association needs
paired samples, so neither seems to fit
So, what you want is a good test to compare
counts of apples and oranges and watermelons
versus counts of dogs and cats?
What field do you work in?
--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html
I'm comparing apples with apples, however the measurements are not
paired. Basically I'm asking about the distribution of chi-squared
statistic where instead of expected frequencies I substitute estimates
based on finite sample from the population |
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| Richard Ulrich |
| Posted: Wed Apr 30, 2008 10:10 pm |
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On Wed, 30 Apr 2008 14:25:51 -0700 (PDT), Yaroslav Bulatov
<yaroslavvb@gmail.com> wrote:
Quote: On Apr 25, 8:52 pm, Richard Ulrich <Rich.Ulr...@comcast.net> wrote:
On Fri, 25 Apr 2008 09:32:12 -0700 (PDT), Yaroslav Bulatov
yarosla...@gmail.com> wrote:
On Apr 25, 8:26 am, Paul Rubin <ru...@msu.edu> wrote:
Yaroslav Bulatov wrote:
Is there an analogue of two-sample t-test for categorical data? In
other words, I'm given a sample of a multinomial random variable X and
of a multinomial random variable Y and want to test if X and Y are the
same
Try the two sample Kolmogorov-Smirnov test:http://en.wikipedia.org/wiki/Kolmogorov-Smirnov.
/Paul
Kolmogorov Smirnoff seems to require an ordering on the sample space
of the random variable, whereas chi-squared test of association needs
paired samples, so neither seems to fit
So, what you want is a good test to compare
counts of apples and oranges and watermelons
versus counts of dogs and cats?
What field do you work in?
--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html
I'm comparing apples with apples, however the measurements are not
paired.
Paired? Counts in contingency tables might be said to have
two coordinates; one of them is often the sample or group
identifier, and the other is the thing being counted. We don't
call that "paired".
Quote: Basically I'm asking about the distribution of chi-squared
statistic where instead of expected frequencies I substitute estimates
based on finite sample from the population
That sounds straight-forward. An ordinary contingency table.
That doesn't sound like what you said before.
Want to try again? I would help if you were more concrete,
since being abstract has failed.
--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html |
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| David Winsemius |
| Posted: Thu May 01, 2008 9:20 am |
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Yaroslav Bulatov <yaroslavvb@gmail.com> wrote in
news:4efaff93-f47b-4bfe-b877-b5f16e1607b6@c19g2000prf.googlegroups.com:
Quote: On Apr 25, 8:26 am, Paul Rubin <ru...@msu.edu> wrote:
Yaroslav Bulatov wrote:
Is there an analogue of two-sample t-test for categorical data?
In other words, I'm given a sample of a multinomial random
variable X and of a multinomial random variable Y and want to
test if X and Y are the same
Try the two sample Kolmogorov-Smirnov
test:http://en.wikipedia.org/wiki/Kolmogorov-Smirnov.
/Paul
Kolmogorov Smirnoff seems to require an ordering on the sample space
of the random variable, whereas chi-squared test of association
needs paired samples, so neither seems to fit
I am trying to figure out why you think the chi-square test of
association needs paired samples. It doesn't.
--
David Winsemius |
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