Testing difference in means for two bimodal distributions?
0
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I have two bimodal distributions of data with two peaks (one around 0 and the other around 1). I have provided an example of one of the distributions.
Although their means and variances are different, they both have peaks around the same x-axis markers. How do I test for difference in means using statistically rigorous approaches? Can I still use a t-test even though the data is not normally distributed?
statistics probability-distributions normal-distribution statistical-inference hypothesis-testing
asked Dec 18 '18 at 2:05
Jane SullyJane Sully
1084
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add a comment |
0
$begingroup$
I have two bimodal distributions of data with two peaks (one around 0 and the other around 1). I have provided an example of one of the distributions.
Although their means and variances are different, they both have peaks around the same x-axis markers. How do I test for difference in means using statistically rigorous approaches? Can I still use a t-test even though the data is not normally distributed?
statistics probability-distributions normal-distribution statistical-inference hypothesis-testing
asked Dec 18 '18 at 2:05
Jane SullyJane Sully
1084
$endgroup$
$begingroup$
What exactly is your testing question? What are you trying to determine -- whether the two are the same vs. different?
$endgroup$
– Clement C.
Dec 18 '18 at 2:06
$begingroup$
Yeah. If one of the means if 0.55 and the other is 0.45, what approach do I use to determine if they are different using a statistical approach (other than visualizing, comparing means, etc.)
$endgroup$
– Jane Sully
Dec 18 '18 at 2:13
$begingroup$
I have a pointer to a paper solving this problem (namely, testing $p=q$ vs. $d(p,q)> varepsilon$ using an order-optimal number of samples, when $p,q$ are assumed to be discrete bimodal distributions), if you want. Where $d$ refers to the total variation/statistical distance. (Though I believe it actually also works for continuous ones (?) over $[0,1]$.)
$endgroup$
– Clement C.
Dec 18 '18 at 2:17
$begingroup$
ieeexplore.ieee.org/document/7354450 (free version on the authors' website or arxiv: cseweb.ucsd.edu/~dakane/closeness-structured.pdf)
$endgroup$
– Clement C.
Dec 18 '18 at 2:20
$begingroup$
Cross post : stats.stackexchange.com/q/383507/119261.
$endgroup$
– StubbornAtom
Dec 18 '18 at 6:40
add a comment |
0
0
0
$begingroup$
I have two bimodal distributions of data with two peaks (one around 0 and the other around 1). I have provided an example of one of the distributions.
Although their means and variances are different, they both have peaks around the same x-axis markers. How do I test for difference in means using statistically rigorous approaches? Can I still use a t-test even though the data is not normally distributed?
statistics probability-distributions normal-distribution statistical-inference hypothesis-testing
asked Dec 18 '18 at 2:05
Jane SullyJane Sully
1084
$endgroup$
I have two bimodal distributions of data with two peaks (one around 0 and the other around 1). I have provided an example of one of the distributions.
Although their means and variances are different, they both have peaks around the same x-axis markers. How do I test for difference in means using statistically rigorous approaches? Can I still use a t-test even though the data is not normally distributed?
statistics probability-distributions normal-distribution statistical-inference hypothesis-testing
statistics probability-distributions normal-distribution statistical-inference hypothesis-testing
asked Dec 18 '18 at 2:05
Jane SullyJane Sully
1084
asked Dec 18 '18 at 2:05
Jane SullyJane Sully
1084
asked Dec 18 '18 at 2:05
Jane SullyJane Sully
1084
asked Dec 18 '18 at 2:05
Jane SullyJane Sully
1084
asked Dec 18 '18 at 2:05
Jane SullyJane Sully
1084
1084
$begingroup$
What exactly is your testing question? What are you trying to determine -- whether the two are the same vs. different?
$endgroup$
– Clement C.
Dec 18 '18 at 2:06
$begingroup$
Yeah. If one of the means if 0.55 and the other is 0.45, what approach do I use to determine if they are different using a statistical approach (other than visualizing, comparing means, etc.)
$endgroup$
– Jane Sully
Dec 18 '18 at 2:13
$begingroup$
I have a pointer to a paper solving this problem (namely, testing $p=q$ vs. $d(p,q)> varepsilon$ using an order-optimal number of samples, when $p,q$ are assumed to be discrete bimodal distributions), if you want. Where $d$ refers to the total variation/statistical distance. (Though I believe it actually also works for continuous ones (?) over $[0,1]$.)
$endgroup$
– Clement C.
Dec 18 '18 at 2:17
$begingroup$
ieeexplore.ieee.org/document/7354450 (free version on the authors' website or arxiv: cseweb.ucsd.edu/~dakane/closeness-structured.pdf)
$endgroup$
– Clement C.
Dec 18 '18 at 2:20
$begingroup$
Cross post : stats.stackexchange.com/q/383507/119261.
$endgroup$
– StubbornAtom
Dec 18 '18 at 6:40
add a comment |
$begingroup$
What exactly is your testing question? What are you trying to determine -- whether the two are the same vs. different?
$endgroup$
– Clement C.
Dec 18 '18 at 2:06
$begingroup$
Yeah. If one of the means if 0.55 and the other is 0.45, what approach do I use to determine if they are different using a statistical approach (other than visualizing, comparing means, etc.)
$endgroup$
– Jane Sully
Dec 18 '18 at 2:13
$begingroup$
I have a pointer to a paper solving this problem (namely, testing $p=q$ vs. $d(p,q)> varepsilon$ using an order-optimal number of samples, when $p,q$ are assumed to be discrete bimodal distributions), if you want. Where $d$ refers to the total variation/statistical distance. (Though I believe it actually also works for continuous ones (?) over $[0,1]$.)
$endgroup$
– Clement C.
Dec 18 '18 at 2:17
$begingroup$
ieeexplore.ieee.org/document/7354450 (free version on the authors' website or arxiv: cseweb.ucsd.edu/~dakane/closeness-structured.pdf)
$endgroup$
– Clement C.
Dec 18 '18 at 2:20
$begingroup$
Cross post : stats.stackexchange.com/q/383507/119261.
$endgroup$
– StubbornAtom
Dec 18 '18 at 6:40
$begingroup$
What exactly is your testing question? What are you trying to determine -- whether the two are the same vs. different?
$endgroup$
– Clement C.
Dec 18 '18 at 2:06
$begingroup$
What exactly is your testing question? What are you trying to determine -- whether the two are the same vs. different?
$endgroup$
– Clement C.
Dec 18 '18 at 2:06
$begingroup$
Yeah. If one of the means if 0.55 and the other is 0.45, what approach do I use to determine if they are different using a statistical approach (other than visualizing, comparing means, etc.)
$endgroup$
– Jane Sully
Dec 18 '18 at 2:13
$begingroup$
Yeah. If one of the means if 0.55 and the other is 0.45, what approach do I use to determine if they are different using a statistical approach (other than visualizing, comparing means, etc.)
$endgroup$
– Jane Sully
Dec 18 '18 at 2:13
$begingroup$
I have a pointer to a paper solving this problem (namely, testing $p=q$ vs. $d(p,q)> varepsilon$ using an order-optimal number of samples, when $p,q$ are assumed to be discrete bimodal distributions), if you want. Where $d$ refers to the total variation/statistical distance. (Though I believe it actually also works for continuous ones (?) over $[0,1]$.)
$endgroup$
– Clement C.
Dec 18 '18 at 2:17
$begingroup$
I have a pointer to a paper solving this problem (namely, testing $p=q$ vs. $d(p,q)> varepsilon$ using an order-optimal number of samples, when $p,q$ are assumed to be discrete bimodal distributions), if you want. Where $d$ refers to the total variation/statistical distance. (Though I believe it actually also works for continuous ones (?) over $[0,1]$.)
$endgroup$
– Clement C.
Dec 18 '18 at 2:17
$begingroup$
ieeexplore.ieee.org/document/7354450 (free version on the authors' website or arxiv: cseweb.ucsd.edu/~dakane/closeness-structured.pdf)
$endgroup$
– Clement C.
Dec 18 '18 at 2:20
$begingroup$
ieeexplore.ieee.org/document/7354450 (free version on the authors' website or arxiv: cseweb.ucsd.edu/~dakane/closeness-structured.pdf)
$endgroup$
– Clement C.
Dec 18 '18 at 2:20
$begingroup$
Cross post : stats.stackexchange.com/q/383507/119261.
$endgroup$
– StubbornAtom
Dec 18 '18 at 6:40
$begingroup$
Cross post : stats.stackexchange.com/q/383507/119261.
$endgroup$
– StubbornAtom
Dec 18 '18 at 6:40
add a comment |
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$begingroup$
What exactly is your testing question? What are you trying to determine -- whether the two are the same vs. different?
$endgroup$
– Clement C.
Dec 18 '18 at 2:06
$begingroup$
Yeah. If one of the means if 0.55 and the other is 0.45, what approach do I use to determine if they are different using a statistical approach (other than visualizing, comparing means, etc.)
$endgroup$
– Jane Sully
Dec 18 '18 at 2:13
$begingroup$
I have a pointer to a paper solving this problem (namely, testing $p=q$ vs. $d(p,q)> varepsilon$ using an order-optimal number of samples, when $p,q$ are assumed to be discrete bimodal distributions), if you want. Where $d$ refers to the total variation/statistical distance. (Though I believe it actually also works for continuous ones (?) over $[0,1]$.)
$endgroup$
– Clement C.
Dec 18 '18 at 2:17
$begingroup$
ieeexplore.ieee.org/document/7354450 (free version on the authors' website or arxiv: cseweb.ucsd.edu/~dakane/closeness-structured.pdf)
$endgroup$
– Clement C.
Dec 18 '18 at 2:20
$begingroup$
Cross post : stats.stackexchange.com/q/383507/119261.
$endgroup$
– StubbornAtom
Dec 18 '18 at 6:40