Statistical testing for uniform distribution
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Given are $N$ categories and $x_i$ occurrences of events within these categories, where $i = 1dots N$. The null hypthesis is that there is a uniform distribution, i.e. each category should contain roughly the same number of events. What is the correct statistical test to determine if the null hypothesis is acceptable for a given p-value?
I've tried to use the Chi-Square test for this, but for the number of categories (in my case 256) it seems to be quite unstable. As an example, when I generate 10 million truly random samples and ran 100 trials, I got Chi-Square values from 228 to 310. Using 255 degrees of freedom, I looked up that out of these 100 trials only 2 indicated that that there is statistical significance (i.e., Chi-Square values 295 and 310, p = 0.05). My interpretation is that 98 of these truly random samples are indicated to be not truly random, when they are indeed.
statistics uniform-distribution hypothesis-testing
asked Nov 13 at 16:29
itecMemory
11
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Given are $N$ categories and $x_i$ occurrences of events within these categories, where $i = 1dots N$. The null hypthesis is that there is a uniform distribution, i.e. each category should contain roughly the same number of events. What is the correct statistical test to determine if the null hypothesis is acceptable for a given p-value?
I've tried to use the Chi-Square test for this, but for the number of categories (in my case 256) it seems to be quite unstable. As an example, when I generate 10 million truly random samples and ran 100 trials, I got Chi-Square values from 228 to 310. Using 255 degrees of freedom, I looked up that out of these 100 trials only 2 indicated that that there is statistical significance (i.e., Chi-Square values 295 and 310, p = 0.05). My interpretation is that 98 of these truly random samples are indicated to be not truly random, when they are indeed.
statistics uniform-distribution hypothesis-testing
asked Nov 13 at 16:29
itecMemory
11
See wikipedia for a starter. Please include your own effort and the specific difficulties you faced, otherwise the post is likely to be closed.
– Lee David Chung Lin
Nov 14 at 1:50
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Given are $N$ categories and $x_i$ occurrences of events within these categories, where $i = 1dots N$. The null hypthesis is that there is a uniform distribution, i.e. each category should contain roughly the same number of events. What is the correct statistical test to determine if the null hypothesis is acceptable for a given p-value?
I've tried to use the Chi-Square test for this, but for the number of categories (in my case 256) it seems to be quite unstable. As an example, when I generate 10 million truly random samples and ran 100 trials, I got Chi-Square values from 228 to 310. Using 255 degrees of freedom, I looked up that out of these 100 trials only 2 indicated that that there is statistical significance (i.e., Chi-Square values 295 and 310, p = 0.05). My interpretation is that 98 of these truly random samples are indicated to be not truly random, when they are indeed.
statistics uniform-distribution hypothesis-testing
asked Nov 13 at 16:29
itecMemory
11
Given are $N$ categories and $x_i$ occurrences of events within these categories, where $i = 1dots N$. The null hypthesis is that there is a uniform distribution, i.e. each category should contain roughly the same number of events. What is the correct statistical test to determine if the null hypothesis is acceptable for a given p-value?
I've tried to use the Chi-Square test for this, but for the number of categories (in my case 256) it seems to be quite unstable. As an example, when I generate 10 million truly random samples and ran 100 trials, I got Chi-Square values from 228 to 310. Using 255 degrees of freedom, I looked up that out of these 100 trials only 2 indicated that that there is statistical significance (i.e., Chi-Square values 295 and 310, p = 0.05). My interpretation is that 98 of these truly random samples are indicated to be not truly random, when they are indeed.
statistics uniform-distribution hypothesis-testing
statistics uniform-distribution hypothesis-testing
asked Nov 13 at 16:29
itecMemory
11
asked Nov 13 at 16:29
itecMemory
11
edited Nov 15 at 9:11
asked Nov 13 at 16:29
itecMemory
11
asked Nov 13 at 16:29
itecMemory
11
asked Nov 13 at 16:29
itecMemory
11
11
See wikipedia for a starter. Please include your own effort and the specific difficulties you faced, otherwise the post is likely to be closed.
– Lee David Chung Lin
Nov 14 at 1:50
add a comment |
See wikipedia for a starter. Please include your own effort and the specific difficulties you faced, otherwise the post is likely to be closed.
– Lee David Chung Lin
Nov 14 at 1:50
See wikipedia for a starter. Please include your own effort and the specific difficulties you faced, otherwise the post is likely to be closed.
– Lee David Chung Lin
Nov 14 at 1:50
See wikipedia for a starter. Please include your own effort and the specific difficulties you faced, otherwise the post is likely to be closed.
– Lee David Chung Lin
Nov 14 at 1:50
add a comment |
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See wikipedia for a starter. Please include your own effort and the specific difficulties you faced, otherwise the post is likely to be closed.
– Lee David Chung Lin
Nov 14 at 1:50