I am doing computer simulation of a certain random process. During the simultaion I have eight counters arranged symmetrically on a circle. I suspect that counters 1,3,5,7 count significantly less than counters 2,4,6,8.

For instance in one such simulation I got counts

2083149, 2082863, 2082617, 2082678

for odd counters and

2083562, 2084692, 2086878, 2085004

for even counters. Statistics is not my area, so I went to the book "Introction to Probability and Statistics" by Mendenhall (5th edition), follow the method "inference from low counts", calculated "t" with the result t=-3.1596. As I understand itmay be considered significant.

But then I have made another simulation, with a different random seed, calculated "t" with these other numbers, and got t = -0.454533. Another simulation, with a different number of total events gives yet another t.

This suggests that I am probably used not the right method for this particular hypothesis test.

I would appreciate a hint: what kind of a statistical test should I apply to this kind of a problem if I want to get a reliable answer?

P.S. After some thinking and some more reading it occurs to me that I should make my hypothesis stronger: that each of the even counters registers more counts than any of the odd counters. Will have to experiment whether this makes the whole check more stable.

P.S.2 Following the idea of PS1 I have changed the parameters of the generating process which has made the difference more distinct. For the 16 differences between even and odd I got:

6143, 4605, 7243, 7745, 4408, 2870, 5508, 6010, 1935, 397, 3035, 3537, 799, -739, 1899, 2401

If I am not mistaken, the calculated t value is 23.2215 which should be enough for rejecting the hypothesis of pure chance. But since I am going to include it in a book I am writing about quantum events, I would appreciate advice from experts!

For instance in one such simulation I got counts

2083149, 2082863, 2082617, 2082678

for odd counters and

2083562, 2084692, 2086878, 2085004

for even counters. Statistics is not my area, so I went to the book "Introction to Probability and Statistics" by Mendenhall (5th edition), follow the method "inference from low counts", calculated "t" with the result t=-3.1596. As I understand itmay be considered significant.

But then I have made another simulation, with a different random seed, calculated "t" with these other numbers, and got t = -0.454533. Another simulation, with a different number of total events gives yet another t.

This suggests that I am probably used not the right method for this particular hypothesis test.

I would appreciate a hint: what kind of a statistical test should I apply to this kind of a problem if I want to get a reliable answer?

P.S. After some thinking and some more reading it occurs to me that I should make my hypothesis stronger: that each of the even counters registers more counts than any of the odd counters. Will have to experiment whether this makes the whole check more stable.

P.S.2 Following the idea of PS1 I have changed the parameters of the generating process which has made the difference more distinct. For the 16 differences between even and odd I got:

6143, 4605, 7243, 7745, 4408, 2870, 5508, 6010, 1935, 397, 3035, 3537, 799, -739, 1899, 2401

If I am not mistaken, the calculated t value is 23.2215 which should be enough for rejecting the hypothesis of pure chance. But since I am going to include it in a book I am writing about quantum events, I would appreciate advice from experts!

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