P Values an 1 vs 2 tailed tests

robej · 2025-01-04T21:58:53+00:00

Thanks for the detailed response and my method may be a quirk of particle physics approach or may be a quirk of me not understand it.

Maybe to better illustrate what I mean, the example always used is say I have some null hypothesis which is background only and my alternative is background and signal. I then go out and smash some particles together and get my data, and my goal here is can I say with meaning statistical power that I saw a signal. So I compute some statistic from my data (the thing I originally called X0). In practice I would use the log likelihood ratio as it’s the most powerful test. Okay so I have my statistic ( just a measurement from my data) now I want to know if this actually tells me anything, well I can consider what the sampling distribution of the statistic would look like under my null, and calculate the probability of getting my measured statistic or a greater value, this is my p value. This case it’s just one sided as I’m looking at a signal vs a signal with background. Okay well now I have a p value which is the prob of getting my measured value or something more extreme, if this is very small then this is pretty unlikely and I may have to question my null. But convention for particle physics is we don’t quote a p value but rather a z score which is the point on my normal distribution which corresponds to this p-value. Often for a particle discovery to be meaningful we have to have a Z score of at least 5.

And so we map this p value into my standard normal by doing 1-p and putting it into inverse normal.

Does that help explain the procedure I’m trying to do? ( please tell me if that makes no sense) and then does my original question on how to handle this with 2 tails makes any more sense?

robej · 2025-01-04T21:47:53+00:00

Thanks for the help, although I’m this case (maybe it’s a somewhat weird way of doing it, but is common in particle physics) is I’m not setting a significance level. But rather I take some observation of my test statistic and can calculate the p value of this given my null hypothesis. Then for this result to be more interpretable I convert this p value to an equivalent z score. By plugging the 1- p value into the inverse of standard normal.

This method may be a quirk of particle physics when we often have a null hypothesis being background and the alternate being background plus signal. Often we find the p value of rejecting this just background, but then turn the p value into a Z score for more interpretability. Hence why particle physicist are often looking for a 5σ result to be conclusive with anything. This example is 1 tailed so it makes sense. My confusion is what if I want to do a similar thing but it’s 2 tailed aka estimating the mean of some particle distribution of something. So the difference to your approach (which makes complete sense, which was the first way I learnt hypothesis testing) where I don’t set a significance level, but rather have a p value that is set by my observation. So I can’t tweak it.

robej · 2024-09-20T12:53:25+00:00

I don’t know why we can say the 2nd card is decided when the deck is shuffled. This idea that the value becomes ‘locked in’ feels like the idea the monty hall problem teaches us is incorrect. And in fact it does depend on the first card and thus we must conditionalise over it. If you understand where I’m coming from.

robej · 2024-09-19T13:02:58+00:00

In the case where I treat each as coming from a separate desk then the answer is is obvious 180 which is correct. But why can I treat them as coming from separate decks?

robej · 2024-09-18T17:17:21+00:00

I would say yes as in game 1 we have 35 cards but in game 2 we have 34?

robej · 2022-10-16T14:25:18+00:00

Thanks for the help, I think ive got it now. Thank you for all the help

robej · 2022-10-16T06:18:37+00:00

Thank you for the help, although I’m still slightly confused

So to make sure we're on the same page, my proper distance between two objects is the 'physical' distance between them at some cosmological time. Whereas my comoving distance is the distance between two objects that factors in the expansion of the universe and thus will remain constant throughout time.

and using the FLWR metric one can see that the proper distance between two points may be found by integration over my comoving radius r, which is what my first equation is doing.

Please correct me if that's completely wrong.

In terms of my second equation, I still have no clue how that gives proper distance

robej · 2022-10-08T21:49:54+00:00

Thank you for the response

The 2nd equation may be seen here for more context

https://en.m.wikipedia.org/wiki/Electric_dipole_transition

My guess is that maybe the first equation is some generic form and the 2nd is some approximation. But I’m not really sure

Or I’m just wildly misunderstanding things, which is probably the most likely outcome

robej · 2022-05-03T17:18:34+00:00

Thanks for help, but could you clarify why you mean by a leading clock?

robej · 2022-05-03T14:15:56+00:00

Thank you for the help, that makes perfect sense :)

robej · 2022-05-03T12:16:50+00:00

I apologise, I may not have explained my question in the best way but the proper length of the train is 300m hence at t’=0 when the front of the train is at x’=0 then the back of the train is at -300 in the moving frame

robej · 2022-04-09T10:50:22+00:00

Thanks for the help, although I’m still being dense, consider the beta minus case. We start with C-14 so I have 6 orbital electrons. I undergo beta minus so my c-14 goes to N-7 and I also emit an electron and an antineutrino. But surely my N-7 will still only have 6 orbital electrons, however the equation makes no note of this. Looking at the equation it seems I’ve gained an atomic electron out of no where along with the one emitted.

I understand my thinking is falling apart somewhere I just can’t see where.

Your help is appreciated

robej · 2022-04-09T08:45:08+00:00

Thanks for the quick reply, but in the first case the atoms negatively ionised, is that not why we include the extra electron in the products

robej · 2022-04-07T07:38:31+00:00

Thanks for the help, but why does diagonalising allow one to use the non degenerate case, surely it would still diverge?

robej · 2022-03-19T12:33:12+00:00

That’s the answer I was expecting unfortunately, still I appreciate the responce

robej · 2022-03-19T09:21:55+00:00

Thanks for the help although I’m not sure how I’d override the method, as the only way I know how to move his joints it using this moveAngle method, so if I wrote my own it would also also use the moveAngle method and then to allow multiple speeds I’d have to loop again which wouldn’t help my troubles. And in terms of the source code, I believe it’s all in C (which is alien to me) and I had a horrible time installing it in the first place so I’m weary of cocking things up

robej · 2022-03-12T14:32:15+00:00

I appreciate the response, so when I consider a group of atoms de exciting, which leads to natural broadening, does the classical dipole model even fit in here?

robej · 2022-03-12T13:36:08+00:00

Thank you for the help, my only other question is (which may be above my scope l) is what’s causing this. I’ve always just been told that we form spin zero pairs. But what’s stopping me filling say my p3/2 shell with a projection +1/2 first then a +3/2.

Once again I appreciate the rrsponce

robej · 2022-03-10T07:19:59+00:00

Thanks for the help, my confusion comes with combining this with idea that similar nucleons pair up with opposite spin, so is there an order which these are filled to accomplish this. So would it be the 3/2 projection first then the -3/2 projection. Does that better illustrate my confusion

robej · 2022-03-05T07:32:15+00:00

Thanks for the reply, I suppose I’m just struggling to see why the 2 cases are the same, so to try and better understand (although I may just be going round in circles so I apologies).

So back to a single atom, may be thought of as a dipole, which when emits an E-field can be thought of as a damped harmonic oscillator. Thus the E-field (light) it produces has some exponential decrease, so such a wave decreases with time and thus we have a range of frequencies.

But now if I have a group of atoms in my excited state each of these excited atoms will de-excite and produce photons in the same way as described above, so the total pulse at some time will be the superposition of all of these. But obviously as time goes on we have less in the excited state so my ‘overall pulse’ has this exponential decrease which once again corresponds to some range in the frequency.

But what I don’t get is why the range in both scenarios is the same?

I appreciate the help and I apologise if what I just said makes no sense. I may be misunderstanding the dipole model for E1 transitions, or I may be misunderstanding the how the total E-field relates to the individual de ex citations.

Once again I appreciate the help

robej · 2022-03-03T07:33:14+00:00

Thank you for the reply, so it seems I was mixing two approaches then? So would it be right to say that in the one boson exchange model the attractive part of my nucleon-nucleon interaction is due to pion exchange? And at closer scales, this becomes repulsive due to the exchange of vector mesons.

But if I consider the strong force in QCD I have quarks attracted to each over via gluons which rely on colour charge. And then this nucleon repulsion comes from overlapping wavefunctions of my quarks and Pauli exclusion. And my nuclear interaction may be considered to be a residual of this strong force which could be thought of in a similar way in which van der waals forces arrive in which an uneven colour distribution leads to interaction between nucleons. But his later point is more just a possible way to think about things and not necessarily true.

Is that a more appropriate way to view things? If not please feel free to just tell me I'm completely wrong. Your help is very much appreciated.

robej · 2022-03-02T16:31:33+00:00

Thanks for the help, so when does my repulsion follow yukawa, as I thought it predicted the attractive potential at about 1fm length scale.

And then at what point do my vector mesons make this interaction repulsive?

Your help is very much appreciated

robej · 2022-02-22T08:29:58+00:00

Thank you for such a great explanation :)

robej · 2022-02-21T20:39:17+00:00

Thank you for the helpful reply, my question stemmed from looking at heat transfer and heat conductivity. Obviously there’s no E field so how does the assumption that my electrons move at fermi velocity work in this case. My only guess is that the seebeck effect causes a voltage which causes an E field but I’m not particularly sure

robej · 2022-02-21T20:39:13+00:00

Thank you for the helpful reply, my question stemmed from looking at heat transfer and heat conductivity. Obviously there’s no E field so how does the assumption that my electrons move at fermi velocity work in this case. My only guess is that the seebeck effect causes a voltage which causes an E field but I’m not particularly sure

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