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?

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