Usage of $t$-test in HEP experiments I was brushing up on some statistics and thinking about what I'd learned in my undergraduate degree, which is what led me to this topic:
Is the (Student's) $t$-test, and $t$-distribution used anywhere in HEP experimental analyses?
I don't believe it was covered in whatever undergrad stats which were officially taught in my (UK) physics degree, and going into theory afterwards meant sidestepping statistics courses later. It is a little embarrassing to come across this in e.g the biological and social science literature and have just a rough idea about this machinery.
On the other hand, the nice little book by Barlow explains that the $t$-test is "probably more familiar to doctors and economists than it is to physicists and chemists" because the whole concept is centered around not knowing the intrinsic population variance/s.d. of a property. Indeed, I don't think the topic is at all mentioned in the book by Glen Cowan, nor in the PDG review on statistics.
I initially thought that in HEP, since we basically expect the physical value of a particle mass (ignoring all the beta function and RGE evolution) to be a sharply (like Dirac delta sharp) peaked about some positive value, with zero spread, the technique is largely irrelevant.
But I then started thinking about resonances, and the Breit-Wigner distribution for production cross-sections, and wondered: isn't it true that we could take the mass of e.g. the Z-boson to be $M_Z \pm \Gamma_Z$, and let the decay rate $\Gamma_Z$ represent the inherent spread in the mass?
Or surely there are other parameters in HEP where the parameter has some inherent spread? Or perhaps it's even the resolution in e.g. some calorimeter that sets the width in this problem?
If there are any experimentalists on here it would be great to hear your take - or anyone else, your reason why I'm overlooking something trivial!
 A: Sometimes, the $t$ distribution is used in Bayesian inference to represent distributions that have fatter tails than a Gaussian (although this is not the t test per say). There's an example in Eq 26 of this paper, which is about testing GR by looking for non-tensor polarizations from rotating neutron stars (a promising but so-far unseen source of gravitational waves): https://arxiv.org/pdf/1703.07530.pdf
A: Having thought about it a bit more, I think there are a couple of answers to this.
One is that maximum (log-)likelihood methods are heavily used in physics, and especially in HEP. Confidence intervals, even for data sets with low numbers of statistics, can be constructed by plotting contours of constant likelihood in parameter space, where e.g for 2 parameters represented by $\vec{\theta}$, the contour corresponding to  a drop in  $\ln L(\vec{\theta})$ of $\sim 0.23$ from the maximum value encloses the $90\%$ Confidence Region for those parametners (see here).
I think the second is that, unlike in say, psychology or medicine, the dynamics of particle physics can (in principle!) be straight-forwardly simulated on a computer, and so it is possible to generate vast numbers of Monte Carlo data relating to particle interactions. These can then be used to construct PDFs for parameters and so it is possible to have an estimate of e.g. the standard deviation of the population of such measurements.
