Is There a Difference Between Trusting Scientists and Trusting Preachers?

[Alex K]

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Another trouble is that the results of science aren't simple truths, they are often theory dependent, with shades of grey and degrees of certainty.

To give an example from a field I know (risking to sound like a broken record) - so people were using the Large Hadron Collider to look for the Higgs Boson, a particle that had been predicted by a very successful theory in which it was pretty much the last undiscovered piece. Now, in 2012 a discovery was announced because a deviation of ~5 standard deviations from the null hypothesis (no new physical effect beyond the known ones takes place) was seen.

Now, if you want to interpret this, you have to unravel a whole series of assumptions and observations.  First of all, was it a real discovery or a statistical fluke? The more measurements in different places you make, the more likely it becomes to see a 5 standard deviations fluke. This possibility was discarded because first of all, 5 sigma was still very unlikely to occur in the same place in two experiments, but also because of theoretical prior knowledge telling you that a particle is expected in this and this place with such and such properties, and the signals matched this expectation within experimental accuracy. Ok, so you have convinced yourself that it is not a fluke, and the signal looks like a new particle. But what particle? Is it *the* Higgs boson your theory predicted, and what does that even mean. So you keep measuring and the error bars shrink and the properties of the new thing are still within the predicted ones from your theory. Still, you haven't measured everything and there is still wiggle room because measurements always have error bars, and the new thing could be something closely related to the theoretically predicted Higgs Boson, but not exactly the same thing. Especially since you know that the very theory that gave you the prediction of the Higgs boson doesn't really describe the Masses of Neutrinos nor Dark Matter and therefore is necessarily incomplete, so the Higgs boson you discovered cannot possibly be *exactly* the one your theory predicted. Initially, they hadn't really measured the spin of the thing yet, and the relative certainty that it was a spin-0 particle like a Higgs boson is supposed to be, came as much from actual measurements of its spin as from the knowledge that it would be a huge coincidence for particles of spin-2 to accurately reproduce all the properties expected from the Higgs boson. If you see so many more than expected that it is 5 standard deviations away from the expected number, it is a priori so unlikely that such a large fluctuation appears by chance, that one usually assumes that a new phenomenon was discovered

So after all those considerations, what do you tell everyone? CERN Director General Rolf Heuer on July 4, 2012 put it thusly:
"As a layman, I would say, I think we have it"

In the hedging and slight vagueness of those words lie all the considerations I outlined above, and probably more I don't even know.

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As a lay person, I could ask you first what you mean by deviation. What is deviating and what is it deviating from and how do you know this?

Excellent question. That's not too hard to understand. Imagine you perform a series of particle collisions, and you calculate how often pairs of photons with, say Energies between 120...130 GeV should come out of the collision - based on your theory without a Higgs boson in it. Imagine your calculation says it should be a 100 photon pairs *on average*. Basic statistics then tells you (roughly speaking) that it is nevertheless 17% likely that you get 110 or more photon pairs by chance. That's one standard deviation; and that it is only 2.5% likely that you get 120 photon pairs or more by chance. That would be two standard deviations. It's how much more often of some kind of event you measure occurs than is expected from your "null hypothesis" theory prediction