> For instance, studies that compute the gyromagnetic ratio of the electron (to 10 decimal places no less) and then compare that against the experimentally obtained value would be classified as "high rigor".

You mean like, say, measuring the elementary charge of an electron to high precision? ;) Richard Feynman has something to say about the rigor of those experiments...

> We have learned a lot from experience about how to handle some of the ways we fool ourselves. One example: Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right. It's a little bit off because he had the incorrect value for the viscosity of air. It's interesting to look at the history of measurements of the charge of an electron, after Millikan. If you plot them as a function of time, you find that one is a little bit bigger than Millikan's, and the next one's a little bit bigger than that, and the next one's a little bit bigger than that, until finally they settle down to a number which is higher.

> Why didn't they discover the new number was higher right away? It's a thing that scientists are ashamed of—this history—because it's apparent that people did things like this: When they got a number that was too high above Millikan's, they thought something must be wrong—and they would look for and find a reason why something might be wrong. When they got a number close to Millikan's value they didn't look so hard. And so they eliminated the numbers that were too far off, and did other things like that...

[from "Surely You're Joking, Mr. Feynman!" via Wikipedia–I know this isn't exactly what you were talking about in your comment, but I thought it makes for an interesting discussion regardless]

Interesting paper on this here: http://arxiv.org/pdf/physics/0508199v1.pdf and also another example here with the Hubble constant here: http://www.pnas.org/content/101/1/8/F2.expansion.html

Even in Mullikan's case, the paper I linked seems to suggest he might have intentionally omitted data that didn't fit his narrative (I only know what I've read in that paper, so I wouldn't like to make any stronger claims than that). Whether he was 'right' to do that is an interesting question. Clearly the oil drop experiment was ground-breaking, and the results hugely important, but omitting inconvenient results is clearly a huge ethical violation. However, his intuition was correct, and he was observing a real effect, and the measurements he kept were good. So who can say? Science seems to be about asking the right questions as much as finding the right answers. Sometimes good science is just to get smart people talking about the "right" things, and the correct answers come later.

Perhaps peripheral, but another favourite example of mine is the Lennard-Jones potential for modelling e.g. noble gases. It has an attractive term and a repulsive term. The attractive term is distance to the power 6 and based on good physical reasoning; the repulsive term is distance to the power 12 and entirely arbitrary, just because it was easier to calculate since you'd already calculated the power 6 term. So, in a sense, it was completely made up. But it was still a useful tool because it helped people start asking the right questions, and exploring these systems, even if it was, in a sense, wrong.