The Luminiferous Ether.
An instructive case-history is found in the recent history of science. In the 19th century most physicists accepted the old idea that all of space is filled with an elusive substance called the "luminiferous ether". It was well known that light, and all other electromagnetic waves traveled very well through a vacuum. Yet other waves, sound, for example, required a material medium, and a common classroom experiment showed that a ringing bell in a glass vacuum jar could not be heard, yet it could be clearly seen to be vibrating. At this time, analogical thinking was rather prevalent in physics, and by analogy, physicists assumed that light must also have some material medium, a medium that was present even in the best vacuum we could produce in a bell-jar.
Once a concept is fixed in the mind, one often perceives confirmation of it elsewhere. Some thought that the shift of the perihelion of the planet Mercury was due to ether drag on the planet. Astronomers thought the shape and orientation of comet tails were also the result of ether drag as comets moved through the ether. All of this seemed to be more evidence for the reality of the elusive ether. Textbooks cited such evidence, and even used it to calculate the density, viscosity, refractive index and other physical properties of the luminiferous ether. 
The Michelson-Morley experiment of 1887 was designed to detect the ether's effect on the speed of light, to find out whether the earth's speed relative to the ether could be detected. Michelson did many other independent experiments with the same purpose over many years. All found no evidence for the ether. Then along came Einstein's relativity in 1910, which accounted for the experimental observations without ever invoking an ether. So gradually it dawned on physicists that the ether idea simply wasn't necessary, and never had been. So it died, though gradually, over the next decade. Today it hardly rates a footnote in textbooks.
One of Michelson's experiments, at the University of Chicago, was specifically designed to test the idea that the earth dragged ether along with it. It used an interferometer that extended from the basement to the top floor of a building. Again, no ether effects were found. By that time, Michelson, who believed in the ether, was resigned to the fact that it couldn't be detected, and expected the experiment to fail, as had all of those before. Sir Oliver Lodge in England built an ingenious device to test whether ether was dragged along in the narrow space between two rapidly spinning steel disks. Again, failure. No ether drag was found. But Lodge so firmly believed in the ether, that he said "The experiment may have to be 'explained away'."
Actually, the astronomer James Bradley had earlier (in 1725) done an experiment on stellar aberration that was intended to demonstrate ether drag near the earth, but it showed that starlight coming toward the earth was bent in the opposite direction to that predicted by the ether drag theory. The correct (and very simple) explanation was quickly found, and it didn't require the assumption of an ether.
All the other "manifestations of the ether", such as comet's tails and the perihelion of Mercury, that had once seemed such persuasive evidence for the ether, were found to have other explanations. 
Did these experiments "disprove the ether"? I wouldn't put it that way. None of these, or any other experiment could disprove the general idea of an all-pervading ether. The point is that there is simply no experimental evidence for the ether, and no need for it in any of our physical laws or theories. You can't disprove something that isn't there, or something that doesn't affect anything material in any way. Yet even today, there are non-scientists who desperatly seek to revive this 19th century ether concept. Why? The idea seems so "right" to them. They cannot imagine light moving through "nothing". They are a classic case of people who have an emotional commitment to an appealing naive concept, and will bend physics and logic in order to justify that idea.
Keep this example in mind as we look at the notion of the "intelligent designer", for we will see that it parallels the case of the luminiferous ether in many significant ways.
Stevenson, Loyd S. Jr. (1972). The Aetherial Ether. Austin, University of Texas Press.