Quick Summary

"My opinion about Miller's experiments is the following. ... Should the positive result be confirmed, then the special theory of relativity and with it the general theory of relativity, in its current form, would be invalid. Experimentum summus judex. Only the equivalence of inertia and gravitation would remain, however, they would have to lead to a significantly different theory."
Albert Einstein, in a letter to Edwin E. Slosson, July 1925

"I believe that I have really found the relationship between gravitation and electricity, assuming that the Miller experiments are based on a fundamental error. Otherwise, the whole relativity theory collapses like a house of cards."
Albert Einstein, in a letter to Robert Millikan, June 1921 (in Clark 1971, p.328)

Dayton Miller was an associate of Edward Morley of the original MMX. It was his and many other respected scientists belief that the null result was likely caused by one or both of two factors. If Aether is a fluid-like substance and interacts with matter in any way, or if it is affected by magnetic fields, then there would be an entrainment effect wherein Aether would be transported along with the Earth; this would make it far more difficult to detect any motion. This is somewhat analogous to trying to measure the speed of the airplane by observing the wind speed in the cabin.

Miller was a consummate scientist and was determined to devote extreme time and care to the resolution of the issue. Not only did he take the experiment out of the basement and into the mountains, but also eliminated other possible interferences such as the magnetic metals in the construction of the original interferometer used by Michelson and Morley. Additionally, he increased the sensitivity of the device by a very large degree and performed hundreds of thousands of tests over many years.

During his lifetime Miller was able to defend his results against all skeptics and was given a prestigious award by the American Association for the Advancement of Science (AAAS) for the detection of the Aether.

Around 14 years after Miller's death, in 1955 Robert S Shankland and associates obtained all of his data with the sole purpose of "finding his error." Because of his association with Einstein, they were fully and admittedly biased in their beliefs and intentions from the start. Shankland alleged that the primary cause of Miller's non-null result was temperature fluctuations. This allegation had previously been made while he was alive and proven false by Miller himself on a much earlier occasion. Regardless of this fact, the scientific community was very intent on closing up any loose ends on a theory they were fully on board with; so from that moment forward Aether was totally disregarded. Any further research or discussion in the area was then, and currently is the target of ridicule.

Consider now the more recent analysis of Maurice Allais, a physicist and Nobel Prize winning economist, as well as the man for whom the Allais Effect is named. The effect, though accidentally discovered, is widely considered General Relativity's Achilles Heel. Here's an article about Maurice Allais and the Allais Effect. Could there be any more qualified individual for statistical analysis of Dayton Miller's work than a Nobel Prize winning economist with a thorough grounding in physics?

Here is one of his many articles as was published by 21st century  Science & Technology, Spring 1998, p. 28

When Allais was able to get enough of Dayton Miller's work from the hands of Shankland, who still possesses much of the material, he was able to determine by statistical analysis that Miller's recorded data coincided exactly with the Earth's orbit. Miller's measurements gradually move from their maximum dimensions around the autumn equinox to a minimum during the spring equinox. These new findings by Allais prove, beyond doubt, that very real non-null readings came from the Miller experiments and thereby invalidate the second postulate of special relativity.