In one of the lab courses I took as an undergraduate, I remember that the professor noted while discussing some statistical test (almost certainly chi-squared) that one could use it to show that a lot of early scientists (prior to the development of rigorous statistical analysis) had data that were too good to be realistic, and thus (with very high probability) were either deliberately falsified or the result of poor experimental design. He in particular cited Mendel as an example of a scientist whose data were far too good to be believable.

Wikipedia has a section related to Mendel's case specifically, and some discussion as to the possibilities. I'm more interested in the general case.

Is it true that a large fraction (relative to today) of prominent scientists before the 20th century presented data to support their conclusions which were statistically too good to be true? And if so, how did they avoid being wrong about a lot of their results?

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    $\begingroup$ Are you interested in data which is statistically implausible (as your question at the end suggests), or in cases where the data was really faked? I think that most prominent scientists didn't resort to outright fakery, by which I mean that the data was freely invented. $\endgroup$ – Felix Oct 30 '14 at 12:57
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    $\begingroup$ "common" and "large fraction" are subjective. I recommend changing the language to "more than today" or similar wording. $\endgroup$ – BMS Oct 30 '14 at 15:56
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    $\begingroup$ Apparently, this goes far back. Some of Ptolemy's astronomical "observations" were fabricated by extrapolating Hipparchus's data, Richard Newton even called him "the most successful fraud in the history of science". adsabs.harvard.edu/full/1980QJRAS..21..253G $\endgroup$ – Conifold Oct 30 '14 at 19:26
  • $\begingroup$ @Felix I don't think statistics alone can hope to tell us whether the data was statistically implausible because the scientists simply made it up or because of poor experimental design. Hence, I'm not specifying explicitly in the question, but I'm really interested in both cases. $\endgroup$ – Logan M Oct 30 '14 at 23:32
  • $\begingroup$ the result for Buffon's needle experiment by Mario Lazzarini (en.wikipedia.org/wiki/Buffon%27s_needle) was probably cooked up. $\endgroup$ – mau Nov 6 '14 at 17:15

The notion of "rigged data" evolved with time. Some ancient scientists are accused (by modern scientists) in rigging of the data.

One notable example is Ptolemy. I do not want to discuss here the accusation of Ptolemy by Robert Newton, but here is another well-known example.

In his Optics, Ptolemy gives a table of refraction. It looks like he measured refraction of the light ray passing from the air to other media (water, glass). He gives a little table, in such a way that a modern reader may conclude that these are experimental data. Some even consider this the oldest surviving example of an experiment in physics. However they are most likely made up. The data are inconsistent with the Snell law. If you plot the numbers they better fit a parabola rather than a sinusoid (as it should be). It is clear from the text that Ptolemy had some theory about refraction (incorrect theory), and his table was most likely computed according to this theory.

On the other hand, he never states unambiguously that he actually performed this experiment, and does not give any detail.

The most serious accusation against Ptolemy is that he forged his star catalog. That is he took the 200 years old catalog of Hipparchus, and corrected the data for precession. And used the wrong constant of precession which was not known exactly at that time. There is a large controversy about this among historians of astronomy, and as I understand, there is no consensus.

EDIT. Let me add that I am not aware of any famous stories of forgery and rigged data in physics and mathematics. None prior to 20 century and VERY few in 20 century. Unlike in "humanitarian sciences" like archeology or "finding some ancient manuscripts" which was quite common in 18 and 19 centuries.

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  • $\begingroup$ Not that few in 20th century, unfortunately. One famous piece of fake data, published in a very respected peer-reviewed medical journal, led to anti-vaccination movement that in turn caused preventable outbreaks and deaths. Wakefield, MMR vaccination and autism, The Lancet $\endgroup$ – Michael Jun 13 '19 at 20:47

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