Did Rhine achieve success?
I realize your question was addressed to Ersby, but here are a few general excerpts about Rhine from a few books anyway.
"And so it was that at that time I began to explore Rhine's work, I was only vaguely aware that someone named Rhine had once done research on purportedly psychic phenomena at Duke University. Of one thing I was certain, however: that whatever the experiments had been, they'd been discredited as poorly controlled, the results discredited as well. I, like many people, knew enough to know Rhine's name and to have it solidly associated with pseudoscience - or, in a more generous mood, maybe just not very good science.
But then I'd taken the trouble to look into the actual history. I'd begun with the Rhines' scientific past and the start of their lab. I'd gone on to examine the earlier experiments. I discovered the rigor surrounding their work, a far cry from what I'd heard. And then I started examining the history of criticism around the Rhine work. I looked into what the criticisms were, how the best of them had been taken into account by the Rhines, and how other attacks were disputed, discredited, and even formally retracted. It amounted to quite a story.
[...]
It was yet another sixty years before I started asking colleagues what they knew about the Rhine research. It turned out most were like me; they'd heard of it, but dismissed it. Also like me, they thought they knew what they were dismissing. The fact was, we were all misinformed. So much for priding ourselves on judging by the evidence."
Extraordinary Knowing: Science, Skepticism, and the Inexplicable Powers of the Human Mind
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"Another prominent figure who was distressed with Kellogg's attack [on Rhine] was E.V. Huntington, a mathematician at Harvard. After corresponding with Rhine, Huntington decided that, rather than further confuse the public with a technical rely to Kellogg's arguments, a simple statement should be made to the effect that the mathematical issues in Rhine's work had been resolved. Huntington must have successfully convinced his former student, Burton Camp of Wesleyan, that this was a wise approach. Camp was the 1937 President of IMS (Institute of Mathematical Statistics). When the annual meetings were held in December of 1937 (jointly with AMS [American Mathematical Society] and AAAS [American Association for the Advancement of Science]), Camp released a statement to the press that read:
"Dr. Rhine's investigations have two aspects: experimental and statistical. On the experimental side mathematics, of course, has nothing to say. On the statistical side, however, recent mathematical work has established the fact that, assuming that the experiments have been properly performed, the statistical analysis is essentially valid. If the Rhine investigation is to be fairly attacked, it must be on other than mathematical grounds." [Camp, 1937].
The Parapsychology Revolution: A Concise Anthology of Paranormal and Psychical Research
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"While work continued at Duke - the team began precognition experiments in 1934 as well as psychokinesis studies, the latter being kept very quiet - other researchers began to report some success using Rhine's methods. Word came of successful replications at Tarkio (Missouri) College, Bard College in New York State, and from England. Word also arrived that a young German researcher, Hans Bender, had conducted a successful series of clairvoyance experiments, which Rhine regarded as an independent corroboration of his own work. As momentum built, Rhine was able to secure additional funding, and more researchers joined the team.
[...]
Criticism also focused on the question of whether all sensory cues really had been excluded. Critics quickly noticed that the cards in some early commercially produced ESP decks could be read from the back because of the printing impression. But these were not the same cards that had been used in the early Duke testing, and of course the problem did not exist in the many experiments in which the subject was not permitted to see even the back of the cards. This did not stop some critics form trying to portray the entire body of results as worthless, however."
Parapsychology: The Controversial Science
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"Psychologists sketched all manner of scenarios in which Rhine, his colleagues, and their subjects variously were depicted to have engaged in collusion to yield significant data, to fudge (distort) the data, or to construct entirely fictitious data. Over the ensuing years as more and more researchers in laboratories around the world performed statistically significant ESP experiments this argument became increasingly tenuous. As Eysenck (1957, pp. 131-132) asks, Why should dozens of academics engage in an international conspiracy of such proportions? If they achieve anything at all it is only to put their careers in jeopardy."
An Introduction to Parapsychology
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"As for concerns about the quality of the experiments, philosopher Fiona Steinkamp has analyzed the Rhine-era ESP card tests in detail. She found that as controls improved against such potential problems as sensory cues, recording errors, and investigator fraud the results did decline slightly, but even the most highly controlled studies had odds against chance of 375 trillion to 1."
Entangled Minds: Extrasensory Experiences in a Quantum Reality