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Statistics and Precognition

February 10, 2011

"There are three kinds of lies: lies, damned lies, and statistics."

This quotation was popularized by Mark Twain, who thought it had been said by British Prime Minister Benjamin Disraeli. In a previous article (Second Law of Thermodynamics, February 7, 2011), I reviewed the idea that the second law of thermodynamics is unlike other physical laws, since it's a statistical law. Statistics are important to the analysis of experiments, and they've been taken to an extreme in the Design of Experiments methodology that attempts to derive models of quasi-linear systems from a minimum of experiments.

Since many of our experimental findings are based on statistics, we need to ask ourselves, what do we really know? Physicists typically rely on the 95% confidence interval, but that convention has led to the discovery of some subatomic particles that appear and disappear, not because they're virtual particles, but because the statistics change as more data are collected. As I wrote in a previous article (The End is Nigh (Maybe), July 27, 2007), Richard Gott, a professor of astrophysics at Princeton University, extended the logic of the 95% confidence interval to an extreme by predicting the demise of the human race. His Doomsday Argument is based on a calculation of how many people will be born into the world from the present time to the end of time. It's based on the idea that the number of people who have been born to date is somewhere within 2.5% to 97.5% of that range; namely, the 95% confidence interval. Using reasonable estimates for life expectancy, etc., Gott calculates that humans will exist for only another 9,000 years, maximum.

The use of statistics in science has become a hot topic once again with the publication of a paper in the Journal of Personality and Social Psychology that provides experimental evidence for extrasensory perception.[1-2] The paper, by Daryl J. Bem, an Emeritus Professor at Cornell University, demonstrates statistical evidence for precognition; or, more plainly, knowledge of the future. The experiments were well constructed and the paper passed peer review; but there is considerable commentary, including a rebuttal paper immediately following[3] and an editorial statement.[4]

The paper contains the results of nine experiments with more than 1000 college student participants. In one experiment, the college students were asked to guess behind which of two simulated curtains on a computer screen an erotic picture could be found. This appears to be an apt test for college students, who were right 53% of the time.[2] If you apply the usual statistics (a t-test) to this result, you get a p-value of 0.01. This means that there's less than a 1% chance that an experiment would get these data if ESP did not exist. Psychologists generally conclude that any p-value below 0.05 indicates great statistical significance; that is, there must be something happening. However, a p-value of 0.01 doesn't mean that there's a 99% probability that ESP does exist.

Bem says that he used the t-test, and not some other statistical tests, since the t-test is what psychologists use. If he used something else, he would have been accused of using "fancy statistics" to get the result he wanted.[2] On the topic of "fancy statistics," one is reminded of the history of the Princeton Engineering Anomalies Research Lab, which I mention without commentary.

David Krantz, a statistician at Columbia University, is quoted in Science as saying,
"The real lesson to be learned from this is not that ESP exists, it's that the methods we're using aren't protecting us against spurious results."[2]

An alternative statistic, one used in the analysis of pooled data for clinical trials, is Bayesian Inference. Bayesian Inference is a means to refine your probabilities as more data are obtained, so it's a living statistical measure, unlike the t-test that looks at a single experiment. Jeffrey Rouder of the Perception and Cognition Lab, Department of Psychological Sciences, the University of Missouri (Columbia), used the Bayesian approach to combine all nine of Bem's experiments. His result is a "Bayes factor" of forty.[2] What this means is that if your prior probability of ESP existence (let's say, that's your current prejudice) is a million to one against, you need to refine that to a lesser 25,000 to one. If you think there's a fifty-fifty chance that ESP exists, then your odds jump to 40:1 in favor.

So, what do I say about all this? I have a "vision" that there will be much more written on this matter in 2011. Lest you think that only psychologists have ventured into the extrasensory realms, I refer you to Refs. 5-6.

Figure caption

Cassandra, fair as golden Aphrodite standing on Pergamus (Homer, Iliad, Bk. 24, l. 699). The god, Apollo, awed by her beauty, gave Cassandra the gift of prophecy. Cassandra repelled his advances. Miffed, Apollo cursed her so that no one would believe her predictions. Cassandra warned the Trojans about the Trojan Horse, but to no avail. ("Cassandra by Evelyn de Morgan (1855-1919), c. 1898 (Wikimedia Commons Image).


  1. Daryl J. Bem, "Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect," Journal of Personality and Social Psychology (Jan 31, 2011), doi: 10.1037/a0021524.
  2. Greg Miller, "ESP Paper Rekindles Discussion About Statistics," Science, vol. 331 no. 6015 (January 21, 2011), pp. 272-273.
  3. Eric–Jan Wagenmakers, Rudd Wetzels, Denny Borsboom and Han L. J. van der Maas, "Why psychologists must change the way they analyze their data: The case of psi: Comment on Bem (2011)," Journal of Personality and Social Psychology (Jan 31, 2011), doi: 10.1037/a0022790.
  4. Charles M. Judd and Bertram Gawronski, "Editorial Comment," Journal of Personality and Social Psychology (Jan 31, 2011), doi: 10.1037/0022789.
  5. R. Targ and H.E. Puthoff, "Information transfer under conditions of sensory shielding," Nature, vol. 251, no. 5476 (October 18, 1974), pp.602-607.
  6. H.E. Puthoff and R. Targ, "A Perceptual Channel for Information Transfer over kilometer distances: Historical perspective and recent research," Proc. IEEE, vol. 64, no. 3 (March, 1976), pp.329-254.

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Linked Keywords: Mark Twain; Benjamin Disraeli; second law of thermodynamics; physical law; statistical law; experiment; design of experiments; DOE; quasi-linear system; physicists; 95% confidence interval; subatomic particles; virtual particles; Richard Gott; Princeton University; human race; doomsday argument; end of time; life expectancy; Journal of Personality and Social Psychology; Extrasensory perception; Daryl J. Bem; Cornell University; precognition; peer review; t-test; p-value; fancy statistics; Princeton Engineering Anomalies Research Lab; David Krantz; Columbia University; Bayesian Inference; Jeffrey Rouder; Perception and Cognition Lab, Department of Psychological Sciences; University of Missouri (Columbia); Cassandra; Aphrodite; Pergamus; Homer, Iliad, Bk. 24, l. 699; Apollo; Trojans; Trojan Horse; Evelyn de Morgan (1855-1919).