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June 17, 1998
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PDF icon CIA-RDP96-00787R000200090023-8.pdf156.34 KB
Approved For Release 2400/08/10 : CIA-RDP96-00787R0Q200090023-8 SG1I ANALYSIS OF SERIES PRODUCED BY ESP EXPERMENTS ical ESP experiments involve the comparison of guesses with external states presumably both uncontrolablerand unperceivable by the percipient by normal sensory means. The following note points out statistical variables available &'r~analysis in these experiments and their possible interpretation in terms of ESP effects. The SRI experiments with the 4-state random number generator are experiments of this type.., In the following, for simplicity, a 2-state or binary choice device is assumed, but by obvious extension the ideas may be applied to an analysis of 4 as well.- Denoting the two states of the machine by +2. and -~ the series produced by the machine during the test is a time-ordered series (nZi ) where m., takes the value of #1 or -:1 , and denotes the position in the series N(total number of states in test). The corresponding guesses made by the percipient form another series 94 ) where % is either +1 or -j ,and again L indexes the guess. Yet another time-ordered series is that produced by the machine during a calibration run with no percipient which we denote ( Ci ) and assume 4 = 1,2,??? N. as before with the same value of N, There are thus three time-ordered series to be analys&d and compared. 1. ( MI ) the series produced by the machine during the test 2` ( 9Z ) the series of guesses of the percipient 3: ( CZ ) the calibration series of the machine Approved For Release 2000/08/10 : CIA-RDP96-00787R000200090023-8 i. 2 Approved For Release 2,QPO/08/10 : CIA-RDP96-00787ROO4200090023-8 The statistical properties of each series separately is described by a heirarchy of correlation functions: I d1Z~ mean value (average properties) m. > = - N L. CM (y)'v 1 M4m4#i i emrn,n (,k) 2nd order autocorrelation ( displacement within series b t1 ? . /fc,k 3d order autocorrelation Higher order correlations If randomness is at issue it can be determined from the measured values of these functions compared with the probable values they would have for a truly random series. For most purposes it is deemed sufficient to use no higher than 2nd order correlations. A further simplification is to restrict attention to transition probabilities, i.e. cm (I) with j =:t, only. The cut-off point in the analysis is dictated by practical considerations of sample size ( magnitude of N), or convenience of computation. In inei g, however, the entire heirarchy is required for a complete analysis. In addition to the autocorrelations, the cross-correlations of the series with each other may be computed. There are threee(3) 2nd order- crossacorrelation functions among the three series above. mg (~ ,) '~" fn4 94a-a' machine test- percipient test 4, in ccf~ machine test- machine calibration Cce / C 9d.* machine calibration-percipient test The essential point of this note is that a proper description of, an ESP experiment requires a computation of these correlation functions together with embody the very information sought in the experiment. . They Approved For Release 2000/08/10 : CIA-RDP96-00787R000200090023-8 Approved For Release 2WO/08/10 : CIA-RDP96-00787ROQ 00090023-8 The significance of the various functions is as follows.- l.- Averages and autocorrelations Determine whether each of the series is random, and especially and ('j) determine whether other than random strategy is used by percipient? x.'/n> and ) compared with