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 SG1 I ANALYSIS OF SERIES PRODUCED BY ESP EXPERMENTS
 Typical 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 ffbr~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 Z-state or binary choice
 device is assumed., but by obvious extension the ideas 'may be applied to
 an analysis of /+-state-data 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 ( Mi )
 where M., takes the value of 41 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 -:Z ,and again i. 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' z 1,.2,9,.## N
 as before with the same value of N,
    There are thus threetime-ordered series to be analys&d and compared.
 1, ( MI ) the series prod-aced by the machine during the test
 2 * ( 9z the series of guesses of the percipient
 5~6 CL the calibration series of the machine
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 The statistical properties of each series separately is described by
        a heirarchy of correlation functions:
 4 /n > = --L I M~
 N
 M4 M4.0i
 em MM (v,
 mean value (average properties)
 2nd order aiitocorrelation
                   f is
 displacement within series)
 3M ord'er a-atocorrelation
 Higher order correlations
 If randomness is at issue it can be determined from the measured val*aes
 of these functions compared with the probable values they wo-ula have for
 a truly random series. For most purposes it is deemed sufficient touse
 no higher than 2nd order correlations. A further simplification is to
 restrict attention to transition probabilities, Lea CMr4 (I) with j =:tj
 only, The mt-off point in the analysis is dictated by practical considerations
 of sample size ( magnitude of N), or convenience of computation. In priadi*19r,
 however,, the entire heirarchy is required for a complete analysis.
 In addition to the aixtocorrblations,, the cross-correlations of the series
 with each other may be computed. There are threer(3) 2nd order-crossacorrelation
 functions among the three series above*
 rZ14 94-1-al machine test- percipient test
 machine test- machine calibration
 Cce C-4 9d.*i machine calibration-percipient test
 The essential point of this note is that a proper description of, an ESP
 e=eriment reouires a com-p-atation of these correlation functions together with
 a statistical arA&Mis of their likelyhood of ocgj=gnce by chance,. They
 embody the very information sought in the experimento
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 The Significance of the various functions is as followst
 l.- Averages and autocorrelations
 Determine whether each of the series is random., and especially
 <9> and ~,(J) determine whether other than random strateg:t is used
 by percipient.
  4m and '4 ' ) compared with ec > and determine whether
 > &-'QV
 statistics of machine alters between calibration and actual test.
 ( An indicator of psychokinetic, or other effects)
 2-* CrosIL-corrgLations
 compares two simultaneous time series.
 C
 for ~-- 0 measures correspondence of guess and machine state
 for joo measures correspondence-between guess and future
 machine state,
           for > measures correspondence between gaess-and past machine
 state
 compares two non-simultaneous series so likely of no interest., but
 could indicate statistically significant regularities in the series
 produced by the machine for different Yuns.
 compares two non-simaltaneous, series so perhaps not significant.,
 but indicates whether guessing sequence is related to calibration
 performance of machine.
                                 Calibrat EMerimen6
                                    4C > Gj <MI>
 C Myn
                 (MC) Machine
 >
            ~Cq Percipient
 F
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