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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
2
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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
C Myn
(MC) Machine
>
~Cq Percipient
F
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