CIA-RDP96-00787R000200090023-8

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Approved For Release 2000/08/10 : CIA-RDP96-00787R000200090023-8
SG11
ANALYSIS OF SERIES PRODUCED BY ESP EXPERIMENTS
Typical ESP experiments involve the comparison of guesses with
external states presumably both uncontrolable and unperceivable by the
percipient by normal sensory means. The following note points out
statistical variables available for 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-state data as well.
Denoting the two states of the machine by +1 and -1 the series
produced by the machine during the test is a time-ordered series ( mi )
where m; takes the value of +1 or - 1 , and i
denotes the position
in the series
2 = 1,2, ..... N(total number of states in test). The
corresponding guesses made by the percipient form another series
(9:)
where 9; is either +1 or -1 , and again & indexes the guess. Yet
another time-ordered series is that produced by the machine during a calibration
run with no percipient which we denote
( C ; ) and assume
¿ = 1,2, ... N
as before with the same value of N.
There are thus three time-ordered series to be analysed and compared.
1. ( mi
)
the series produced by the machine during the test
2. ( 92
)
the series of guesses of the percipient
3. (
c
)
the calibration series of the machine
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Approved For Release 2000/08/10 : CIA-RDP96-00787R000200090023-8
The statistical properties of each series separately is described by
a heirarchy of correlation functions:
<m>=NEM;
Mean value (average properties)
Cmm (j) ~ {m2 mitj
2nd order autocorrelation ( ៛ is
displacement within series)
Cmmm (J,k)~{m&m1+jmc+k
3rd 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. Cmm
(
)
with y == 1
only. The cut-off point in the analysis is dictated by practical considerations
of sample size ( magnitude of N), or convenience of computation. In principle,
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 three(3) 2nd order cross correlation
functions among the three serdes above.
Cmq (1)~{m, g+j
machine test- percipient test
Cmc (g)~ Em2C+j
machine test- machine calibration
Ccg (y) ~ { C, g+j
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
a statistical analysis of their likelyhood of occurrence by chance .. They
embody the very information sought in the experiment.
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Approved For Release 2000/08/10 : CIA-RDP96-00787R000200090023-8
The significance of the various functions is as follows:
1. Averages and autocorrelations
Determine whether each of the series is random, and especially
<9> and (g(y)
determine whether other than random strategy is used
by percipient.
<m> and Cm
compared with << > and Ced(y)
determine whether
statistics of machine alters between calibration and actual test.
( An indicator of psychokinetic, or other effects)
2.
Cross-correlations
Cmq (y)
compares two simultaneous time series.
for
J=0
measures correspondence of guess and machine state
for
1<0
measures correspondence between guess and future
machine state
for
1>0
measures correspondence between guess and past machine
state
Cmc (g )
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 suns.
Ccg (g)
compares two non-simultaneous series so perhaps not significant,
but indicates whether guessing sequence is related to calibration
performance of machine.
Calibration
Experiment
Cmc (1)
<< >
Cc.
<m>
Cmm
(Ci)
(m.)
Machine
KU
Cm (y)
Cca (1)
<97 Cgg
(9% )
Percipient
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