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A figure of merit can be calculated for each session.
For a series of sessions, the FM
may
be
used
to
assess
a
viewer’s
progress
on
either
a
session-by-session
or
descriptor-by-descriptor basis or both.
ABSOLUTE FIGURE OF MERIT - A METHOD OF CONTROL
We have obtained an estimate of the meaning of FM on an absolute basis.
Given the
hypothetical situation in which ten viewers contribute 50 sessions each to a remote viewing series,
a figure of merit can be calculated by the above technique for each session.
If we add the number
of responses for
all viewers
for each of the descriptor
bits, we can obtain an estimate
as to
“response/analysis” bias that may have occurred during the series.
For example,
if bit number
were asserted 40 times in 500 sessions, we can assume on the average for this series (accounting
for all known and unknown conditions) that the probability that bit
1 will be asserted in a given
response
is 40/500 or 0.08.
By repeating this calculation for each of the descriptor bits, we can
determine the probability of occurrence for all bits under exactly the same conditions that were
used
in the
series.
Since
this procedure
displays
all response/analysis biases that may have
developed during the series, we are able to use this information to construct computer-generated
“random” responses, with a total absence of psi functioning, that are subject to exactly the same
biases that were observed
in the
series. Therefore, we are
able to simulate the
ideal control
condition, which addresses an important question
that is frequently asked by our critics: namely,
how would an average viewer respond to a no-target session
(i.e. the “monkey on a typewriter"
scenario)?
A simple
bit-by-bit random generation
of a
response
is
completely inadequate
because
it does not account for the response biases observed during the series.
The method for
producing “random” sessions that do account for the biases
is described below.
A random number generator
is used to create pseudo-responses that are assumed to be
devoid of psi functioning.
Each bit in a given pseudo-response
is generated from the empirical
“bias” described above.
Once the complete response
is generated, the same logical consistency
rules (described above) are applied to finalize the pseudo-response. By this technique, a large set
of
pseudo-responses
containing
no
psi
information
can
be
generated.
To
use
these
pseudo-responses, we must select, on a random basis, targets from the same set that were used
during the series from which the biases were observed. A complete pseudo-session consists of a
single pseudo-response and a
single randomly selected
target.
The standard
figure of merit
analysis is applied to all of the pseudo-sessions in order to calculate figures of merit that have, by
definition, no psi content.
The resulting FMs are
fit with a gaussian distribution to provide an
estimate of the mean and standard deviation FM for random data.
Figure
1 shows the
results of one such
fit for a
total of 300 pseudo-sessions, using the
remote viewings from a photon-production experiment (Hubbard, May, and Puthoff,
1985)
as
the bias data. From the chi-square, we note that a gaussian is a correct function to use for the
fit.
Since the
gaussian
is truncated
at zero
figure
of merit, we must modify
the
usual
z-score
techniques to provide p-values
for the individual session
figure of merits.
By
definition, the
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probability of observing a figure of merit,
or greater is the area under the FM-gaussian for f
fo divided by the total area under the FM-gaussian.
An exact p-value
is calculated as follows:
Define the minimum value of a Z-like statistic as
z= - —
.
mm
<7
where
|x and
cr
are the mean and standard deviation of the best-fit gaussian respectively
( ji = 0.132 and
cr = 0.163 in the example).
Define a second Z-like statistic as
Zo
where
f0
is the observed figure of merit.
Let Pmln
and P0
be the p-values calculated in the
usual way assuming z
and Z 0
were valid z-scores.
Then, the correct p-value
is given by
min
u
p-value
^
Utts and May (1985) have provided an exact method for combining p-values to enable an overall
series evaluation.
For mean p-values calculated for a series greater than
.1, and the number of
sessions greater than 6, a close approximation for the combined Z-score
is given by (Edgington,
1972)
Combined
(0.50 - p
) x V 12 N
,
where p
is the average p-value for N sessions.
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Figure
BEST-FIT GAUSSIAN TO CONTROL FMs
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CONCLUSIONS AND SUGGESTIONS FOR EXTENSIONS
We are proposing a target-pool independent method
(figure of merit analysis)
for scoring
free-response material.
The FMA provides a number of advantages over previous methods.
•
Figures of merit can be used in correlation studies.
•
FMA provides a novel technique for free-response controls.
•
Target pool independent exact p-values can be computed for each
free-response session.
•
Since the FM
is computed by simple counting, the computer coding
burden
is sharply reduced.
Because of the lack of descriptor bit independence (and thus a need for logically consistent
rules) the effective number of descriptor bits is reduced. We are presently investigating a way to
utilize a hierarchical descriptor
list:
that
is, each
level of the hierarchy consists of a
variable
number of independent
descriptors.
Finally, the
ideal descriptor
list would include arbitrary
weighting factors for the level of hierarchy as well as for the individual descriptors within the level.
REFERENCES
Dunne,
B.J., Jahn, R.G., and Nelson, R.D., "Precognitive Remote Perception,” Engineering
Anomalies Research Laboratory, School of Engineering/Applied Science, Princeton
University, Princeton NJ, Technical Note PEAR 83003 (August 1983)
Hubbard, G.S., May, E.C., and Puthoff, H.E., “Possible Production of Photons During a
Remote Viewing Task:
Preliminary Results,” Proceedings of the 28th Convention of the
Parapsychological Association,
(Radin, D.I, ed.) Tufts University, Medford, MA,
(August 1985)
Jahn, R.G., Dunne,
B.J., and Jahn, E.G., "Analytical Judging Procedure for Remote
Perception Experiments,” The Journal of Parapsychology, Vol. 44, No.
3, pp. 207-231
(September 1980).
Utts, J.M., and May, E.C., “An Exact Method for Combining P-values,” Proceedings of the
28th Convention of the Parapsychological Association,
(Radin, D.I, ed.) Tufts
University, Medford, MA, (August 1985)
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APPENDIX B
PSI EXPERIMENTS WITH RANDOM NUMBER GENERATORS;
META-ANALYSIS PART 1
(This Appendix Is Unclassified)
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