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Decision Augmentation Theory: Toward a Model 8
Decision Augmentation Theory:
Toward a Model
of
Anomalous Mental Phenomena
by
Edwin C. May, Ph.D
Science Applications International Corporation
Menlo Park, CA
Jessica M. Utts, Ph.D.
University of California, Davis
Department of Statistics
Davis, CA
and
S. James P. Spottiswoode
Science Applications International Corporation (Consultant)
Menlo Park, CA
Abstract
Decision Augmentation Theory (DAT) holds that humans integrate information obtained by anoma-
lous cognition into the usual decision process. The result is that, to a statistical degree, such decisions
are biased toward volitional outcomes. We introduce DAT and define the domain for which the model
is applicable. In anomalous mental phenomena research, DAT is applicable to the understanding of
effects that are within a few sigma of chance. We contrast the experimental consequences of DAT with
those of models that treat anomalous perturbation as a causal force. We derive mathematical expres-
sions for DAT and causal models for two distributions, normal and binomial. DAT is testable both retro-
spectively and prospectively, and we provide statistical power curves to assist in the experimental design
of such tests. We show that the experimental consequences of DAT are different from those of causal
models except for one degenerate case.
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Decision Augmentation Theory: Toward a Model of AMP
Introduction
We do not have positive definitions of the effects that generally fall under the heading of anomalous
mental phenomena (AMP). * In the crassest of terms, AMP is what happens when nothing else should, at
least as nature is currently understood. In the domain of information acquisition, or anomalous cogni-
tion (AC), it is relatively straightforward to design an experimental protocol (Honorton et al., 1990,
Hyman and Honorton, 1986) to assure that no known sensory leakage of information can occur. In the
domain of causation, or anomalous perturbation (AP), however, it is very difficult, if not impossible
(May, Humphrey, and Hubbard, 1980 and Hubbard, Bentley, Pasturel, and Issacs, 1987); thus, making
the interpretation of results equally difficult.
We can divide AP into two categories based on the magnitude of the putative effect. Macro-AP include
phenomena that generally do not require sophisticated statistical analysis to tease out weak effects
from the data. Examples include inelastic deformations in strain gauge experiments, the obvious bend-
ing of metal samples, and a host of possible "field phenomena" such as telekinesis, poltergeist, tele-
portation, and materialization. Conversely, micro-AP covers experimental data from noisy diodes, ra-
dioactive decay and other random sources. These data show small differences from chance expectation
and require statistical analysis.
One of the consequences of the negative definitions of AMP is that experimenters must assure that the
observables are not due to "known" effects. Traditionally, two techniques have been employed to guard
against such interactions:
(1) Complete physical isolation of the AP-target system.
(2) Counterbalanced control and effort periods.
Isolating physical systems from potential "environmental" effects is difficult, even for engineering spe-
cialists. It becomes increasingly problematical the more sensitive the Macro-AP device. For example
Hubbard, Bentley, Pasturel, and Issacs (1987) monitored a large number of sensors of environmental
variables that could mimic AP effects in an extremely isolated piezoelectric strain gauge. Among these
were three-axis accelerometers, calibrated microphones, and electromagnetic and nuclear radiation
monitors. In addition, the sensors were mounted in a government-approved enclosure to assure no
leakage (in or out) of electromagnetic radiation above a given frequency, and the enclosure itself was
levitated on an air suspension table. Finally, the entire setup was locked in a controlled access room
which was monitored by motion detectors. The system was so sensitive, for example, that it was possible
to identify the source of a perturbation of the strain gauge that was due to innocent, gentle knocking on
the door of the closed room. The financial and engineering resources to isolate such systems rapidly
become prohibitive.
The second method, which is commonly in use, is to isolate the target system within the constraints of
the available resources, and then construct protocols that include control and effort periods. Thus, we
trade complete isolation for a statistical analysis of the difference between control and effort periods.
The assumption implicit in this approach is that environmental influences of the device will be random
* The Cognitive Sciences Laboratory has adopted the term anomalous mentalphenomena instead of the more widely known psi.
Likewise, we use the terms anomalous cognition and anomalous perturbation for ESP and PK, respectively. We have done so
because we believe that these terms are more naturally descriptive of the observables and are neutral with regard to mecha-
nisms. These new terms will be used throughout this paper.
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and uniformly distributed in both the control and effort conditions, while AP will tend to occur in the
effort periods. Our arguments in favor of an anomaly, then, are based on statistical inference and we
must consider, in detail, the consequences of such analyses, one of which implies a generalized model
for AMP.
Background
As the evidence for AMP becomes more widely accepted (Bem and Honorton, 1994, Utts, 1991, Radin
and Nelson, 1989) it is imperative to determine the underlying mechanisms of the phenomena. Clearly,
we are not the first to begin thinking of potential models. In the process of amassing incontrovertible
evidence of an anomaly, many theoretical approaches have been examined; in this section we outline a
few of them. It is beyond the scope of this paper, however, to provide an exhaustive review of the
theoretical models of AMP; a good reference to an up-to-date and detailed presentation is Stokes
(1987).
Brief Review of Models
Two fundamentally different types of models have been developed: those that attempt to order and
structure the raw observations in AMP experiments (i.e., phenomenological), and those that attempt to
explain AMP in terms of modifications to existing physical theories (i.e., fundamental). In the history of
the physical sciences, phenomenological models, such as the Snell's law of refraction or Ampere's law
for the magnetic field due to a current, have nearly always preceded fundamental models of the phe-
nomena, such as quantum electrodynamics and Maxwell's theory. In producing useful models of AMP it
may well be advantageous to start with phenomenological models, of which DAT is an example.
Psychologists have contributed interesting phenomenological approaches. Stanford (1974a and 1974b)
proposed PSI-mediated Instrumental Response (PMIR) as a descriptive model. PMIR states that an
organism uses AMP to optimize its environment. For example, in one of Stanford's classic experiments
(Stanford, Zenhausern, Taylor, and Dwyer 1975) subjects were offered a covert opportunity to stop a
boring task prematurely if they exhibited unconscious AP by perturbing a hidden random number gen-
erator. Overall, the experiment was significant in the unconscious tasks; it was as if the participants
were unconsciously scanning the extended environment for any way to provide a more optimal situation
than participating in a boring psychological task!
As an example of a fundamental model, Walker (1984) proposed a literal interpretation of quantum
mechanics in that since superposition of eigenstates holds, even for macrosystems, AMP might be due
to macroscopic examples of quantum phenomena. These concepts spawned a class of theories, the so-
called observation theories, that were based either upon quantum formalism conceptually or directly
(Stokes, 1987). Jahn and Dunne (1986) have offered a "quantum metaphor" which illustrates many
parallels between AMP and known quantum effects. Unfortunately, these models either have free pa-
rameters with unknown values, or are merely hand waving metaphors and therefore have not led to test-
able predictions. Some of these models propose questionable extensions to existing theories. For ex-
ample, even though Walker's interpretation of quantum mechanical formalism might suggest wave-like
properties of macrosystems, the physics data to date not only show no indication of such phenomena at
room temperature but provide considerable evidence to suggest that macrosystems lose their quantum
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Decision Augmentation Theory: Toward a Model of AMP
coherence above 0.5 Kelvins (Washburn and Webb, 1986) and no longer exhibit quantum wave-like be-
havior.
This is not to say that a comprehensive model of AMP will not eventually require quantum mechanics as
part of its explanation, but it is currently premature to consider such models as more than interesting
speculation. The burden of proof is on the theorist to show why systems, which are normally considered
classical (e.g., a human brain), are, indeed, quantum mechanical. That is, what are the experimental
consequences of a quantum mechanical system over a classical one?
Our Decision Augmentation Theory is phenomenological and is a logical and formal extension of Stan-
ford's elegant PMIR model. In the same manner as early models of the behavior of gases, acoustics, or
optics, it tries to subsume a large range of experimental measurements into a coherent lawful scheme.
Hopefully this process will lead the way to the uncovering of deeper mechanisms. In fact DAT leads to
the idea that there may be only one underlying mechanism of all AMP effects, namely a transfer of in-
formation between events separated by negative time intervals.
Historical Evolution of Decision Augmentation
May, Humphrey, and Hubbard (1980) conducted a careful random number generator (RNG) experi-
ment. What makes this experiment unique is the extreme engineering and methodological care that
was taken in order to isolate any potentially known physical interactions with the source of randomness.
It is beyond the scope of this paper to describe this experiment completely; however, those specific de-
tails which led to the idea of Decision Augmentation are important for the sake of historical complete-
ness.
May, Humphrey, and Hubbard were satisfied in that RNG study, that they had observed a genuine sta-
tistical anomaly. In addition, because of an accurate mathematical model of the random device and the
engineering details of the experiment, they were equally satisfied that the deviations were not due to
any known physical interactions. They concluded, in their report, that some form of AMP-mediated
data selection had occurred. They named it then Psychoenergetic Data Selection.
Following a suggestion by Dr. David R. Saunders of MARS Measurement and Associates, we noticed
in 1986 that the effect size in binary RNG studies varied on the average as the square root of the number
of bits in the sequence. This observation led to the development of the Intuitive Data Sorting model that
appeared to describe the RNG data to that date (May, Radin, Hubbard, Humphrey, and Utts, 1985).
The remainder of this paper describes the next step in the evolution process. We now call the model
Decision Augmentation Theory (DAT).
Decision Augmentation Theory-A General Description
Since the case for AC-mediated information transfer is now well established, it would be exceptional if
we did not integrate this form of information gathering into the decision process. For example, we rou-
tinely use real-time data gathering and historical information to assist in the decision process. Perhaps,
what is called intuition may play a important role. Why, then, should we not include AC information?
DAT holds that AC information is included along with the usual inputs that result in a final human deci-
sion that favours a "desired" outcome. In statistical parlance, DAT says that a slight, systematic bias is
introduced into the decision process by AC.
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P
This philosophical concept has the advantage of being quite general. We know of no experiment that is
devoid of at least one human decision; thus, DAT might be the underlying basis for AMP. To illustrate
the point, we describe how the "cosmos" determines the outcome of a well-designed, hypothetical ex-
periment. To determine the sequencing of an RNG experiment, suppose that the entry point into a
table of random numbers will be chosen by the square root of the barometric pressure as stated in the
weather report that will be published seven days hence in the New York Times. Since humans are notori-
ously bad at predicting or controlling the weather, this entry point might seem independent of a human
decision; but why did we "chose" seven days in advance? Why not six or eight? Why the New York Times
and not the London Times? DAT would suggest that the selection of seven days, the New York Times, the
barometric pressure, and square root function were optimal choices, either individually or collectively,
and that other decisions would not lead to as significant an outcome.
Other non-technical decisions may also be biased by AC in accordance with DAT. When should we
schedule a Ganzfeld session; who should be the experimenter in a series; how should we determine a
specific order in a tri-polar protocol?
It is important to understand the domain in which a model is applicable. For example, Newton's laws
are sufficient to describe the dynamics of mechanical objects in the domain where the velocities are very
much smaller than the speed of light, and where the quantum wavelength of the object is very small
compared to the physical extent of the object. If these conditions are violated, then different models
must be invoked (e.g., relativity and quantum mechanics, respectively).
The domain in which DAT is applicable is when experimental outcomes are in a statistical regime (i.e., a
few standard deviations from chance). In other words, does the measured effect occur under the null
hypothesis? This is not a sharp-edged requirement and DAT becomes less apropos the more a single
measurement deviates from mean-chance-expectation (MCE). We would not invoke DAT, for exam-
ple, as an explanation of levitation if one found the authors hovering near the ceiling!
All this may be interesting philosophy, but DAT can be formulated mathematically and subjected to rig-
orous examination.
Development of a Formal Model
While DAT may have implications for AMP in general, we develop the model in the framework of un-
derstanding experimental results. In particular, we consider AP vs AC in the form of DAT in those ex-
periments whose outcomes are in the few-sigma, statistical regime.
We define four possible mechanisms for the results in such experiments:
(1) Mean Chance Expectation, The results are at chance. That is, the deviation of the dependent vari-
able meets accepted criteria for MCE. In statistical parlance, we have measurements from an un-
perturbed parent distribution with unbiased sampling.
(2) Anomalous Perturbation. Nature is modified by some anomalous interaction. That is, we expect a
causal interaction of a "force" type. In statistical parlance, we have measurements from a perturbed
parent distribution with unbiased sampling.
(3) Decision Augmentation. Nature is unchanged but the measurements are biased. That is, AC in-
formation has "distorted" the sampling. In statistical parlance, we have measurements from an
unperturbed parent distribution with biased sampling.
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(4) Combination. Nature is modified and the measurements are biased. That is, both AP and AC are
present. In statistical parlance, we have conducted biased sampling from a perturbed parent dis-
tribution.
General Considerations
Since the formal discussion of DAT is statistical, we will describe the overall context for the development
of the model from that perspective. Consider a random variable, X, that can take on continuous values
(e.g., the normal distribution) or discrete values (e.g., the binomial distribution). Examples of X might
be the hit rate in an RNG experiment, the swimming velocity of cells, or the mutation rate of bacteria.
Let Y be the average computed over n values of X, where n is the number of items that are collectively
subjected to an AMP influence as the result of a single decision-one trial. Often this may be equivalent
to a single effort period, but it also may include repeated efforts. The key point is that, regardless of the
effort style, the average value of the dependent variable is computed over the n values resulting from
one decision point. In the examples above, n is the sequence length of a single run in an RNG experi-
ment, the number of swimming cells measured during the trial, or the number of bacteria-containing
test tubes present during the trial.
Assumptions for DAT
We assume that the parent distribution of a physical system remains unperturbed; however, the mea-
surements of the physical system are systematically biased by some AC-mediated informational pro-
cess.
Since the deviations seen in experiments in the statistical regime tend to be small in magnitude, it is safe
to assume that the measurement biases might also be small; therefore, we assume small shifts of the
mean and variance of the sampling distribution. Figure 1 shows the distributions for biased and un-
biased measurements.
Unbiased -
4- Biased
11-+
-
po= 0
Mz
Normalized Sampling Variable Z = (u - Mo) In
Figure 1. Sampling Distribution Under DAT.
The biased sampling distribution shown in Figure 1 is assumed to be normally distributed as:
Z ~ N(2, 02),
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where the notation means that Z is distributed as a normal distribution with a mean of uz and a standard
deviation of oz.
Assumptions for an AP Model
For comparison sake, we develop a model for AP interactions. With a few exceptions reported in the
poltergeist literature, AP appears to be a relatively "small" effect in laboratory experiments. That is, we
do not readily observe anomalous and obvious mental interactions with the environment. Thus, we be-
gin with the assumption that a putative AP force would give rise to a perturbational interaction. What
we mean is that given an ensemble of entities (e.g., binary bits, cells), a force acts, on the average, equal-
ly on each member of the ensemble. We call this type of interaction perturbational AP (PAP).
Figure 2 shows a schematic representation of probability density functions for a parent distribution un-
der the PAP assumption and an unperturbed parent distribution. In the PAP model, the perturbation
induces a change in the mean of the parent distribution but does not effects its variance. We parameter-
ize the mean shift in terms of a multiplier of the initial standard deviation. Thus, we define an AP-effect
size as:
EAp = 4]
(16) - 110)
,
where u1 and po are the means of the perturbed and unperturbed distributions, respectively, and where
Og is the standard deviation of the unperturbed distribution.
Probability Density
00
μη= μο + ε Άρδο
Dependent Variable
Figure 2. Parent Distribution for Perturbational AP.
For the moment, we consider EAp as a parameter which, in principle, could be a function of a variety of
variables (e.g., psychological, physical, environmental, methodological). As we develop DAT for specif-
ic distributions and experiments, we will discuss this functionality of EAp.
Calculation of E(Z2)
We compute the expected value and variance of Z2 under MCE, PAP, and DAT for the normal and bino-
mial distributions. The details of the calculations can be found in the Appendix; however, we summa-
rize the results in this section. Table 1 shows the results assuming that the parent distribution is normal.
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Table 1.
Normal Parent Distribution
Mechanism
Quantity
MCE
PAP
DAT
E(Z2)
1
1 + cấpn
u2 + 0}
Var(72)
2
2(1 + 282pn)
2(02 + 20}02)
Table 2 shows the results assuming that the parent distribution is binomial. In this calculation, po is the
binomial event probability and co = Vpo(1-po).
Table 2.
Binomial Parent Distribution
Mechanism
Quantity
MCE
PAP
DAT
E(Z2)
1
1 + Exp (n - 1) + AP (1 - 2po)
u2 + 0?
Var(Z2)
2 + nog ( 1
1(1 - 602)
1
2(1 + 282pn)*
2(02 + 24302)
* The variance shown assumes po = 0.5 and n >> 1. See the Appendix for other cases.
We wish to emphasize at this point that in the development of the mathematical model, the parameter
EAP for PAP, and the parameters uz, and oz in DAT may all possibly depend upon n; however, for the
moment, we assume that they are all n-independent. We shall discuss the consequences of this assump-
tion below.
Figure 3 displays these theoretical calculations for the three mechanisms graphically.
large
--
PAP
E(Z2)
small
DAT
MCE
n
Figure 3. Predictions of MCE, PAP, and DAT.
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Within the constraints mentioned above, this formulation predicts grossly different outcomes for these
models and, therefore, is ultimately capable of separating them, even for very small perturbations.
Retrospective Tests
It is possible to apply DAT retrospectively to any body of data that meet certain constraints. It is critical
to keep in mind the meaning of n-the number of measures of the dependent variable over which to
compute an average during a single trial following a single decision In terms of their predictions for
experimental results, the crucial distinction between DAT and the PAP model is the dependence of the
results upon n; therefore, experiments which are used to test these theories must be those in which ex-
periment participants are blind to n. In a follow-on to this theory-definition paper, we will retrospec-
tively apply DAT to as many data sets as possible, and examine the consequences of any violations of
these criteria.
Aside from these considerations, the application of DAT is straight forward. Having identified the unit
of analysis and n, simply create a scatter diagram of points (Z2, n) and compute a least square fit to a
straight line. Tables 1 and 2 show that for the PAP model, the square of the AP-effect size is the slope of
the resulting fit. A student's t-test may be used to test the hypothesis that the AP-effect size is zero, and
thus test for the validity of the PAP model. If the slope is zero, these same tables show that the intercept
may be interpreted as an AC strength parameter for DAT. The follow-on paper will describe these tech-
niques in detail.
Prospective Tests
A prospective test of DAT will not only test the AMP hypothesis against mean chance expectation, but
will also test for a PAP contribution. In such tests, n should certainly be a double-blind parameter and
take on at least two values. If you wanted to check the prediction of a linear functional relationship
between n and the E(Z2) that is suggested by PAP model, the more values of n the better. It is not pos-
sible to separate the PAP model from DAT at a single value of n.
In any prospective test, it is helpful to know the number of runs, N, that are necessary to determine with
95% confidence, which of the two models best fits the data. Figure 4 displays the problem graphically.
EAC (Z2)
EAP (72)
Probability Density
A
-- - -
ZAP - 1.645 AR
Figure 4. Model Predictions for the Power Calculation.
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Under PAP, 95% of the values of Z2 will be greater than the point indicated in Figure 4. Even if the
measured value of Z2 is at this point, we would like the lower limit of the 95% confidence interval for this
value to be greater than the predicted value under the DAT model. Or:
ZAP - 1.645AP - 1.960GA" > EAc (Z2).
Solving for N in the equality, we find:
N =
EAP (Z2) - EAC(Z2)
3.605 OAP
2
(1)
Since oAP _CAC, this value of N will always be the larger estimate than that derived from beginning with
DAT and calculating the confidence intervals in the other direction.
Suppose, from an earlier experiment, one can estimate a single-trial effect size for a specific value of n,
say n1. To determine whether the PAP model or DAT is the proper description of the mechanism, we
must conduct another study at an additional value of n, say n2. We use Equation 1 to compute how many
runs we must conduct at n2 to assure a separation of mechanism with 95% confidence, and we use the
variances shown in Tables 1 and 2 to compute @AP . Figure 5 shows the number of runs for an RNG-like
experiment as a function of effect size for three values of n2.
We chose n1 = 100 bits because it is typical of the numbers found in the RNG database and the values of
n2 shown are within easy reach of today's computer-based RNG devices. For example, assuming oz =
1.0 and assuming an effect size of 0.004, one we derived from a publication of PEAR data (Jahn, 1982),
then at n1 = 100,/2 = 0.004 x 100 = 0.04 and EAC(Z2) = 1.0016. Suppose n2 = 104. Then EAP(Z2) =
1.160 and @AP = 1.625. Using Equation 1, we find N = 1368 runs, which can be approximately obtained
from Figure 5. That is in this example, 1368 runs are needed to resolve the PAP model from DAT at n2 =
104 at the 95% confidence level. Since these runs are easily obtained in most RNG experiments, an
ideal prospective test of DAT, which is based on these calculations, would be to conduct 1500 runs ran-
domly counterbalanced between n = 102 and n = 104 bits/trial. If the effect size at n = 102 is near 0.004,
than we would resolve the AP vs AC question with 95% confidence.
105
Required Number of Runs
104
103
2 = 105
2 = 104
102
n2 = 106
101
100
0.001
0.010
0.100
AC Effect Size at n1 = 100 bits
Figure 5. Runs Required for RNG Effect Sizes
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Figure 6 shows similar relationships for effect sizes that are more typical of biological AP as reported in
the Former Soviet Union (May and Vilenskaya, 1994).
Similarly, for biological oriented AP experiments, we chose n = 2 because use two simultaneous AP
targets is easily accomplished. If we assume an effect size of 0.3 and oz = 1.0, at n2 = 10 we compute
EAC(Z2) = 1.180, EAP(Z2) = 1.900, WAP = 2.366 and N = 140, which can be approximately obtained
from Figure 6.
We have included n2 = 100 in Figure 6, because this is within reach in cellular experiments although it is
probably not practical for most biological AP experiments.
10000
Required Number of Runs
1000
100
n2 = 10
10
n2 = 20
n2 = 100
1
0.1
1.0
AC Effect Size at n1 = 2 units
Figure 6. Runs Required for Biological AP Effect Sizes
We chose n1 = 2 units for convenience. For example in a plant study, the physiological responses can
easily be averaged over two plants and n2 = 10 is within reason for a second data point. A unit could be a
test tube containing cells or bacteria; the collection of all ten test tubes would simultaneously have to be
the target of the AP effort to meet the constraints of a valid test.
The prospective tests we have described so far are conditional; that is, given an effect size, we provide a
protocol to test if the mechanism for AMP is PAP or DAT. An unconditional test does not assume any
effect size; all that is necessary is to collect data at a large number of different values of n, and fit a
straight line through the resulting Z2s. The mechanism is PAP if the slope is non-zero and may be DAT if
the slope is zero.
Discussion
We now address the possible n-dependence of the model parameters. A degenerate case arises if EAP is
proportional to Vn; if that were the case, we could not distinguish between the PAP model and DAT by
means of tests on the n dependence of results. If it turns out that in the analysis of the data from a vari-
ety of experiments, participants, and laboratories, the slope of a Z2 vs n linear least-squares fit is zero,
then either £AP = 0.0 or EAP is exactly proportional to Vn depending upon the precision of the fit (i.e.,
errors on the zero slope). An attempt might be made to rescue the PAP hypothesis by explaining the Vn
dependence of Z2 in the degenerate case as a fatigue or other time dependence effects. That is it might
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be hypothesized that human participants might become AP-tired as a function of n; however, it seems
improbable that a human-based phenomena would be so widely distributed and constant and give ex-
actly the Vn dependency in differing protocols needed to imitate DAT. We prefer to resolve the degen-
eracy by wielding Occam's razor: if the only type of AP which fits the data is indistinguishable from AC,
and given that we have ample demonstrations of AC by independent means in the laboratory, then we
do not need to invent an additional phenomenon called AP. Except for this degeneracy, a zero slope for
the fit allows us to reject all PAP models, regardless of their n-dependencies.
DAT is not limited to experiments that capture data from a dynamic system. DAT may also be the mech-
anism in protocols which utilize quasi-static target systems. In a quasi-static target system, a random
process occurs only when a run is initiated; a mechanical dice thrower is an example. Yet, in a series of
unattended runs of such a device there is always a statistical variation in the mean of the dependent
variable that may be due to a variety of factors, such as Brownian motion, temperature, humidity, and
possibly the quantum mechanical uncertainty principle (Walker, 1974). Thus, the results obtained will
ultimately depend upon when the run is initiated. It is also possible that a second-order DAT mecha-
nism arises because of protocol selection; how and who determines the order in tri-polar protocols. In
second order DAT there may be individuals, other than the formal subject, whose decisions effect the
experimental outcome and are modified by AC.
Finally, we would like to close with a clear statement of what is meant by DAT: the decisions on which
experimental outcomes depend are augmented by AC to capitalize upon the unperturbed statistical
fluctuations of the target system. In our follow-on paper, we will examine retrospective applications to a
variety of data sets.
Acknowledgements
Since 1979, there have been many individuals who have contributed to the development of DAT. We
would first like to thank David Saunders without whose remark this work would not have been. Beverly
Humphrey kept the philosophical integrity intact at times under extreme duress. We are greatly appre-
ciative of Zoltán Vassy, to whom we owe the Z-score formalism, to George Hansen, Donald McCarthy,
and Scott Hubbard for their constructive criticisms and support.
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References
Bem, D. J. and Honorton, C. (1994). Does psi exist? Replicable evidence for an anomalous process of
information transfer. Psychological Bulletin. 115, No. 1, 4-18.
Honorton, C., Berger, R. E., Varvoglis, M. P., Quant, M., Derr, P., Schechter, E. I., and Ferrari, D. C.
(1990) Psi Communication in the Ganzfeld. Journal of Parapsychology, 54, 99-139.
Hubbard, G. S., Bentley, P. P., Pasturel, P. K., and Isaacs, J. (1987). A remote action experiment with a
piezoelectric transducer. Final Report - Objective H, Task 3 and 3a. SRI International Project
1291, Menlo Park, CA.
Hyman, R. and Honorton, C. (1986). A joint communiqué: The psi ganzfeld controversy. Journal of
Parapsychology. 50, 351-364.
Jahn, R. G. (1982). The persistent paradox of psychic phenomena: an engineering perspecitve.
Proceedings of the IEEE. 70, No. 2, 136-170.
Jahn R. G. and Dunne, B. J. (1986). On the quantum mechanics of consciousness, with application to
anomalous phenomena. Foundations of Physics. 16, No 8, 721-772.
May, E. C., Humphrey, B. S., Hubbard, G. S. (1980). Electronic System Perturbation Techniques. Final
Report. SRI International Menlo Park, CA.
May, E. C., Radin, D. I., Hubbard, G. S., Humphrey, B. S., and Utts, J. (1985) Psi experiments with
random number generators: an informational model. Proceedings of Presented Papers Vol 1. The
Parapsychological Association 28th Annual Convention, Tufts University, Medford, MA, 237-266.
May, E. C. and Vilenskaya, L. (1994). Overview of Current Parapsychology Research in the Former
Soviet Union. Subtle Energies. 3, No 3. 45-67.
Radin, D. I. and Nelson, R. D. (1989). Evidence for consciousness-related anomalies in random
physical systems. Foundations of Physics. 19, No. 12, 1499-1514.
Stanford, R. G. (1974a). An experimentally testable model for spontaneous psi events I. Extrasensory
events. Journal of the American Society for Physical Research, 68, 34-57.
Stanford, R. G. (1974b). An experimentally testable model for spontaneous psi events II. Psychokinetic
events. Journal of the American Society for Physical Research, 68, 321-356.
Stanford, R. G., Zenhausern R., Taylor, A., and Dwyer, M. A. (1975). Psychokinesis as psi-mediated
instrumental response. Journal of the American Society for Physical Research, 69, 127-133.
Stokes, D. M. (1987). Theoretical parapsychology. In Advances in Parapsychological Research 5.
McFarland & Company, Inc. Jefferson NC, 77-189.
Utts, J. (1991). Replication and meta-analysis in parapsychology. Statistical Science. 6, No. 4, 363-403.
Walker, E. H. (1974). Foundations of Paraphysical and Parapsychological phenomena. Proceedings of
an International Conference: Quantum Physics and Parapsychology. Oteri, E. Ed. Parapsychology
Foundation, Inc. New York, NY, 1-53.
Walker, E. H. (1984). A review of criticisms of the quantum mechanical theory of psi phenomena.
Journal of Parapsychology. 48, 277-332.
Washburn S. and Webb, R. A. (1986). Effects of dissipation and temperature on macroscopic quantum
tunneling in Josephson junctions. In New Techniques and Ideas in Quantum Measurement Theory.
Greenburger, D. M. Ed. New York Academy of Sciences, New York, NY, 66-77.
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Decision Augmentation Theory: Toward a Model
Appendix
Mathematical Derivations for the Decision Augmentation Theory
In this appendix we develop the formalism for the Decision Augmentation Theory (DAT). We consider
cases for the mean-chance-expectation (MCE), anomalous perturbation (AP), and anomalous cogni-
tion (AC) under two assumptions-normality and Bernoulli sampling. For each of these three models,
we compute the expected values of Z and Z2, and the variance of Z2*
Mean Chance Expectation (MCE)
Normal Distribution
We begin by considering a random variable, X, whose probability density function is normal, (i.e., N(u0,
002)1). After many unbiased measures from this distribution, it is possible to obtain reasonable ap-
proximations to po and og2 in the usual way. Suppose n unbiased measures are used to compute a new
variable, Y, given by:
YK= HEXx.
Then Y is distributed as N (o, on 2), where on2 = 002/n. If Z is defined as
Z = "
YK - HO
then Z is distributed as N(0, 1) and E(Z) is given by:
EMCE(Z) = 1
-
- 00
00
8
ze - 0.522dz = 0.
(1)
Since Var(Z) = 1 = E(Z2) - E2(Z), then
8€
EMCE(Z2) = -
=
1
z2e -0.52 dz = 1.
(2)
The Var(Z2) = E(Z4) - E2(Z2) = E(Z4) - 1. But
* We wish to thank Zoltan Vassy for originally suggesting the Z2 formalism.
t Throughout this appendix, this notation means:
N(, 02) = _=- 0.5 *= 4|2.
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L'MCE(Z4) =
/2T
00
) =2º -OS2 dz = 3 .
- 00
So
VarMcr(Z2) = 2.
(3)
Bernoulli Sampling
Let the probability of observing a one under Bernoulli sampling be given by po. After n samples, the
discrete Z-score is given by:
Z = "
k - npo
where
00 = Po(1 - Po),
and k is the number of observed ones ( 0) << < n). The expected value of Z is given by:
EMCE(Z) = 1, 5 (k - npo)Bx(n, po),
Join k=0
(4)
where
B.(n,po) = (k) P:(1 - po) *-*.
The first term in Equation 4 is the E(k) which, for the binomial distribution, is npo. Thus
EMCE(Z) =
Join k=0
n
1
> (k - npo)Bk(n, po) = 0.
(5)
The expected value of z2 is given by:
EMCE(Z2) = Var(Z) + E2(Z),
Var(k - npo)
=
no?
+ 0,
nc ( 2) = mo = 1 .
(6)
As in the normal case, the Var(Z2) = E(Z4) - E2(Z2) = E(Z4) - 1. But*
* Johnson, N. L., and S. Kotz, Discrete Distributions, John Wiley & Sons, New York, p. 51, (1969).
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Decision Augmentation Theory: Toward a Model of AMP
ENICE (Z4) = -
1
MCE
n204.
0 k =0
> (k - npo)4B&(n,po)
= 3+
1(1 - 60%).
So,
+ now ( 1 .
90
Var Mı(Z2) = 2 + 02(1 - 602) = 2 - 2}, (po = 0.5).
(7)
0
Anomalous Perturbation (AP)
Normal Distribution
Under the perturbation assumption described in the text, we let the mean of the perturbed distribution
be given by uo+ Eap00, where £ap is an AP strength parameter, and in the general case may be a function
of n and time. The parent distribution for the random variable, X, becomes N(u0 + Eap00, 002). As in the
MCE case, the average of n independent values of X, is Y ~ N(up+ Eap00, Ơn2). Let
y = Ho + &ap00 + 4y,
where
dy = y - (uo + Eap00).
For a mean of n samples, the Z-score is given by
Z = :
y -Mo
Eap00 + dy
= Eap Fn +5.
where ¿ is distributed as N(0, 1) and is given by Ay / on. Then the expected value of Z is given by
EN,(Z) = EAr(Fap [n + 5) = &.ap Vn + E(S) = Eap In.
(8)
and the expected value of Z2 is given by
EN (Z2) = EAP([ap Vn + []2) = neap + E(52) + 26p VM E(5)
= 1 + can,
(9)
since E(C) = 0 and E((2) = 1.
In general, Z2 is distributed as a non-central X2 with 1 degree of freedom and non-centrality parameter
NEap2, X2(1, n&ap2). Thus, the variance of Z2 is given by'
Var™ (Z2) = 2(1 + 2nc2,).
(10)
Bernoulli Sampling
As before, let the probability of observing a one under MCE be given by po, and the discrete Z-score be
given by:
* Johnson, N. L., and S. Kotz, Continuous Univariate Distributions-2, John Wiley & Sons, New York, p. 134, (1970).
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Decision Augmentation Theory: Toward a Model of AMP
z = k - npo
Join
where k is the number of observed ones ( 0 Sk < n). Under the perturbation assumption, we let the
mean of the distribution of the single-bit probability be given by p1 = po + Eap00, where Eap is an AP
strength parameter. The expected value of Z is given by:
ER (Z) =
1
Jon k=0
>(k - npo)B(n,p1),
n
where
B&(n,P1) = (k) P(1 - P1)" -*.
The expected value of Z becomes
E" (Z) =
1
E KB(n, p1) - npo
k=0
=
(P1 - Po) Vn
00
= Eap Vn.
(11)
Since Eap = E(Z)/Vn, so Eap is also the binomial effect size. The expected value of Z2 is given by:
E' (Z2) = Var(Z) + [2(Z),
Var(k - np.)
=
no2
p1(1 - p1)
NO
+ Eapn,
=
+ 8apr
Expanding in terms of p1 = po + £ap00,
EA,(Z2) = 1 + cap(n - 1) + +gp (1 - 2po).
(12)
If po = 0.5 (i.e., a binary case) and n >> 1, then Equation 12 reduces to the E(Z2) in the normal case,
Equation 9.
We begin the calculation of Var(Z2) by using the equation for the jth moment of a binomial distribution
m; = #(q + pe)] |1=0.
Since Var(Z2) = E(Z4) - E2(Z2), we must evaluate E(Z4). Or,
År(Z4) = = {(k - npo) B(n,P1).
0 k=0
Expanding n-200-4(k-npo)4, using the appropriate moments, and subtracting E2(22), yields
Var(Z2) = Co + Cin + C_In-1.
(13)
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Decision Augmentation Theory: Towar
Where
Co= 2 - 362p + 10g4 + 8-2 (1 - 2po)(1 - 2820) + 6-4
σ
£ 2
C1 = 482,(1 - Exp) + 4% (1 - 2po), and
C_1 = 48 - 6[82 - 3/2 + 120 (1 - 2po) + (-/Exp) + EaB (1 - 2po)(12pc - 12p0 + 1).
0
Under the condition that Eap << 1 (a frequent occurrence in the perturbation approximation for AP), we
ignore any terms of higher order than Eap2. Then the variance reduces to
Var(2) = 2 - 36E2p + 8kap (1 - 2po) + 6000 + 482,n +
ñ
(1 - 782)
- 6 + 3682p +
6€2 + 20) + (1 -2p)(12p2 - 1200 + 1)
We notice that when & = 0, the variance reduces to the MCE case for Bernoulli sampling. Whenn >> 1, 8
< 1, and po = 0.5, the variance reduces to that derived under the normal distribution assumption. Or,
Var"p(Z2) = 2(1 + 2nc2).
( 14 )
Anomalous Cognition (AC)
The primary assumption for AC is that the parent distribution remains unchanged, (i.e., N(u0, 002). It
further assumes that because of a AC-mediated bias the sampling distribution is distorted leading to a
Z-distribution as N(uac, Oac2). In the most general case, fac and @ ac may be functions of n and time. Lett
be given by
The expected value of Z is given by (by definition)
EN (Z) = Mac-
( 15)
The expected value of Z2 is given by definition as
EN (Z2) = u2 + 02.
(16)
The Var(Z2) can be calculated by noticing that
2 - Xh (1, 4gr).
So the Var(Z2) is given by
Var (2) = 2(1 +2 ℃)
-
VarN (Z2) = 2(04 + 2u2002).
(17)
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As in the normal case, the primary assumption is that the parent distribution remains unchanged, and
that because of a psi-mediated bias the sampling distribution is distorted leading to a discrete Z-dis-
tribution characterized by Hac (n) and Oac2(n). Thus, by definition, the expected values of Z and Z2 are
given by
E"c(Z) = płac
E'(Z2) = Mac + 02.
(18)
For any value of n, estimates of these parameters are calculated from N data points as
1 c = + Ez, and
j=1
N
2
Z
N
-
Ở ac
~2
(N - 1)
N
The Var(Z2) for the discrete case is identical to the continuous case. Therefore
Var (Z2) = 2(0 . + 2Hà, 02.).
(19)
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Appendix: 6