APPLICATIONS OF DECISION AUGMENTATION THEORY

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• Publication Date: August 25, 1994
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Applications
of
Decision Augmentation Theory
by
Edwin C. May, Ph.D
Science Applications International Corporation
Menlo Park, CA
Jessica M. Utts, Ph.D.
University of California, Davis
Division of Statistics
Davis, CA
and
S. James Spottiswoode (Consultant), Christine L. James
Science Applications International Corporation
Menlo Park, CA
Abstract
Decision Augmentation Theory (DAT) provides an informational mechanism for a class of anomalous
mental phenomena which have hitherto been viewed as a causal, force-like, mechanism. Under the
proper conditions, DAT's predictions for micro-anomalous perturbation databases are different from
those of all force-like mechanisms, except for one degenerate case. For large random number genera-
tor (RNG) databases, DAT predicts a zero slope for a least squares fit to the (Z2, n) scatter diagram,
where n is the number of bits resulting from a single run and Z is the resulting Z-score. We find a slope of
(1.73?3.19) X 10-6 (t = 0.543, df = 126, p :!~ 0.295) for the historical binary random number generator
database. In a 2-sequence length analysis of a limited set of RNG data from the Princeton Engineering
Anomalies Research laboratory, we find that a force-like explanation misses the observed data by 8.6-u;
however, the observed data is within 1.1-u of the DAT prediction. We also apply DAT to one PRNG
study and find that its predicted slope is not significantly different from the expected value. We review
and comment on six published articles that discussed DAT's earlier formalism (i.e., Intuitive Data Sort-
ing-IDS). Our DAT analysis of Braud's hemolysis study confirms his finding in favor of a causal model
over a selection one (i.e.,p < 0.023); so far, this is the only studywe have found that supports anomalous
perturbation (AP). We provide six circumstantial arguments, which are based upon experimental out-
comes against the perturbation hypothesis. Our anomalous cognition (AC) research suggests that the
quality of AC data is proportional to the total change of Shannon entropy. We demonstrate that the
change of Shannon entropy of a binary sequence from chance is independent of sequence length; thus,
we have provided a fundamental argument in favor of DAT over causal models. In our conclusion, we
suggest that, except for one degenerate case, the physical RNG database cannot be explained by any causal
model, and that Braud's contradicting evidence should inspire more AP investigations of biological systems
in a way that would allow a valid DAT analysis.
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Introduction
May, Utts, and Spottiswoode (1994) proposed Decision Augmentation Theory (DAT) as a general
model of anomalous mental phenomena (AMP)." DAT holds that anomalous cognition (AC) informa-
tion is included along with the usual inputs that result in a final human decision that favours a "desired"
outcome. In statistical parlance, DAT says that a slight, systematic bias is introduced into the decision
process byAC.
This 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. May et al. (1994) mathe-
matically developed this concept and constructed a retrospective test algorithm than can he applied to
existing databases. In this paper, we summarize the theoretical predictions of DAT, review the criteria
for valid retrospective tests, and analyze the historical random number generator (RNG) database. In
addition, we summarize the findings from one prospective test of DAT (Radin and May, 1985) and com-
ment on the published criticisms of an earlier formulation, which was then called Intuitive Data Sorting.
We conclude with a discussion of RNG results that provide a strong circumstantial argument against a
causal explanation. As part of this review, we show that one biological-AP experiment is better de-
scribed by an influence model (Braud, 1990).
Review of Decision Augmentation Theory
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). Examples of X might be the hit rate in an RNG experiment when the
number of binary bits in the sequence is large, the swimming velocity of cells, or the mutation rate of
bacteria. Let Ybe 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, and let Z be the
appropriate Z-score corresponding to Y. Often this may he 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 then values resulting from one decision point. In the exam-
ples above, n is the sequence length of a single run in an RNG experiment, the number of swimming cells
measured during the trial, or the number of bacteria-containing test tubes present during the trial.
Under DAT, we assume that the underlying parent distribution of a physical system remains unper-
turbed; however, the measurements of the physical system are systematically biased by anAC-mediated
informational process. Since the deviations seen in actual experiments tend to be small in magnitude, it
is safe to assume that the measurement biases are small and that the sampling distribution will remain
normal; therefore, we assume the bias appears as small shifts of the mean and variance of the sampling
distribution as:
Z -- MY', az).
The Cognitive Sciences Laboratory has adopted the term anomalous mental phenomena instead of the more widely knownpsi.
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 in that they do not imply
mechanisms. These new terms will be used throughout this paper.
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This notation means that Z is distributed as a normal distribution with a mean of ,ec, and a standard
deviation of oZ. Under the null hypothesis, = 0.0 and aZ = 1.0.
Review of a Causal Model
For comparison sake, we summarize a model forAP interactions. We begin with the assumption that a
putative AP force would give rise to a perturbational interaction. What we mean is that given an en-
semble of entities (e.g., random binary bits), a small force perturbs, on the average, each member of the
ensemble. We call this type of interaction perturbational AP (PAP).
In the simplest PAP model, the perturbation induces a change in the mean of the parent distribution but
does not effect its variance. We parameterize the mean shift in terms of a multiplier of the initial stan-
dard deviation. Thus:
/1i =YO + -AP (70,
where ?l and ?p are the means of the perturbed and unperturbed distributions, respectively, and where
ap is the standard deviation of the unperturbed distribution. eAp can be considered theAP effect size.
Under the null hypothesis for binary RNG experiments, u, = Ito = 0.5, ap = 0.5, and eqp = 0.
The expected value and variance of Z2 under the mean-chance-expectation (MCE), PAP, and DAT as-
sumptions for the normal distribution are shown in Table 1. The details of the calculations can be found
in May, Utts, and Spottiswoode (1994).
Quantit
Mechanism
y
MCE
PAP
DAT
E(Z2)
1
1 + e,~,Pn
Itz + a;
Var(ZZ)
2
2(1 + 2E2 p n)
2(a= + 2fczoz)
Figure 1 displays these theoretical calculations for the three mechanisms graphically.
E(Z2)
Figure 1. Predictions of MCE, PAP, and DAT.
large
4
PAP
small
DAT
MCE
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This formulation predicts grossly different outcomes for these models and, therefore, is ultimately ca-
pable of separating them, even for very small perturbations.
Retrospective Tests
It is possible to apply DAT retrospectively to any body of data that meets 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 ideally should be those in
which experiment participants are blind to n, and where the distribution of n does not contain extreme
outliers.
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 weighted least square
fit to a straight line. Table 1 shows that for the PAP model, the slope of the resulting fit is the square of
the AP-effect size. 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 maybe interpreted as an AC strength parameter for DAT. In other words, an intercept larger
than one would support the DAT model, while a slope greater then zero would support he PAP model.
Monte Carlo Verification
The expressions shown in Table I are representations which arise from simple algebraic manipulations
of the basic mathematical assumptions of the PAP and DAT models. To verify that these expressions
give the expected results, we used a published pseudo random number generator (Lewis, 1975) with
well-understood properties to produced data that mimicked the results under three models (i.e., MCE,
PAP and DAT). Our standard implementation of the PRNG allows the integers in the range (0,215-1]
as potential seeds. For the sequence lengths 100, 500, 1000, and 5000, we computed Z-scores for all
possible seeds with an effect size of 0.0 to simulate MCE and an effect size of 0.03 to simulate PAP. We
used the fact that if the effect size varies as 1 / Vn, DAT and PAP are degenerate to simulate DAT. For
this case we used effect sizes of 0.030, 0.0134, 0.0095, and 0.0042 for the above sequence lengths, respec-
tively. Figures 2a-c show the results of 100 trials, which were chosen randomly from the appropriate
Z-score data sets, at each of the sequence lengths for each of the models. In each Figure, MCE is indi-
cated by a horizontal solid line a ZZ = 1.
The slope of a least squares fit computed under the MCE simulation was - (2.81+2.49) x 10-6, which
corresponded to ap-value of 0.812 when tested against zero, and the intercept was 1.007?0.005, which
corresponds to ap-value of 0.131 when tested against one. Under the PAP model, an estimate of the
effect size using the expression in Table 1 was F.qp = 0.0288?0.002, which is in good agreement with
0.03, the value that was used to create the data. Similarly, under DAT the slope was -(2.44?57.10) x
10-8, which corresponded to a p-value of 0.515 when tested against zero, and the intercept was
1.050?0.001, which corresponds to ap-value of 2.4 x 10-4 when tested against one.
Thus, we are able to say that the Monte Carlo simulations confirm the simple formulation shown in
'Fable 1.
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0
1200 2400 3600 4800
(a)
0 1200 2400 3600 4800 6000
(b)
0.0
0 1200 2400 3600 4800 6000
Figure 2. Z2vs n for Monte Carlo Simulations of MCE, PAP, and DAT.
Historical Binary RNG Database
Radin and Nelson (1989) analyzed the complete literature (i.e., over 800 individual studies) of con-
sciousness-related anomalies in random physical systems. They eloquently demonstrated that a robust
statistical anomaly exists in that database. Although they analyzed this data from a number of perspec-
tives, they report an average Z / Vn effect size of approximately 3 x 10-4, regardless of the analysis
type. Radin and Nelson did not report p-values, but they quote a mean Z of 0.645 and a standard devi-
ation of 1.601 for 597 studies. We compute a single-mean t-score of 9.844, df = 596 (p < 3.7 X 10-23
We returned to the original publications of all the binary RNG studies from those listed by Radin and
Nelson and identified 128 studies in which we could compute, or were given, the average Z-score, the
number of runs, N, and the sequence length, n, which ranged from 16 to 10,000. For each of these stud-
ies we computed:
Z2=fI2+(N- 1)s;.
J
(1)
Since we were unable to determine the standard deviations of the Z-scores from the literature, we as-
sumed that sZ = 1.0 for each study. In addition, if aim directions were reported, we inverted the Z-score
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for the negative aim since the DAT analysis is fundamentally two-tailed. We see from Table 1 that under
MCE the expected variance is 2.0 so that the estimated standard deviations for the 72 from Equation 1
is ,'2 N.
Figure 3 shows a portion of the 128 data points (Z2 n). MCE is shown as a solid line (i.e., Z2 = 1), and
the expected best-fit lines for two assumedAP effect sizes of 0.01 and 0.003, respectively, are shown as
short dashed lines. We calculated a weighted (i.e., using N/2.0 as the weights) least squares fit to an a +
b*n straight line for the 128 data points and display it as a long-dashed line. For clarity, we have offset
and limited the Z2 axis and have not shown the error bars for the individual points, but the weights and
all the data were used in the least squares fit. We found an intercept of a = 1.036?0.004. The 1-stan-
dard error for the intercept is small and is shown in Figure 3 in the center of the sequence range. The
t-score for the intercept being different from 1.0 (i.e., t = 9.1, df = 126, p C 4.8 X 10-20) is in good
agreement with that derived from Raclin and Nelson's analysis. Since we set standard deviations for all
the Z's equal to one; and since Raclin and Nelson showed that the overall standard deviation was 1.6, we
would expect that our analysis would he more conservative than theirs.
The important result, however, was that the slope of the best-fit line was h = (1.73?3.19) X 10-6
(t = 0.543, df = 126, p C 0.295), which is not significantly different from zero. The 1-0 standard error for
the slope encompasses zero. Even though a very small AP effect size might fit the data at large sequence
lengths, it is clear in Figure 3 what happens at small sequence lengths; an e4p = 0.003, suggests a linear
fit that is significantly below the actual fit.
0 2000 4000 6000 8000 10000
Sequence Length (n)
Figure 3. Binary RNG Database: Slope and Intercept for Best Fit Line
The sequence lengths from this database are not symmetric nor are they distributed and do contain
ourliers (i.e., median = 64, average = 566). Figure 4 shows that the lower half of the data, however, is
symmetric and nearly uniformly distributed (i.e., median = 35, average = 34). Since the criteria for a
valid retrospective test is that n should be uniform, we analyzed the two median halves independently.
The intercept for the weighted best-fit line for the uniform lower half is a = 1.022?0.006 (t = 3.63, df =
62, p G 2.9 x 10-4), and the slope is b = (-0.034?3.70) x 10-4 (t = -0.010, df = 62,p< 0.504). The
Cep = 0.0 ,
o
o
Best Fit
intercept SE=
a: 1.036?0.004 h: (1.730?3.194) X 10-6
t: 9.10, df = 126 t: 0.543, df = 126
p: 4.8 X 10-20 p: 0.295
e?p=0.003
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fits for the upper half yield a = 1.064?0.005 (t = 13.47, df = 62, p < 1.2 x 10-4') and b =
(-4.52?2.38) X 10-6 (t = -1.903, df = 62, p < 0.969), for the intercept and slope, respectively.
Since the best retrospective test for DAT is one in which the distribution of n contains no outliers, the
statistically zero slope for the fit to the lower half of the data is inconsistent with a simple AP model.
Although the same conclusion could he reached from the fits to the database in its entirety (i.e., Figure
3), we suggest caution in that this fit could possibly be distorted by the distribution of the sequence
lengths. That is, a few points at large sequence lengths can easily influence the slope. Since the slope for
the upper half of the data is statistically slightly negative, it is problematical to assign an imaginaryAP
effect size to these data. More likely, the results are distorted by a few outliers in the upper half of the
data.
0.00 f I
0 20
Sequence Length (n)
Figure 4. Historical Database: Distribution of Sequence Lengths < 64.
From these analyses, it appears that Z2 does not linearly depend upon the sequence length; however,
since the scatter is so large, even a linear model is not a good fit (i.e.,X2 = 171.2, df = 125, p< 0.0038),
where X2 is a goodness-of-fit measure in general given by:
Xz z
_ z (Yi - ~i)
where the aj are the errors associated with data point yj, fj is the falue of the fitted function at point j, and
v is the number of data points.
A "good" fit to a set of data should lead to a non-significant X2. The fit is not improved by using higher
order polynomials (i.e.,X2 = 170.8, df = 124,-X2= 174.1, df= 123; for quadratics and cubics, respective-
ly). If, however, the AP effect size was any monotonic function of n other than the degenerate case
where theAP effect size is exactly proportional to 1 / \/n, it would manifest as a non-zero slope in the
regression analysis.
Within the limits of this retrospective analysis, we conclude for RNG experiments that we must reject all
causal models of AP which propose a shift of the mean of the parent distribution.
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Princeton Engineering Anomalies Research Laboratory RNG Data
The historical database we analyzed does not include the extensive RNG data from the Princeton Engi-
neering Anomalies Research (PEAR) laboratory since their total number of hits exceeds the total
amount in the entire historical database. For example, in a recent report Nelson, Dobyns, Dunne, and
Jahn (1991) analyze 5.6 x 106 trials all at n = 200. In this section, we apply DAT retrospectively to their
published work where they have examined other sequence lengths; however, even in these cases, they
report over five times as much data as in the historical database.
Jahn (1982) reported an initial RNG data set with a single operator at n = 200 and 2,000. Data were
collected both in the automatic mode (i.e., a single button press produced 50 trials at n) and the manual
mode (i.e., a single button press produced one trial at n). From a DAT perspective, data were actually
collect at four values of n (i.e., 200, 2000, 200 x 50 = 10,000, and 2000 x50 = 100,000). Unfortunately
data from these two modes were grouped together and reported only at 200 and 2, 000 bit/trial. It would
seem, therefore, we would be unable to apply DAT to these data. Jahn, however, reports that the differ-
ent modes "...give little indication of importance of such factors in the overall performance." This qual-
itative statement suggests that the PAP model is indeed not a good description for these data, because,
under PAP, we would expect stronger effects at the longer sequence lengths.
Nelson, Jahn, and Dunne (1986) describe an extensive RNG and pseudorandom RNG (PRNG) data-
base in the manual mode only (i.e., over 7 x 106 trials); however, whereas Jahn provide the mean and
standard deviations for the hits, Nelson et al. report only the means. We are unable to apply DAT to
these data, because any assumption about the standard deviations would be highly amplified by the
massive data set.
As part of a cooperative agreement in 1987 between PEAR and the Cognitive Sciences Program at SRI
International, we analyzed a set of RNG data from a single operator.* Since they supplied the raw data
for each button press, we were able to analyze this data at two extreme values of n. We combined the
individual trial Z-scores for the high and low aims by inverting the sign of the low-aim scores, because
our analysis is two-tailed, in that we examine Z2.
Given that the data sets at n = 200 and 100,000 were independently significant (Stouffer's Z of 3.37 and
2.45, respectively), and given the wide separation between the sequence lengths, we used DAT as a ret-
rospective test on these two data points.
Because we are examining only two values of n, we do not compute a best-fit slope. Instead, as outlined
in May, Utts, and Spottiswoode (1994), we compare the PAP prediction to the actual data at a single
value of n.
At n = 200, 5918 trials yielded Z = 0.044 ? 1.030 and Z-2 = 1.063 ? 0.019. We compute aproposedAP
effect size Z /x/200 = 3.10 x iO-3. With this effect size, we computed what would be expected under
thePAP model at n = 100,000. Using the theoretical expressions in Table 1, we computed 72 = 1.961 t
0.099. The 1-sigma error is derived from the theoretical variance divided by the actual number of trials
(597) at n = 100,000. The observed values were Z = 0.100 ? 0.997 and 7 = 1.002 ? 0.050. A t-test
between the observed and expect values of Z2 gives t = 8.643, df = 1192. Considering this t as equivalent
to a Z, the data at n = 100,000 fails to meet what would be expected under the causal PAP model by
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8.6-a. Suppose, however, that the effect size observed at n = 100,000 (3.18 X 10-4) better represents
theAP effect size. We computed the predicted value of Z2 = 1.00002 ? 0.018 for n = 200. Using at-test
for the difference between the observed value and this predicted one gives t = 2.398, df=11,834. The
PAP model fails in this direction by more than 2.4-a. DAT predicts that Z2 would be statistically equiva-
lent at the two sequence lengths, and we find that to be the case (t = 1.14, df = 6513, p < 0.127).
Jahn (1982) indicates in their 1982 PEAR RNG data that "Traced back to the elemental binary samples,
these values imply directed inversion from chance behavior of about one or one and a half bits in every
one thousand...." Assuming 1.5 excess bits/1000, we calculate an AP effect size of 0.003, which is consis-
tent with the observed value in their n = 200 data set. Thus, we are forced to conclude that this data set
from PEAR is inconsistent with the simple PAP model, and that Jahn's statement is not a good descrip-
tion of the anomaly.
We urge caution in interpreting these calculations. As is often the case in a retrospective analysis, some
of the required criteria for a meaningful test are violated. These data were not collected when the oper-
ators were blind to the sequence length. Secondly, these data represent only a fraction of PEAR's RNG
database.
A Prospective Test of DAT
In developing a methodology for future tests, Radin and May (1986) worked with two operators who
had previously demonstrated strong AP ability in RNG studies. They used a pseudorandom number
generator (PRNG), which was based on a shift-register algorithm by Kendell and has been shown to
meet the general criteria for "randomness" (Lewis, 1975), to create the binary sequences so that timing
considerations could be examined.
The operators were blind to which of nine different sequences (i.e., n = 101, 201, 401, 701, 1001, 2001,
4001, 7001, 10001 bits)* were used in any given trial, and the program was such that the trials lasted for a
fixed time period and feedback was presented only after the trial was complete. Thus, the criteria for a
valid test of DAT had been met, except that the source of the binary hits was a PRNG.
We re-analyzed the combined data from this experiment with the current Z-score formalism of DAT.
For the 200 individual runs (i.e. 10 at each of the sequence lengths for each of the two participants) we
found the best fit line to yield a slope = 4.3 X 10-8 + 1.6 X 10-6 (t = 0.028, df = 8, p S 0.489) and an
intercept = 1.16 ? 0.06 (t = 2.89, df = 8, p < 0.01). The slope easily encompasses zero and is not
significantly different from zero, the significance level is consistent with what Radin and May reported
earlier.
Since the PRNG seeds and bit streams were saved for each trial, it was possible to determine if the ex-
periment sequences exactly matched the ones produced by the shift register algorithm; they did. Since
our UNIX-based Sun Microsystems workstations were synchronized to the system clock, any momen-
tary interruption of the clock would "crash" the machine, but no such crashes occurred. Therefore, we
believe no casual interaction occurred.
To explore the timing aspects of the experiment Radin and May reran each run with PRNG seeds rang-
ing from -5 to +5 clock ticks (i.e., 20 ms/tick) from the actual seed used in the run. We plot the resulting
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run effect sizes, which we computed from the experimental F-ratios (Rosenthal, 1991), for operator 531
in Figure 5. The estimated 1-standard errors are the same for each seed shift and equal 0.057.
0.00 L_ .._--- 1 -..---._..--1
-6 -.2 0 2 4 6
Figure 5. Seed Timing for Operator 531 (298 Runs).
Radin and May erroneously concluded that the significant differences between zero and adjacent seed
positions was meaningful, and that the DAT ability was effective within 20 milliseconds. In fact, the
situation shown in Figure 5 is expected. Differing from true random number generators in which slight
changes in timing produce essentially the same sequence, PRNGs produced totally different sequences
as a function of single digit seed changes. Thus, itwould be surprising if the seed-shift display produced
anything but a spike at seed shift zero. We will return to this point in Our analysis of some of the pub-
lished remarks on our theory.
From this prospective test of DAT, we conclude that for PRNGs it is possible to select a proper entry
point into a bit stream to produce significant deviations from MCE that are independent of sequence
length.
The Literature: Review and Comment
We have identified six published articles that have commented upon the Intuitive Data Sorting (IDS)
theory, the earlier name for DAT. In this section, we chronologically summarize and comment on each
report.
Walker - September 1987
In his first of two criticisms of IDS, Walker (1987) suggested that his Monte Carlo simulations did not fit
the predictions of the IDS model. He generated a single deviant set of 100 hits (i.e., Z = 2.33, p C 0.01),
and he inserted this same sequence as the first 100 bits of 400 otherwise randomly generated sequences
ranging from 100 to 106 hits in length. Walker's analysis of these sequences did not yield a least square's
slope of -0.5 as predicted under the IDS formalism. Walker concluded that the IDS theory was incor-
rect. Walker's sequences, however, are not the type that are generated in AP experiments or the type for
which the DAT/IDS model is valid.
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May et al. (1985) were explicit about the character of the sequences that fit the IDS model. Specifically,
Walker quotes May et a]. "Using psi-acquired information, individuals are able to select locally deviant
subsequences from a large random sequence." (Italics are used in the original May paper.) The very next
sentence on page 249 of the reference says, "Such an ability, if mediated by precognition, would allow
individuals (subjects or experimenters) to initiate a collection unit of continuous samples (this has been
reported as a trial, a block, a run, etc.) in such a way as to optimize the final result. (Italics added here for
emphasis.) Walker continued, "Indeed, the only way the subject can produce results that agree with the
data is to wait for an extra-chance run that matches the experimental run length." In the final analysis,
Walker actually supported our contention that individuals select deviant subsequences. Both from our
text and the formalism in our 1.985 paper, it is clear that what we meant by a "large random sequence,"
was large compared to the trial length, n.
In his second criticism of IDS in the same paper, Walker proposed that individuals would have to exhibit
a physiologically impossible control over timing (e.g., when to press a button). As evidence apparently
in favor of such an exquisite timing ability, he referred to the data presented by Radin and May (1986)
that we have discussed above. (Please see Figure 5.) Walker suggested that Radin and May's result,
therefore, supported his quantum mechanical observer theory. It is beyond the scope of this paper to
critique Walker's quantum mechanical models, but we would hope they do not depend upon his analysis
of Radin and May's results. The enhanced hitting at zero seed and the suppressed values f one 20 ms
clock tick that we show in Figure 5 is the expected result based upon the well-understood properties of
PRNG's and does not represent the precision of the operator's reaction time.
We must consider how it is possible with normal human reactions to obtain significant scores, which can
only happen in 20 ms windows. In typical visual reaction time measurements, Woodworth and Schlos-
berg (1960) found a standard deviation of 30 ms. If we assume these human reactions are typical of
those forAC performance and are normally distributed, we compute the maximum probability of being
within a 20 ms window, which is centered about the mean, of 23.5%. For the worst case, the operators
must "hit" significant seeds less often than 23.5% of the time. Radin and May do not report the number
of significant runs, so we provide a worst-case estimate. Given that they quote ap-value of 0.005 for 500
trials, we find that 39 trials must be independently significant. That is, the accumulated binomial proba-
bility is 0.005 for 39 hits in 500 trials with an event probability of 0.05. This corresponds to a hitting rate
(i.e., 39/500) of only 7.8%, a value well within the capability of human reaction times. We recognize that
it is not a requirement to hit only on significant seeds; however, all other seeds leading to positive Z-
scores are less restrictive then the case we have presented.
The zero-center "spike" in Figure 5 misled Walker and others into thinking that exceptional timing was
required to produce the observed deviations. As we have shown this is not the case, and, therefore,
Walker's second criticism of the IDS theory is not valid.
Bierman - 1988
Bierman (1988) attempted to test the IDS model with a gifted subject. His experimental design ap-
peared to meet most of the criteria for a valid test of the model; however, Bierman found no evidence
forAMP and stated that no conclusions could be drawn from his work. We encourage Bierman to con-
tinue with this design and to he specific with what he would expect to see if DATwere the correct mecha-
nism compared to if it were not.
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Braud and Schlitz - 1989
Braud and Schlitz (1989) conducted an electrodermal PK experiment specifically to test the IDS model.
They argued that if the mechanism of the effect were informational, then allowing participants more
opportunities to select locally deviant values of the dependent variable should yield stronger effects. In
their experiment, 12 electrodermal sampling epochs were either initiated individually by a press of a
button, or all 12 were determined as a result of the first button press. Braud and Schlitz hypothesized
that under IDS, they would expect to see a larger overall effect in the former condition. They found that
the single button press data yielded a significant result; whereas the multiple press data scored at chance
(tsing1el31] = 2.14, tmultel3lf = -0.53). They concluded, therefore, that their data were more consistent
with an influence mechanism than with an informational one.
In both button-press conditions, the dependent variable was averaged over all 12 epochs; therefore, the
formalism discussed in this paper cannot be applied because the data should have been averaged over at
least two different values. The idea of multiple decision points, however, is still valid. As stated in their
paper, the timing of the epochs was such that 20 seconds of the 30 second epoch was independent of the
button-press condition and could not, therefore be subjected to a DAT-like selection. To examine the
consequence of this overlap, we computed the effect size for the single button case as 0.359 (Rosenthal,
1991, Page 19, Equation 2.16). Since data for the 20 seconds is the same in each condition, the operator
can only make AC-mediated decisions for the first 10 seconds of the data. If we assume that on the
average the remaining 20 seconds meets mean chance expectation and the effect size is constant, then
we would expect an effect size of (0.359 + 0 + 0) / 3 = 0.119. * The measured effect size was 0.095, which
is consistent with this prediction.
Braud and Schlitz's idea was good and provides a possible way to use DAT effectively. Because of the
epoch timing and the consistency of the effect sizes, however, we believe they have interpreted their
results in favor of causal mechanism prematurely. Aside from the timing issues, their protocol compli-
cates the application of DAT further. To observe an enhanced effect because of multiple decision
points, Z-scores should be computed for each decision and combined as a Stouffer's Z where the de-
nominator is the square root of the number of decision points. In their protocol, they only combine the
dependent variable.
Vassy -1990
Vassy (1990) used a similar timing argument to refute the IDS model as did Walker (1987). Vassy gener-
ated PRNG single bits at a rate of one each 8.7 ms. He argued that if IDS were operating, that a subject
would be more likely to identify bursts of ones rather than single ones given the time between consecu-
tive bits. While he found significant evidence for the primary task of "selecting" individual bits, he
found no evidence that these hits were imbedded in excess clusters of ones.
We compute that the maximum probability of a hit within an $.71nswindow centered on the mean of the
normal reaction curve with a standard deviation of 30 ms (Woodworth and Schlosberg, 1960) is 11.5%.
Vassy quotes an overall Z-score for 100 runs of 2.39. From this, we compute a mean Z of 0.239 for each
run of 36 bits. To obtain this result requires an excess hitting of 0.717 bits, which corresponds to an ex-
Asa function of n, DA Tpred icts a 1I /n dependency in the effect size; however, at a fixed n, as in this case, the effect size should
be constant.
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cess hitting rate of 2%. Given that 11.5% is the maximum one can expect with normal human reaction
times, Vassy's results easily allow for individual bit selection, and, thus, cannot be used to reject the DAT
model on the basis of timing.
Braud -1990
In a cooperative effort with SRI International, Braud (1990) conducted a biological AP study with hu-
man red blood cells as the target system. The study was designed, in part, as a prospective test of DAT, so
all conditions for a valid test were satisfied. Braud found that a significant number of individuals were
independently able to "slow" the rate of hemolysis (i.e., the destruction of red blood cells in saline solu-
tion) in what he called the "protect" mode. Using data from the nine significant participants, Braud
found support in favor of PAP over DAT. Figure 6 shows the results of our re-analysis of all of Braud's
raw data using our more modern formalism of DAT.
O Effort Data
^ Control Data
x Predicted AP
? Predicted DAT
-2L L _ .
0 2 4 6 8 10
Number of Test Tubes
Figure 6. DAT Analysis of Hemolysis Data.
The solid line indicates the theoretical expected value for MCE. The squares are the mean values of Z2
for the control data, and the error bars indicate the l-standard error for the 32 trials in the study. We
notice that the control data with eight test tubes is significantly below MCE (t = -2.79, df = 62, p C
0.996). Compared to the MCE line, the effort data is significant (t = 4.04, df = 31, p :!E~ 7.6 x 10-5) for
eight test tubes and nearly so for n = 2 (t = 2.06, df = 31, p ~ 0.051). The x at n = 8 indicates the
calculated value of the mean of Z2 assuming that the effect size at n = 2 was entirely because of AP;
similarly, the X at n = 2 indicates the calculated value assuming that the effect size, which was observed
at n = 8, was totally due to AR These AP predictions are not significantly different from the observed
data (t = 0.156, p < 0.431, df = 62 and t = 0.906, p < 0.184, df = 62, at n = 2 and 8, respectively).
Whereas DAT predicts no differences between the data at the end points for n, we find a significant
difference (t = 2.033, p < 0.023, df = 62). That is, to a statistical degree the data at n = 8, cannot be
explained by selection alone. Thus, we concur with Brand's original conclusion; these results indicate a
possible causal relationship between mental intent and biological consequences.
It is difficult to conclude from our analysis of a single study with only 32 trials thatAP is part of nature;
nonetheless, this result is very important. It is the first data we have encountered that supports the PAP
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hypothesis, which is in direct opposition to the substantial support against PAP resulting from the analy-
sis of the RNG data sets. In addition, May and Vilenskaya (1993) .and Vilenskaya and May (1994) re-
port that the preponderance ofAMP research in the Former Soviet Union is the study ofAP on biologi-
cal systems. Their operators, as do ours, report their internal experiences as being a causal relationship
between them and their biological targets.
Dobyns - 1993
Dobyns (1993) presents a method for comparing what he calls the "influence" and "selection" models,
corresponding to what we have been calling DAT and PAP. He uses data from 490 "tripolar sets" of
experimental runs at PEAR. For each set, there was a high aim, a baseline and a low aim condition.
The three values produced were then sorted into which one was actually highest, in the middle, and
lowest for each set. The data were then summarized into a 3 x 3 matrix, where the rows represented the
three intentions, and the columns represented the actual ordering. If every attempt had been success-
ful, the diagonal of the matrix would consist of the number of tripolar sets, namely 490. We present the
data portion of Dobyns' Table from page 264 of the reference as our Table 2:
Scoring Data From Dobyns (1993)
t
l
A
Intention
c
ua
High
Middle
Low
Total
High
180
167
143
490
Baseline
159
156
175
490
Low
151.
167
172
490
Total
490
490
490
Dobyns computes an aggregate likelihood ratio of his predictions for the DAT and PAP models and con-
cludes in favor the the influence model with a ratio of 28.9 to one.
However, there are serious problems with the methods used in Dobyns' paper. In this paper we simply
outline only two of the difficulties. To fully explain them would require a level of technical discussion
not suitable for a short summary such as this.
One problem is in the calculation of the likelihood ratio function using Equation 6, which we reproduce
from page 265 of the reference:
"1 112 11.1 Pi n' PPs "3
P1 P2 z
where p and q are the predicted rank frequencies for each aim under the influence and selection models,
respectively, and the n are the observed frequencies for each aim. We agree that this relationship cor-
rectly gives the likelihood ratio for comparing the two models for one row of Table 2. However, immedi-
ately following that equation, Dobyns writes, "The aggregate likelihood of the hypothesis over all three
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intentions may be calculated by repeating the individual likelihood calculation for each intention, and
the total likelihood will simply be the product of factors such as (6) above for each of the three inten-
tions."
That statement is simply incorrect. A combined likelihood is found by multiplying the individual likeli-
hoods only if the random variables are independent of each other (DeGroot, 1986, p. 145). Clearly, the
rows of the table are not independent. In fact, if you know any two of the rows, the third is determined
exactly! The correct likelihood ratio needs to build that dependence into the formula.*
A second technical problem with the conclusion that the data support the influence model is that the
method itself strongly supports the influence model. As noted by Dobyns, "In fact, applying the test to
data sets that, by construction, contain no effect, yields strong odds (ranging, in a modest Monte Carlo
database, from 8.5 to over 100) in favor of the influence model (page 268)." The actual data in his paper
yielded odds of 28.9 to one in favor of the influence model; however, this value is well within the re-
ported limits from his "influence-less" Monte Carlo data.
Under DAT it is possible thatAC-mediated selection might occur at the protocol level, but the primary
way is through timing-initiating a run to capitalize upon a locally deviant subsequence. How this might
work in dynamic RNG devices is clear; wait until such a deviant sequence is in your immediate future
and initiate the run in time to capture it. With "static" devices, such as PEAR's random mechanical
cascade (RMC) device, how timing enters in is less obvious. Under closer inspection, however, even
with the RMC device there is a statistical variation among unattended control runs. That is, there is
never a series of control runs that give exactly the same mean. Physical effects, such as Browian motion,
temperature gradients, etc., can account for the observed variance in the absence of human operators.
Thus, when a run is initiated to capture favorable local "environmental" factors, even for "static" de-
vices, remains the operative issue with regard to DAT Dobyns does not consider this case at all in his
analysis. If DAT enters in at the protocol selection, as it probably does, it is likely to be a second-order
contribution because of the limited possibilities from which to select (i.e., six in the tripolar case).
Finally, a major problem with Dobyns' conclusion, which was pointed out when he first presented this
paper at a conference (May, 1990), is that the likelihood ratio supports the influence model even for
their PRNG data. Dobyns dismisses this finding (page 268) all too easily given the preponderance of
evidence that suggest that no influence occurs during PRNG studies (Radin and May, 1986).
Aside from the technical flaws in Dobyns' likelihood ratio arguments, and even ignoring the problem
with the PRNG analysis, we reject his conclusions simply because they hold in favor of influence even in
Monte Carlo-constructed and unperturbed data.
Circumstantial Evidence Against an AP Model for RNG Data
Experiments with hardware RNG devices are not new. In fact, the title of Schmidt's very first paper on
the topic (1969) portended our conclusion, "Precognition of a Quantum Process." Schmidt listsPKas a
third option after two possible sources for precognition, and remarks, "The experiments done so far do
not permit a distinction (if such a distinction is at all meaningful) between the three possibilities." From
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A lications of Decision Augmentation Theory ugust 1 4
1969 onward, the RNG research has been strongly oriented toward a PK model. The term micro-PK,
itself, embeds the force concept further into the lexicon of RNG descriptions.
In this section, we examine a number of RNG experimental results that provide circumstantial evidence
against the AP hypothesis. Any single piece of evidence could be easily dismissed; however, taken to-
gether, they demonstrate a substantial case against AP.
Internal Complexity of RNG Devices and Source Independence
Schmidt (1974) conducted the first experiment to explore potential dependencies upon the internal
workings of his generators. Since by definition AP implies a force or influence, it seemed reasonable to
expect that an influence should depend upon the details of the target system. In this study, one genera-
tor produced individual binary bits, which were derived from the fl-decay of 90Sr, while the other
"binary" output was a majority vote from 100 bits, each of which were derived from a fast electronic
diode. Schmidt reports individually significant effects with both generators, yet does not observe a sig-
nificant difference between the generators.
This particular study is interesting, quite aside from the timing and majority vote issues; the binary
streams were derived from fundamentally different physical sources. Radioactive p-decay is governed
by the weak nuclear force, and electronic devices (e.g., noise diodes) are governed by the electromag-
netic force. Schematically speaking, the electromagnetic force is approximately 1,000 times as strong as
the weak nuclear force, and modern high-energy physics has shown them to be fundamentally different
after about 10-10 seconds after the big bang (Rahy, 1985). Thus, a Putative AP-force would have to
interact equally with these two forces; and since there is no mechanism known that will cause the elec-
tromagnetic and weak forces to interact with each other, it is unlikely thatAP will turn out to be the first
coupling mechanism. The lack of difference between n-decay and noise diode generators was con-
firmed years later by May et al. (1980).
We have already commented upon one aspect of the timing issue with regard to Radin and May's (1986)
experiment and the papers by Walker (1987) and Vassy (1990). May (1975) introduced a scheme to
remove any first-order biases in binary generators that also is relevant to the timing issue. The output of
his generator was a match or anti-match between the random bit stream and a target hit. One mode of
the operation of the device, which May describes, included an oscillating target hit-one oscillation per
bit at approximately 1 MHz rate.* May and Honorton (1975) and Honorton and May (1975) reported
significant effects with the RNG operating in this mode. Thus, significant effects can be seen even with
devices that operate in the microsecond time domain, which is three orders of magnitude faster than
any known physiological process.
Effects with Pseudorandom Number Generators
Pseudorandom number generators are, by definition, those that depend upon an algorithm, which is
usually implemented on a computer. Radin (1985) analyzed all the PRNGs commonly in use and found
that they require a starting value (i.e., a seed), which is often derived from the computer's system clock.
As we noted above, Radin and May (1986) showed that the bit stream, which proved to he "successful"
in a PRNG study, was bit-for-bit identical with the stream, which was generated later, but with the same
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Applications of Decision Augmentation eory
seed. With that generator, at least, there was no change from the expected bit stream. Perhaps it is
possible that the seed generator (i.e., system clock) was subjected to some AP interaction. We propose
two arguments against this hypothesis:
(1) Even one cycle interruption of a computers' system clock will usually invoke a system crash; an
event not often reported in PRNG experiments.
(2) Computers use crystal oscillators as the basis for their internal clocks. Crystal manufacturers usual-
ly quote errors in the stated oscillation frequency of the order of 0.001 percent. That translates to
500 cycles for a 50 MHz crystal, or to 10 is in time. Assuming that the quoted error is a 1-a estimate,
and that a putative AP interaction acts at within the ? 2-o domain, then shifting the clock by this
amount might account for only one seed shift in Radin and May's experiment. By Monte Carlo
methods, we determined that, given a random entry into seed-space, the average number of ticks to
reach a "significant" seed is 10; therefore, even if AP could shift the oscillators by 2-o, it cannot
account for the observed data.
Since computers in PRNG experiments are not reported as "crashing" often, it is safe to assume that
PRNG results are only due toAC. In addition, since the results of PRNG studies are statistically insepa-
rable from those reported with true RNGs, it is also reasonable to assume that the mechanisms are simi-
larly A C-based.
Precognitive AC
Using the tools of modern meta-analysis, Honorton reviewed the precognition card-guessing database
(Honorton and Ferarri, 1989). This analysis included 309 separate studies reported by 62 investigators.
Nearly two million individual trials were contributed by more the 50,000 subjects. The combined effect
size was s = 0.020?0.002, which corresponds to an overall combined effect of 11.4x. TWO important
results emerge from Honorton's analysis. First, it is often stated by critics that the best results are from
studies with the least methodological controls. To check this hypothesis, Honorton devised an eight-
point quality measure (e.g., automated recording of data, proper randomization techniques) and
scored each study with regard to these measures. There was no significant correlation between study
quality and study score. Second, if researchers improved their experiments over time, one would expect
a significant correlation of study quality with date of publication. Honorton found r = 0.246, df = 307, p
C 2 x 10-7. In brief, Honorton concludes that a statistical anomaly exists in this data that cannot be
explained by poor study quality or a large variety of other hypotheses; therefore, a potential mechanism
underlying DAT has been verified.
SRI International's RNG Experiment
May, Humphrey, and Hubbard (1980) conducted an extensive RNG study at SRI International in 1979.
They applied state-of-the-art engineering and methodology to construct two true RNGs, one based on
the a-decay of 137Pm and the other based on an MD-20 noise diode from Texas Instruments. It is be-
yond the scope of this paper to describe, in detail, the intricacies of this experiment; however, we will
discuss those aspects, which are pertinent to this discussion.
Technical Details
Each of the two sources were battery operated and optically coupled to a Digital Equipment Corpora-
tion LSI 11/23 computer. Fail-safe circuitry would disable the sources if critical physical parameters
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(e.g., battery voltages and currents, temperature) exceed preset ranges. Both sources were subjected to
environmental testing which included extreme temperature cycles, vibration tests, E&M and nuclear
gamma and neutron radiation tests. Both sources behaved as expected, and the critical parameters,
such as temperature, were monitored and their data stored along with the experimental data.
A source was sampled at 1 KHz rate. After eight milliseconds, the resulting byte was sent to the comput-
erwhile the next byte was being obtained. In this way, a continuous stream of 1 ms data was presented to
the computer. May et al. had specified, in advance, that bit number 4 was the designated target bit.
Thus each byte provided 3 ms of bits prior to the target and 4 ms of hits after the target bit.
A trial was defined as a definitive outcome from a sequential analysis of hit four from each byte. In
exchange for not specifying the number of samples in advance, sequential analysis requires that the
Type I and Type II errors, and the chance and extra-chance hitting rate he specified in advance. In May
et al.'s two-tailed analysis, (x = (1 = 0.05 and the chance and extra-chance hitting rate was 0.50 and 0.52,
respectively. The expected number of samples to reach a definitive decision was approximately 3,000.
The outcome from a single trial could be in favor of a hitting rate of 0.52, 0.48, or at chance of 0.50, with
the usual risk of error in accordance with the specified Type I and Type II errors.
Each of seven operators participated in 100 trials of this type. For an operator's data to reach indepen-
dently statistical significance, the operator had to produce 16 successes in 100 trials, where a successwas
defined as extra-chance hitting (i.e., the exact binomial probability of 16 successes for 100 trials with an
event probability of 0.10 is 0.04 where one less success is not significant). Two operators produced 16
and 17 successful trials, respectively.
Temporal Analysis
We analyzed the 33 trials from the two independently significant operators from May et al.'s experi-
ment. Each of the 33 trials consisted of approximately 3,000 bits of data with -3 bits and +4 bits of 1
ms/bit temporal history surrounding the target hit. We argue that if the significance observed in the
target bits was because of AP, we would expect a large correlation with the target hit's immediate neigh-
bors, which are only ? 1 ms away. As far as we know, there is no known physiological process that can be
cognitively, or in any other way, manipulated within a millisecond. We might even expect a 100% cor-
relation under the complete AP model.
We computed the linear correlation coefficients between bits 3 and 4, 4 and 5, and 3 and 5. For binary
data:
NO2 - XZ(df = 1),
where q5 is the linear correlation coefficient and N is the number of samples. Since we examined three
different correlations for 33 trials, we computed 99 different values of NN2. Four of them producedX2s
that were significant-well within chance expectation. The complete distribution is shown in Figure 7.
We see that there is excellent agreement of the 99 correlations with the X2 distribution for one degree of
freedom, which is shown as a smooth curve.
We conclude, therefore, that there was no evidence beyond chance to suggest that the target bit neigh-
bors were affected even when the target bit analysis produced significant evidence for an anomaly. So,
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knowing the physiological limitations of the human systems, we further concluded that the observed
effects could not have arisen due to a human-mediated force (i.e., AP).
0
r 0.30
cd
,Jj 0.20
4.
0.00..~L~~~~......~1_~~I.,`,
0 7. 3 4 5
X2 (df = 1)
Figure 7. Observed and Theoretical Correlation Distributions.
Mathematical Model of the Noise Diode
Because of the unique construction parameters of Texas Instrument's MD-20 noise diode, May et al.
were able to construct a quantum mechanical model of the detailed workings of the device. This model
contained all known properties of the material and it's construction parameters. For example, the band
gap energy in Si, the effective mass of an electron or hole in the semiconductor, and the impurity con-
centration were among the parameters for the model. The model was successful at calculating the
diode's known and measured behavior as a function of temperature. May et al. were able to simulate
their RNG experiment down to the quantum mechanical details of the noise source. They hoped that
by adjusting the model's parameters so that the computed output agreed with the experimental one,
that they could gain insight as to where the causal influence "entered" the device.
May et al. were not able to find a set of model parameters that mimicked their RNG data. For example,
changing the band gap energy for short periods of time; increasing or reducing the electron's effect
mass; or redistributing or changing the impurity content produced no unexpected changes in the device
output. The only device behavior that could be effected was its known function of temperature.
Because of the construction details of the physical RNG, this result could have been anticipated. The
changes that could be simulated in the model were all in the microsecond domain because of the details
of the device. Both with the RNG and in its model, the diode's multi-MHz output was filtered by a
100-KHz wide bandwidth filter. Thus, any microsecond changes would not pass through the filter. In
short, because of this filtering, the RNG was particularly insensitive to potential changes of the physical
parameters of the diode.
Yet solid statistical evidence for an anomaly was seen by May et al. Since the diode device was shown
mathematically and empirically to he insensitive to environmental and physical changes, these results
must have been as a result ofA C rather than any causalAP. In fact, this observation coupled with the bit
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timing argument, which we have described above, lead May et al. to question causality in RNG studies
in general.
Summary of Circumstantial Evidence Against AP
We have identified six circumstantial arguments that, when taken together, provide increasingly diffi-
cult requirements that must be met by a putative AP force. In summary, the RNG database demon-
strates that:
(1) Data are independent of internal complexity of the hardware RNG device.
(2) Data are independent of the physical mechanism producing the randomness (i.e., weak nuclear or
electromagnetic).
(3) Effects with pseudorandom generators are statistically equivalent to those observed with true
hardware generators.
(4) Reasonable AP models of mechanism do not fit the data.
(5) In one study, bits which are ? 1 ms from a "perturbed" target hit are themselves unperturbed.
(6) A detailed model of a diode noise source, which includes all known physics of the device, could not
simulate the observed data streams.
In addition, AC, which is a mechanism to describe the data, has been confirmed in non-RNG experi-
ments. We conclude, therefore, an AP force that is consistent with the database must
? Be equally coupled to the electromagnetic and weak nuclear forces.
? Be mentally mediated in times shorter than one millisecond.
? Follow a 1 /V n law.
For these to be true, an AP force would he at odds with an extensive amount of verified physics and
common behavioral observables. We are not saying, therefore, thatAP cannot exist; rather, we are sug-
gesting that instead of having to force ourselves to invent a whole new science, we should look for ways
in which AP might fit into the present world view. In addition, as DAT tries to accomplish, we should
invent non-causal and testable alternate mechanisms for the experimental observables.
Conclusions
We have shown that DAT can determine whether a causal or informational explanation is more consis-
tent with a given set of anomalous statistical data. In applying DAT to the substantial physical RNG
database, we showed that an informational mechanism is strongly favored over a large class of perturba-
tional ones. Given that one possible information mechanism (i.e., precognitive AC) can, and has been,
independently confirmed in the laboratory, and given the weight of the empirical, yet circumstantial,
arguments taken together against AP, we conclude that the anomalous results from the RNG studies
arise not because of a mentally mediated force, but rather because of a human ability to be a mental
opportunist by makingAC-mediated decisions to capitalize on the locally deviant circumstances.
Our recent results in the study of anomalous cognition (May, Spottiswoode, and James, 1994) suggest
the the quality of AC is proportional to the change in Shannon entropy. Following Vassy (1990), we
compute the change in Shannon entropy for an extra-chance, binary sequence of length n. The total
change of entropy is given by:
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V
AS= SO S,
where for an unbiased binary sequence of length n, S, = n, and S is given by:
S = - np,log2p1 - n(1 -pi)log2(1 -P1)?
Letpl = 0.5 (1 + s) and assume that c, the effect size, is small compared to one (i.e., typical RNG effect
sizes are of the order of 3 x 10-4). Using the approximation:
ln(1 + E) = E -,
we find that S is given by:
S = n - n 21n2'
or that the total change of entropy for a biased binary sequence is given by;
AS= So - S=n F2
21n2'
Since our analysis of the historical RNG database shows that the effect size is proportional to 1 / Vn
(i.e., Z-score is independent of n), the total change of Shannon entropy becomes a constant that is inde-
pendent of the sequence length. Thus, if entropy is related to what is being sensed by anomalous cogni-
tion, then this argument suggests that informational processes are responsible for the RNG anomaly.
The one exception to this conclusion is Braud's study of AP on red blood cells. It may be that there is
something unique about living systems that can account for this observation. On the other hand, it is the
only biological AP study we could find that could be analyzed by DAT, and the perturbation hypothesis is
only weakly favored over the selection one (i.e., p C 0.023). Before we would be willing to declare that
AP is a valid mechanism, more than a single, albeit well designed and executed, study is needed.
Generally, we suggest that future RNG, PRNG, and biological AP studies be designed in such away that
the criteria, as outlined in this paper and in May, Utts, Spottiswoode (1994), are adhered to for a valid
DAT analysis. Our discipline has evolved to the point where we can no longer be satisfied with yet one
more piece of evidence of a statistical anomaly. We must identify the sources of variance as suggested
by May, Spottiswoode, and James (1994); limit them as much as possible; and apply models, such as
DAT, which can begin to shed light on the physical, physiological, and psychological mechanisms of
anomalous mental phenomena.
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