Hypothesis
Periods of collective attention or emotion in widely
distributed populations will correlate with deviations from
expectation in a global network of physical random number
generators.
The formal hypothesis of the original event-based experiment is very broad.
It posits that engaging global events will correlate with
deviations in the data.
We use "operational definitions" to
establish unambigously what is done in the experiment.
The identification of events and the
times at which they occur are specified case by case, as are
the statistical recipes.
The approach explicitly preserves some latitude of choice,
as is appropriate for an experiment exploring new territory.
Accepting loose criteria for event identification allows exploration
of a variety of categories, while the specification of
a rigorous, simple hypothesis test for
each event in the formal series assures valid statistics.
These are combined to yield a confidence level for
the composite of all formal trials.
This "bottom line" constitutes a general test of the broadly defined formal
hypothesis, and characterizes a well-understood database for
further analysis.
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Analytical Recipes
For a more up to date discussion of formal analysis, see The GCP
Event Experiment by Bancel and Nelson, 2008, and Exploring
Global Consciousness by Nelson and Bancel, 2010 (in
press, actually -- so the link will be dead for a while).
The formal events are fully specified in a
hypothesis registry. Over the years, several different
analysis
recipes were invoked, though most analyses specify the
"network variance" (Squared Stouffer Z). A few specify
the "device variance", which is
the inter-RNG variance (Sum of Z^2).
After the first few months, during which several statistical
recipes were tried, the network variance (netvar) became the "standard method"
which was adopted for almost all events in the formal series.
The event-based experiment
thus has explored several potentially useful analyses, but
has focused primarily on the netvar.
The event statistics usually are calculated at the trial
level -- 1 second -- though other blocking is possible.
The trial statistics are combined across the total time of
the event to yield the formal result.
The results table
has links to details of the analyses, typically including a "cumulative
deviation" graph tracing the history of the second-by-second
deviations during the event, leading to the terminal value
which is the test statistic.
The following table shows the precise algorithms for
the basic statistics used in the analyses.
Control Data
It is possible to generate various kinds of controls, including
matched analysis with a time offset in the actual database, or matched
analysis using a pseudorandom clone database. However, the most general
control analysis is achieved by comparisons with the empirical distributions of the test
statistics.
The event data comprise less than 2% of the whole database,
and the non-event data can be used for resampling to produce
a distribution of
"control" events with the parameters of the formal events,
but random start times.
These provide a rigorous control background and confirm the
analytical results for the formal series of hypothesis tests.
See the figure below, created by Peter Bancel using a
reduced dataset beginning December 1998 and ending December
2009,
which compares the cumulative formal
result against a background of 500 resampled controls.
Compound Result
Over the 12 years since the inception of the project, over 325
replications of the basic hypothesis test have been accumulated.
The composite result
is a statistically
significant departure from expectation of roughly 6 standard
deviations as of late 2010.
This strongly supports the formal hypothesis, but more
important, it provides a sound basis for deeper analysis
using refined methods to
re-examine the original findings and extend them using
other methods. These potentials are developed in recent papers,
including The GCP
Event Experiment by Bancel and Nelson, 2008.
The full formal dataset as of April 2012 is shown in the next figure, where
it is compared with a background of simulated pseudo-event
sequences by drawing
random Z-scores from the (0,1) normal distribution. As
in the resampling case, it is obvious that the real data are
from a different population. Note, however, that it takes a
few dozen events to reach a point where the real score
accumulation is clearly distinguishable from the
simulations.
Sharpening the Focus
The focus of our effort turns now to a more comprehensive program of
rigorous analyses and incisive questions intended to characterize the
data more fully and to facilitate the identification of any non-random
structure.
We begin with thorough documentation of the analytical and
methodological background for the main result, to provide a
basis for new hypotheses and experiments. The goal is to
increase both the depth and breadth of our assessments, to develop
models that can help distinguish classes of potential explanations.
Essentially, we are looking for good tools that will give us
a better understanding of the data deviations.
Deeper Assessments
A variety of analyses have been undertaken to establish the
quality of the data and characterize the output of individual devices
and the network as a whole.
The first stage is a careful search for any data that are problematic
because of equipment failure or other mishap. Such data are removed.
With all bad data removed,
each individual REG or RNG can be
characterized to provide empirical estimates for statistical parameters.
This also allows a shift of analytical emphasis from the events to
trial-level data in order to extract more structural
information from the database.
The approach is to convert the database into a normalized, completely
reliable data resource that facilitates rigorous analysis.
The trial-level data allow a richer
assessment of the multi-year database using sophisticated statistical and
mathematical techniques.
We
can use a broader range of statistical tools to look for small but reliable
changes from expected random distributions that may be correlated with
natural or human-generated variables.
Real Devices vs Theory
Ideally, the trials recorded from the REGs follow the
binomial [200, 0.5] distribution, with expected mean 100, variance
50. However, although they all are high-quality random sources, perfect
theoretical performance is not
expected for these real-world devices. A logical XOR of the raw
bit-stream with a fixed pattern of bits with exactly 0.5 probability
compensates mean biases of the regs.
After XOR'ing, the mean is
guaranteed over the long run to fit theoretical expectation. The trial
variances remain biased, however. The biases are small (about 1 part in
10,000) and generally stable on long timescales. We treat
them as real, albeit tiny biases that need to be corrected by normalization for
rigorous analysis.
They are corrected by converting the trialsums for each individual egg
to standard normal variables (z-scores), based on the emprirical standard
deviations.
Deeper Analysis of the
Event-based Experiment
The normalized and standardized data resource allows us to do a rigorous
re-analysis of the experiment. The result is little
different from the original analysis, but provides
confidence in the foundation for new analytical
investigations. These include the development of orthogonal,
independent measures of structure in the event data, and
examination of questions of temporal and spatial structure
implicit in the general hypothesis. A recent (2008) assessment is detailed
in The GCP
Event Experiment by Bancel and Nelson, Journal of
Scientific Exploration, March 2008.