Super Bowl XLIII Field RNG Demonstration (Part Two)
By, Bryan Williams
In this post, I provide a basic summary of the procedures, statistical analysis, and predictions to be used for the planned Super Bowl XLIII field random number generator (RNG) demonstration at Public Parapsychology. The methods follow those used in my previous Super Bowl field RNG explorations (coming in Part Three), and are closely modeled after those developed by the PEAR Laboratory for use in their field RNG studies (Nelson et al., 1996, 1998), and by the Global Consciousness Project for individual event analysis (Bancel & Nelson, 2008; Nelson, 2001). For more complete details, interested readers are referred to these publications, as well as to other field RNG studies that have used these same methods (e.g., Bierman, 1996; Crawford et al., 2003; Hirukawa & Ishikawa, 2004; Nelson & Radin, 2003; Rowe, 1998). We invite any questions, comments, or concerns from readers regarding these methods.
For each Super Bowl exploration, an Orion RNG  is set up to run continuously on a personal computer (PC) one hour before the football game. This PC is located in a room about twelve feet from where B.W. usually watches the televised Super Bowl broadcast in the living room of his central New Mexico (USA) home. In order to mark the occurrence of notable events (such as kickoff, the scoring of the first two goals, and the halftime period), a paper time log is kept by B.W. as he watches the game, and the time for each event is noted in Mountain Standard Time using a wristwatch that is roughly synchronized to the PC’s internal clock beforehand. The PC’s clock is itself synchronized in advance with an Internet-based timeserver to ensure accurate time. Following the game, the RNG is allowed to run for up to 15 minutes, then it is shut off and the data stored in the PC’s memory is saved to hard disk for analysis.
The PC uses a custom software package  developed by researchers at the Institute of Noetic Sciences to collect 200 random bits per second (= 1 test “trial”) from the RNG. Each bit consists of a binary number (either a “1” or a “0”) that is randomly determined by sampling the electronic noise source. For simplicity, this process can be thought of as being analogous to flipping a coin, with “heads” representing the “1”-bit, and “tails” representing the “0”-bit. When we flip a coin, each side has a 50/50 chance of turning up, and the same goes for each kind of bit (i.e., the theoretical probability of occurrence for each kind of bit is 1/2, or p = .5). Thus, the RNG can be seen as flipping 200 electronic “coins” per second. The software then counts the number of “heads” (i.e., “1”-bits) that came up in the 200 flips, and stores the number as the trial outcome value. Given the 50/50 probability of occurrence in theory, roughly 100 “heads” and 100 “tails” should be generated on average by the RNG over a long sequence of trials. In a traditional test of psychokinesis (PK), the goal is to attempt to upset this balance of heads and tails through mental intention on the RNG, such that more of one outcome is produced over the other. If the mass “group mind” effect is related to PK, then presumably the same should be observed in the field RNG data during moments of focused group attention and emotional response.
Statistical analysis of the RNG data proceeds using techniques that follow from classical statistical methods (Aron & Aron, 1997; Snedecor & Cochran, 1980). For those readers with a technical mind who are curious about the details, the following steps are taken in the analysis (those of you unfamiliar with statistics may want to skip ahead to the predictions):
1.) The trial output of the RNG follows a binomial distribution that has a theoretical mean of 100 and a theoretical standard deviation (SD) of 7.071.  To represent a basic measure of the deviation from the mean, each trial outcome value is converted into a z-score using the equation:
z = (x – M) / SD
where x is the outcome value for each trial, M is the mean, and SD is the standard deviation. Initially, the theoretical mean (100) was used for M, and the theoretical SD (7.071) for SD in the analysis of the Super Bowl data. However, it should be pointed out that, although the Orion RNGs tend to closely match the theoretical values for the binomial distribution overall, it is possible for an individual RNG to produce a small bias of the mean due to the nature of its random source. In other words, the mean and SD of each RNG should not be expected to exactly equal the theoretical values each and every time . For that reason, in May of 2007, I made the decision to begin using the mean and SD empirically calculated from all of the RNG trial outcome values for M and SD, respectively, as a way to account for any potential mean bias in the RNG. This issue becomes relevant for the results of my previous Super Bowl explorations (discussed in Part Three).
2.) Each resulting z-score is squared to form a positive value that is Chi-Square distributed, and that has one degree of freedom (df).
3.) Given that Chi-Square values can be summed together as they are in the standard calculation of the Chi-Square statistic (e.g., Aron & Aron, 1997, p. 235), all of the individual values are added together across time to represent the overall measure of the deviation from the mean in the RNG data. Their associated degrees of freedom are similarly added together. A probability value can then be obtained from the total Chi-Square and degrees of freedom.
4.) The values can be cumulatively plotted over time in a graph as Chi-Square – 1 (i.e., the 1 df is subtracted from each of the associated Chi-Square values) to visualize the trends in the RNG data as time passes.
With the accumulation of RNG data that I collected from previous Super Bowls, it is also possible to examine a combined result across all Super Bowls using a Stouffer’s Z-score, calculated by adding together the z-scores for each individual second (Step 1) from each year, then dividing by the square root of the number of scores added (the analysis then proceeds as in Steps 2 – 4). This will be done with the previous field RNG data, along with the data collected during the planned demonstration, in order to assess the combined result across five consecutive Super Bowls.
To explore a mass group mind effect, two test predictions are annually made for the Super Bowl. The first test prediction is for the football game itself, covering the time spanning from the moment of kickoff to the end of the televised broadcast (the latter was included to allow for any residual effects that may occur in conjunction with the trophy presentation and crowd response). Throughout this time period (averaging around 3.5 hours total), it is predicted that a steadily increasing non-random pattern (i.e., a positive deviation from the expected mean) will be observed in the field RNG data, which overall will be significantly different from chance (based on the resulting probability value for the total Chi-Square and df values).
Considering the excitement and focused crowd attention that is often generated by the halftime concerts, the second test prediction specifically concerns the halftime show, covering the time from the start of the halftime highlights to the beginning of the 3rd Quarter. During this halftime period (averaging around 30 minutes total), another steadily increasing non-random pattern is predicted to occur in the RNG data.
To be consistent with my previous Super Bowl explorations, both of these predictions will be further tested for the planned demonstration. In the next post, we will examine the results of my previous explorations.
The rest of the series can be found in Parts One, Three, and Four.
Bryan Williams is a Native American student at the University of New Mexico, where his undergraduate studies have focused on physiological psychology and physics. He is a student affiliate of the Parapsychological Association, a student member of the Society for Scientific Exploration, and a co-moderator of the Psi Society, a Yahoo electronic discussion group for the general public that is devoted to parapsychology. He has been an active contributor to the Global Consciousness Project since 2001.
 In brief, the Orion RNG is a small external hardware circuit that uses electronic noise as its source of randomness. It is manufactured by Orion/ICATT Interactive Media in Amsterdam, the Netherlands, and detailed specifications of the device can be found on the company’s website.
 This is the Microsoft Windows-based “FRED” software package, developed by researchers associated with the
 This value can be obtained by the statistical equation for the standard deviation of a binomial random variable: SD = Sqrt [Npq], where N is the total number of bits per trial (200), p is the theoretical probability for a bit (.5), and q = 1 – p (Utts & Heckard, 2006, Section 8.4)
 Put another way, whenever the mean and standard deviation of all the trial outcome values generated by the RNG are calculated, they should not be expected in every case to be exactly equal 100 and 7.071, respectively. Instead, they tend to fluctuate somewhere around these two values.
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Bancel, P., & Nelson, R. (2008). The GCP event experiment: Design analytical methods, results. Journal of Scientific Exploration, 22, 309 – 333.
Bierman, D. J. (1996). Exploring correlations between local emotional and global emotional events and the behavior of a random number generator. Journal of Scientific Exploration, 10, 363 – 373.
Crawford, C. C., Jonas, W. B., Nelson, R., Wirkus, M., & Wirkus, M. (2003). Alterations in random event measures associated with a healing practice. Journal of Alternative and Complementary Medicine, 9, 345 – 353.
Hirukawa, T., & Ishikawa, M. (2004). Anomalous fluctuation of RNG data in Nebuta: Summer festival in
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Rowe, W. D. (1998). Physical measurement of episodes of focused group energy. Journal of Scientific Exploration, 12, 569 – 581.
Snedecor, G. W., & Cochran, W. G. (1980). Statistical Methods (7th Ed.).
Utts, J. M., & Heckard, R. F. (2006). Mind on Statistics (3rd Ed.).