Optimal length exploration for field RNG outputs using a Haar wavelet filter: TV audience ratings for New Year's 2012 in Japan/Exploracion longitudinal optima para productos de RNG de campo utilizando un filtro wavelet Haar: indices de audiencia de television para el ano nuevo 2012 en Japon ...
Field random number generator (RNG) studies have found that RNG outputs are significantly biased during periods in which many people focus on the same event at the same time, such as during the 911 terror attacks (Bancel, 2001; Nelson 2001; Nelson, Radin, Shoup, & Bancel, 2002). Devices seem to have the sensitivity to detect field signals even though the audience does not have any intention or knowledge of the existence of the RNG.
The most sensitive time scale or wavelength for RNG outputs during such events remains unclear. At present, 1 s trial generation is the methodological standard in field RNG studies. Bit sequences are generated by an RNG per trial t, creating a bit array (e.g., 0, 1, 0, 0, 1, ... 0), whereas the sum of the 1 bits (ignoring 0s) is binomially distributed (e.g., 251, 267, 248, ... 256, when a trial has a total of 512 bits), and the standardized z score for chance expectation is calculated as:
[z.sub.t] = ([X.sub.t] - N[pi])/[square root of N[pi] (1 - [pi])] = ([X.sub.t] - [mu])/[sigma], (1)
where [pi] is .50, the probability of obtaining a 1, and is the total number of bits per trial generated by the RNG, although trial quantities differ in field RNG studies. If N is large enough, the bit sequence can be converted into a variance measure reflecting the unsigned deviation of the bit sum from chance. The chi square values obtained for one trial t are given as [[chi square].sub.t] = [z.sup.2.sub.t] and cumulative statistics are calculated as:
[[chi square].sub.T] = [T.summation over (t=1)] [z.sup.2.sub.t], df = T, (2)
where T is the total number of trials based on event length.
Compatible Period-Length Exploration
The method for computing RNG outputs is somewhat arbitrary because a 1 s interval is not necessarily natural for most people. Discovery of an optimal length would be advantageous for future micro-PK studies. Such micro-PK phenomena might not approximate physical modeling, but an assumption that RNGs can detect physical signals as waves would be helpful for understanding the characteristics of RNG behavior. In fact, several findings seem to support the possibility that RNGs have an optimally sensitive time scale, because RNG outputs show a significant autocorrelation during highly focused events such as 911 calls (Bancel, 2001; Nelson et al., 2002; Radin, 2006) or events such as workshops that have many participants (Radin & Atwater, 2009). These positive autocorrelations, or persistence effects, suggest that processing using a longer interval (e.g., 2 or 4 s) would show larger variances for these sequences than for sequences with an interval of 1 s.
For this purpose, in the current study we focused on effects of audience rating, because RNG biases may have positive correlations with audience rating during worldwide events and also during local events, such as sports games (Shimizu & Ishikawa, 2012a) and movies played in theaters (Shimizu & Ishikawa, 2010, 2013). These findings support the hypothesis that repeated events with variable audience ratings can reveal the most sensitive period length for detecting field consciousness. We focused on TV programs as variable audience-size events to examine associations between TV ratings and particular wavelengths (i.e., intervals) as time scales that show biases more clearly.
High variability in TV audience ratings was obtained by using New Year's Eve ratings. Many people in Japan return to their family home just before the New Year to celebrate the event with their family, and many people watch TV programs on New Year's Eve. The TV ratings represent the size of the audience watching the programs. As expected, the highest rated program in 2011 was a music program produced by NHK (a major broadcasting company in Japan) with a rating of more than 40%. Such a high rating is rarely observed throughout the year.
One reason why this optimal wavelength issue has not been widely discussed is the methodology of data processing. We use calculation of a wavelet as a method to decompose a signal wave into multiple levels of energy, which is defined as variance, allowing examination of the duration (length) of the signal from field consciousness. Wavelet transformation can decompose original chi squares from RNG outputs into comparable statistics for periods of different lengths (Shimizu, Kokubo, & Ishikawa, 2013).
We predicted that higher TV ratings should produce more bias in RNG outputs of an optimal length. We sought the optimal wavelength to detect signals from field consciousness.
Information on TV audience ratings was provided by Video Research Corporation in Japan, covering the Kanto Area from 5:00 a.m. (in Japan) on December 28, 2011 to 5:00 a.m. January 4, 2012; that is, 3 days before and 3 days after New Year's Eve. This period corresponds to December 27, 2011 at 15:00 to January 3, 2012 at 9:00 UTC. Some long programs were divided into subprograms with a short break for a weathercast (Table 1). The TV audience ratings were based on the population of about 30 million people who live in the Kanto area. However, as most TV programs were broadcast on a national network and ratings in other areas were similar to those in the Kanto Area, the TV audience population is estimated at about 120 million nationwide. Seven major broadcasters provided a total of 1,618 programs. Audience TV ratings ranged from 0.0 to 41.6%, and the lengths of the programs ranged from 1 to 388 min.
To identify the higher rated programs, all 1,618 programs were sorted by audience ratings before being registered as events, unless the program's time range overlapped that of a previously registered program. When a higher rated TV program overlapped another program, only the higher rated program was analyzed (Table 1). A total of 228 programs were finally selected. The analyzed week had a total of 9,468 minutes of program time, which accounted for 93.93% of the week (10,080 min = 1,440 min x 7 days).
Random Number Generation
A total of 11 devices were used as true RNGs (four Psyleron, four Rpg102, and three Orion devices). The Psyleron and Rpg102 devices were connected to four personal computers via a USB port (Acer Aspire One, VAIO Type-G, Type-X, and Dell Dimension 4600). All three Orion devices were registered in the Global Consciousness Project (GCP) and were associated with the following identification numbers: Tokyo (1101), Tsukuba (2201), and Tokorozawa (2202). The four Psyleron, four Rpg102, and one Orion (2201) devices were located within a 1 m circle of the first author's home in Tsukuba before and after the 2012 New Year. They were run continuously in parallel for about one week.
All the RNG devices, except Orion, collected 64 random bits per trial, which consumed 125 ms. Then, they collected random bits at a sampling rate of 512 bits/s. A software application was developed using Visual Studio 2010 to control the Psyleron and Rpg102 devices simultaneously. All the RNG outputs were recorded in a CSV file. GCP RNGs produce more than 8,000 (maximally 16,000) bits/s, and the GCP trials were sums of 200 bits. Data files for Orion were downloaded from the GCP website.
The current analysis used two procedures: (a) sum of squares decomposition of the standard deviation of the bit sum from chance expectation into wavelets and (b) regression analysis using audience TV ratings.
Wavelet decomposition. Discrete wavelet transformation is a method to process real data in which the signal is known only at sampling points, with the spacing dependent on the sampling rates of outputs (Capilla, 2006) such as those from afield RNG. We used the Haar filter (Haar, 1910) to decompose the sum of squares of RNG outputs into multiple levels, each level representing a period length. The procedure is described mathematically in the Appendix. Two of the results of these analyses, dZ and Stouffer's Z, were incorporated in subsequent analyses; dZ represents the output variance for each period length. Stouffer's Z is a single value representing the output variance for all the period lengths combined.
Note that the lengths of the analyzed events (programs) ranged from 1 to 388 min, resulting in different maximum levels for different programs. The longer periods have fewer degrees of freedom, resulting in a worse approximation to the normal distribution. Thus, sums of squares with df < 60 were excluded.
Table 2 shows the number of samples for each RNG in the analysis of the programs.
ANCOVA. Using dZ values as the dependent variable, we conducted an ANCOVA with fixed factors of Period Length (12 levels) and RNG Type (three levels: Psyleron, Rpg102, and Orion), and Audience Rating (continuous variable, N= 228) as a covariate. There also were two interaction terms involving Audience Rating: Period Length x Audience Rating, and RNG Type x Audience Rating. There was no Period Length x RNG Type interaction because the outputs of the Orion device didn't have periods < 1 s. The intercept in the ANCOVA model was excluded because of parameter redundancy. Second, after the ANCOVA model yielded significance, ANCOVAs were conducted for each RNG device separately, including Period Length, Audience Rating, and their interaction. The ANCOVAs were analyzed using JMP 11.0 (SAS Institute).
A significant main effect for Audience Rating would mean that audience size had an influence across all periods. A significant interaction would suggest that the RNGs were more sensitive at some period lengths than at others. A main effect for Period Length would simply reflect bias in the RNGs.
Using 228 TV programs with audience ratings, we tested the hypothesis that peaks would be found for highly sensitive wavelengths, if these exist. There were no undue outliers. Figure 1 shows the Pearson correlations between audience ratings and dZ.
[FIGURE 1 OMITTED]
The global ANCOVA yielded a significant main effect for RNG Type, F(2, 17179) = 4.68, p = .0009, and significant interaction of RNG Type with Audience Rating, F(2, 17179) = 8.72, p =.0002. Table 3 shows results from three ANCOVAs conducted independently for each RNG. Only the ANCOVA using Rpg102 was significant after adjusting the significance level ([alpha] = .05 / 3), F(23,6980) = 2.16, p = .001, permitting us to examine the Rpg102 ANCOVA model in more detail. There was a significant main effect for Audience Rating, F(1,6980) = 13.62, p = .0002, meaning that the variance (i.e., bias) in the output of the Rpg102 devices was positively correlated with audience size. The main effect for Period Length was nonsignificant, but the interaction between Period Length and Audience Rating was significant, F(11,6980) = 1.92, p = .032. Although the Psyleron device had a peak period length of 8 s and the ANCOVA gave a small p value, it was not significant. The Orion device results were also nonsignificant.
In this study, we examined the optimal wavelength as a time interval for RNG outputs, using information on TV programs and audience ratings around New Year's 2012. Outputs of 11 RNG devices were evaluated using Haar wavelet decomposed sums of squares (chi squares).
We hypothesized that a large audience size would increase the variance of [X.sub.t] for a particular period length that would be optimal for picking up signals. The results showed that the output from the Rpg102 device might be sensitive enough to detect field consciousness. Audience rating effects were observed, as expected, but no optimal period lengths were identified. The significant results with Rpg102 for most period lengths suggest that RPgl02 is sensitive to audience size at all the sampled period lengths, from shortest to longest. This is a characteristic of fractal-shaped waves in bit sequences, as was also reported in a field RNG experiment using music that was listened to repeatedly (Shimizu et al., 2013). It is perhaps worthy of note that there was a marked dropoff of the correlation between audience ratings and dZ after 64 s for Rpg102 and the opposite for Psyleron (see Figure 1).
The results also showed device differences in susceptibility to influence by field consciousness. These tendencies have been found in previous reports showing that the Rpg102 device repeatedly shows high sensitivity (Shimizu & Ishikawa, 2010; 2012a, 2012b), whereas Psyleron does not (Shimizu & Ishikawa, 2013). Because these kinds of anomalies are not considered to be influenced by such physical factors, it might appear odd that only a particular RNG, Rpg102 in the current case, showed sensitivity to audience size. We cannot yet conclude that thermal noise, the source of Rpg102 output, was the cause of the sensitivity. Further exploration is needed to determine if this was a unique event or if Rpg102 always has high sensitivity. For this purpose, there is a need to examine the measurement reliability of RNG devices. Good reliability is needed to differentiate individual true (universal) scores from measurement errors. This reliability issue is often discussed in relation to generalizabiIity theory (Cronbach, Gleser, Nanda, & Rajaratnam, 1972).
The results we obtained for wavelets depended on the application of the Haar filter. The current Haar filter is the simplest to use and the best suited for the short period lengths used in this study, but it has relatively low resolution. In contrast, the general filters developed by Daubechies (1992) are better suited for longer lengths, which probably explains their better resolution. Bit generation speed defines the maximum resolution in wavelet analysis, and more bits with a higher resolution can be obtained than was the case in the present study.
It is unlikely that the anomalous RNG behavior we found can be explained exclusively by physical wave modeling in the framework of signal detection, because it appears that the bit stream continues to be generated between trials. This means that the RNG biases were not derived only from wave-like signals, but also from some kind of entanglement of quantum particles.
We had hypothesized that audience size would increase bias in the RNG outputs, but we didn't predict that different RNG devices would have different effects. However, we found that waves coming from one kind of device interfered with waves coming from the other kinds of devices. Thus, as a post hoc test, we evaluated the reliability of the regression coefficients using intraclass correlation (ICC). Excluding the three missing short periods of data for the Orion (N = 9 = 12-3), the ICC (1, 3) was estimated to be -2.24, F(&, 18) = 0.31, p = .95, which is significantly low reliability by a one-tailed test, suggesting that the coefficients for these devices canceled each other out for all period lengths. Such low reliability may keep results from being statistically significant in an analysis that combines data from different types of RNGs.
Cancellation effects between devices have been reported for baseball games (Shimizu & Ishikawa, 2012a) and in reliability analyses of control conditions in field RNG experiments (Shimizu & Ishikawa, 2012b). Fundamental "cancellation pressure" could explain large biases in the variance of RNG outputs during events. For instance, if for a given period length an RNG generates the strongly biased bit array 0, 0, 0, 0, 0, ... 0 following the strongly biased bit array 1, 1, 1, 1, 1, ... 1, the mean of the bit sequence would be the null expected value of 0, increasing the value of the corresponding chi square. Then, to keep the variance at the null expected value of 1, the RNGs would work cooperatively with one another as well as independently. It is premature to discuss such mechanisms as a new hypothesis, and a future task is to examine the possibilities of such cancellation mechanisms.
Bancel, P. (2001). Draft report on autocorrelations in GCP data of September 11, 2001. Retrieved from http://noosphere.princeton.edu/bancel/interegg.corr.html
Capilla, C. (2006). Application of the Haar wavelet transform to detect microseismic signal arrivals. Journal of Applied Geophysics, 59, 36-46.
Cronbach, L. J., Gleser, G. C., Nanda, H., & Rajaratnam, N. (1972). The dependability of behavioral measurements. New York, NY: Wiley.
Dong, X., & Li, H. (2008). Calculating wavelet variance associated with discrete wavelet transform (DWT). Streeter, ND: Central Grasslands Research Extension Center.
Daubechies, I. (1992). Ten lectures on wavelets. Philadelphia, PA: Society for Industrial and Applied Mathematics.
Haar, A. (1910). Zur theorie der orthogonalen funktionensysteme [On the theory of orthogonal function systems]. Mathematische Annalen, 69, 331-371.
Nelson, R. D. (2001). Correlation of global events with REG data: An internet-based, nonlocal anomalies experiment. Journal of Parapsychology, 65, 247-271.
Nelson, R. D., Radin, D. I., Shoup, R., & Bancel, P. A. (2002). Correlations of continuous random data with major world events. Foundations of Physics Letters, 15, 537-550.
Percival, D. B. (1995). On estimation of the wavelet variance. Biometrika, 82, 619-631.
Radin, D. I. (2006). Entangled minds: Extrasensory experiences in a quantum reality. New York, NY: Paraview Pocket Books.
Radin, D. I.., & Atwater, F. H. (2009). Exploratory evidence for correlations between entrained mental coherence and random physical systems. Journal of Scientific Exploration, 23,263-272.
Shimizu, T., & Ishikawa, M. (2010). Field RNG data analysis, based on viewing the Japanese movie "Departures" (Okuribito). Journal of Scientific Exploration, 24, 637-654.
Shimizu, T., & Ishikawa, M. (2012a). Audience size effects in field RNG experiments: The case of Japanese professional baseball games. Journal of Scientific Exploration, 26, 67-83.
Shimizu, T., & Ishikawa, M. (2012b). Reliability of outputs of field random number generator movie experiments. NeuroQuantology, 10, 389-393.
Shimizu, T., & Ishikawa, M. (2013). Exploration of field consciousness signal wavelength: Field RNG experiment at a movie theater. Journal of the International Society of Life Information Science, 31, 17-19.
Shimizu, T., & Ishikawa, M. (2014). Decomposition of field RNG outputs during massive tweets during Laputa: Castle in the sky in Japan. Abstracts of Presented Papers: The Parapsychological Association 57th Annual Convention, 50-51.
Shimizu, T., Kokubo, H., & Ishikawa, M. (2013). Decomposition of field RNG outputs using Plaar wavelets: A music experiment. Abstracts of Presented Papers: The Parapsychological Association 56th Annual Convention, 46.
School of Information and Communication
Kanda-Surugadai 1-1-1, Chiyoda-ku
We thank the Video Research Corporation of Japan for providing the 2011 New Year's Eve TV audience rating data.
A wavelet is a function [psi](t) [member of] [L.sup.2] (R), which is the space of square integral functions and t is time, with the following properties:
[[integral].sup.[infinity].sub.-[infinity]] [psi](t)dt = 0, (3)
as well as [parallel][psi][parallel] = 1, where [parallel].[parallel] is the [L.sup.2] norm. The mother wavelet function [psi] (t) [member of] [L.sup.2] (IE), which is dilated/ scaled by a, and translated by b, and denoted by [[psi].sub.a,b] (t), is given as
[[psi].sub.a,b] (t) = 1/[square root of a] [psi] (t - b/a), (4)
where a is the scale factor determining the extent the wavelet is stretched or compressed, and b is the extent of the shift with which the wavelet is moved along the time or space scale (Dong & Li, 2008); 1/[square root of a] is the normalization factor. The continuous wavelet transform (CWT) of a function f(t) [member of] [L.sup.2] (R) is given as
[W.sub.[psi]] f(a,b) = [[integral].sup.[integral].sub.-[integral]] 1/[square root of a] [bar.(t - b/a)] f(t)dt (5)
where the [psi] term represents the complex conjugate (Daubechies, 1992).
To analyze these one dimensional outputs we again assume that time series [X.sub.t] is the sum of the 1 (not 0) bits in trial t (e.g., 38, 27, 36, 35, 29, 27, ... 34 when a trial has a total of 64 bits generated), and its standardized score ([z.sub.t]), where t = 1, 2, ... T, with T = [2.sup.L] = the number of trials with some positive integer. Wavelet transforms are defined under the restriction that a = [2.sup.j] and b = ak (j, k [member of] Z), where k is the index ranging from 1 to T/[2.sup.j] (the number of trials within a level j), and j is the scale parameter or transform level ranging from 1 to L (1 [less than or equal to] j [less than or equal to] L).
The Haar filter decomposes a sequence of length [2.sup.L] (raw sequence) into coefficients of details (information as differences between outputs at a given level) and scales (information as averages, approximations of the level outputs), as shown below. The mother wavelet of the Haar filter is expressed simply as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)
Then, the computation of the wavelet (or detail) coefficients using the Haar basis is performed from the scaling coefficients [c.sub.j] at scale level
[d.sub.j+1,k] = 1/[square root of 2] ([c.sub.j,2k-1] - [c.sub.j,2k]). (1)
This means that a detail coefficient consists of the difference between two neighbor scales. The value is the deviation and its sums of squares becomes the wavelet variance.
On the other hand, its father wavelet or scaling function is defined as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
The purpose of the scaling is to approximate the sequences. Note that scaling (approximation) coefficients can be expressed
[c.sub.j+1,k] = 1/[square root of 2] ([c.sub.j,2k-1] + [c.sub.j,2k]) (9)
Because these scales become the inputs at the next level, the Haar filter process allows recursive calculation of the "differences" and "sums" of the scale coefficients.
Therefore, this analysis can break down original sequences into scale levels from 1 to L, creating [2.sup.L]--1 detail coefficients and one approximation.
These structures become very simple when it is assumed that all original time series ([X.sub.t]) are standardized ([z.sub.t]) from RNG outputs. Both wavelets and scaling coefficients become standardized, that is, Equation (8) and Equation (10) standardize values in the same way.
The original sequences are available when j = 0 and a = [2.sup.J], whereas the coarsest scale [c.sub.l,k] corresponds to a single data point [c.sub.L,1], representing the signal average, which is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (10)
showing that the final approximation value is actually equal to Stouffer's Z, which is
Stouffer's Z = 1/[square root T] [T.summation over (t=1)] [z.sub.t] (11)
suggesting that using Haar wavelets fits well with previous RNG methodology.
According to Percival (1995), the energy preservation characteristic of the wavelet transform can be expressed in discrete cases as
[T.summation over (t=1)] f[(t).sup.2] = [L.summation over (j=1)] [T/[2.sup.j].summation (k=1)] [d.sup.2.sub.j,k] (12)
suggesting that the sum of squared wavelet coefficients over scales provides an orthogonal decomposition of the total sample sum of squares. The energy contained in scale j can be computed from the wavelet coefficient as
[T/[2.sup.j].summation (k=1)] [d.sup.2.sub.j,k] (13)
Energies at different levels are theoretically independent of one another.
Note that whole energy defined by the above equation is based on the sample mean:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)
whereas field RNG studies usually compute sum of squares from expectation [mu] = 0, as
[T.summation over (k=1)] [([c.sub.0,k] - [mu]).sup.2] = [T.summation over (k=1)] [c.sup.2.sub.0,k] (15)
Then, the decomposition is given as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)
One unsolved issue is the restriction of event lengths, because the wavelet decomposition (Shimizu et al., 2013) assumes a dyadic time series with sample size T = [2.sup.L], where L is a positive integer. To moderate it, we used zero padding (Shimizu & Ishikawa, 2014). Suppose that we have an original time series of length T, and a minimum positive integer L, which fulfills T [less than or equal to] [2.sup.L], where all the points in which the number is more than T are filled with 0 values. The degrees of freedom (df) of the wavelet variance correspond to the number of coefficients, defined as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (17)
At level j = 0 (original); df at the next level, j + 1, then becomes
D[f.sub.j+1,k] = (d[f.sub.j,2k-1] + d[f.sub.j,2k])/2 (18)
As an example, assume an original data set with the values 1.0, 2.0, 3.0, 4.0, and 5.0 (T = 5). The corresponding zero padded values are 1.0, 2.0, 3.0, 4.0, 5.0, 0.0, 0.0, and 0.0 (T = 8, L = 3). For the next level, d[f.sub.1,k] = 1.0, 1.0, 0.5, and 0.0 (T/2 = 4), next level d[f.sub.2,k] = 1.0, 0.25 (T/4 = 2), and finally d[f.sub.3,1] = 0.625 (T/8 = 1). The sum of squares for all the levels are calculated as
[SS.sub.j] = [summation] [d.sup.2.sub.j,k] (19)
And standardized as
D[Z.sub.j] = [square root of 2 x [summation][d.sup.2.sub.jk]] - [square root of 2d[f.sub.j] - 1 (20)
Table 1 Examples of TV Programs Around New Year's 2012 Ratings Start End TV 1 41.6 12/31/2011 12/31/2011 NHK 21:00 23:45 2 35.2 12/31/2011 12/31/2011 NHK 19:15 20:55 3 33.6 12/31/2011 12/31/2011 NHK 20:55 21:00 4 28.5 1/3/2012 1/3/2012 NipponTV 07:50 14:18 5 27.9 1/2/2012 1/2/2012 NipponTV 07:50 14:05 6 25.4 12/31/2011 1/1/2012 NHK 23:45 00:15 7 21.0 12/29/2011 12/29/2011 NipponTV 19:00 20:54 excluded 18.7 12/31/2011 12/31/2011 NipponTV 18:30 21:00 8 18.6 12/28/2011 12/28/2011 NipponTV 21:00 23:30 9 17.7 1/2/2012 1/2/2012 TV Asahi 09:00 23:30 228 0.6 12/29/2011 12/29/2011 TBS 04:25 04:45 Programs 1 62th Kohaku Music Festival (2nd) 2 62th Kohaku Music Festival (1st) 3 News Weather Bulletin 4 The 88th Ekiden Race Backhaul (2nd) 5 The 88th Ekiden Race Approach route (2nd) 6 Old year and new year 7 Gurunai Final (2nd) excluded DownTown's Gakitsuka New Year's Eve Special (1st) 8 Documentary of Big Family Ishida 2011 9 Tonnels Sports King-- 5 hour special (2nd) 228 Kaimono Lab Note. The time zone is based on Tokyo. Orion device data were analyzed after translation into UTC. One program produced by Nippon TV was excluded because it partly overlapped with a higher rated program (2nd). Table 2 Number of Samples for Each RNG Device Based on the Wavelet Decomposition Psyleron Rpg102 Orion Analyzed Base Analyzed Base Analyzed Base Stouffer's Z 912 912 912 912 684 684 250 ms 912 912 912 912 500 ms 912 912 912 912 1 s 912 912 2s 908 912 908 912 681 684 4 s 863 912 863 912 647 684 8s 636 912 636 912 477 684 16s 408 912 408 912 306 684 32 s 264 912 264 912 198 684 64 s 168 912 168 912 126 684 128 s 92 908 92 908 69 681 256 s 16 876 16 876 12 657 512s 840 840 630 1024 s 636 636 477 2048 s 408 408 306 4096 s 264 264 198 8192 s 164 164 123 16834 s 88 88 66 32768 s 12 12 9 N 7003 13316 7003 13316 3200 7935 Note. There were a total of 228 TV programs. Four machines were used, giving a simultaneous sample of 912 (2287 x 4) for the Psyleron and Rpg102 devices, and 684 (228 x 3) for the Orion device. Sample sizes are smaller for longer periods because of the short TV program length. Very short programs did not provide any samples for longer periods. Analyzed samples have sufficient df (< 60) for calculating the standardized dZ scores. Table 3 ANCOVA Models and Effects on dZ Values Using Rpg102 1. Models SS df MS F P Psyleron model 31.6 23 1.37 1.402 .096 error 6842.1 6980 0.98 Rpg102 model 48.9 23 2.12 2.164 .001 error 6851.5 6980 0.98 Orion model 23.1 17 1.36 1.390 .131 error 3112.3 3183 .98 2. Detailed analysis for Rpg102 SS df MS F P Audience Rating 13.35 1 13.36 13.62 .0002 Period Length 6.06 11 .55 .56 .862 Period Length 20.76 11 1.89 1.92 .032 Error 6980
|Printer friendly Cite/link Email Feedback|
|Title Annotation:||random number generator|
|Author:||Shimizu, Takeshi; Ishikawa, Masato|
|Publication:||The Journal of Parapsychology|
|Date:||Mar 22, 2016|
|Previous Article:||Taming the ghost within: an approach toward addressing apparent electronic poltergeist activity/Domando al fantasma interior: un acercamiento a la...|
|Next Article:||Parapsychology: A Handbook for the 21st Century.|