Correlation of global events with reg data: An internet-based, nonlocal anomalies experiment - Statistical Data Included

Journal of Parapsychology, The, Sept, 2001 by Roger Nelson

We calculate the mean, variance, and z-score across eggs for each segment, properly treating missing values. (2) This yields a single time series of parameters representing the composite egg behavior that can then be used in various analyses and explorations. Choosing whether to block the data is usually arbitrary, but it has to be specified in advance rather than by inspection of the results. In some cases, there are specific reasons to use blocking. For example, to create a manageable dataset for 6 days worth of seconds, we may choose to use 15-mm blocks. For some analyses, like the interegg correlations, it is always necessary to block the data to have a viable sample. The following description is a detailed example of the procedure beginning with acquisition of the raw, second-by-second data and continuing through the calculation of a canonical chi-square statistic. Blocked data are treated analogously.

1. An REG produces random bits at high speed for collection via the egg-host computer's serial port. The data are transmitted over the Internet to a central server for archiving and processing.

2. Each egg-site records these data as "trials" at one per second, summing 200 bits for one trial. The 200-bit sums have expected mean = 100 and standard deviation = 7.071.

3. The mean deviation from expectation for a single trial across all eggs, or the mean of a block of trials across eggs, is normalized as a z-score.

4. The z-score is squared, yielding a chi-square-distributed quantity with 1 degree of freedom representing a single trial or a block of time specified in the prediction.

5. Because chi-squares are additive, we may sum across eggs and across blocks of time.

6. The total chi-square represents the deviation for the predicted period of time. It has degrees of freedom equal to the number of segment z-scores.

7. This is compared with the appropriate chi-square distribution to yield a chance probability.

Control data are needed to establish the viability of the statistical results from "active" data generated during the specified events. Because predictions for the GCP are situation dependent, we need specially designed procedures to ensure that the statistical characterizations of the complex array of data are valid. There are several components in the control procedures. We begin with quality-controlled equipment design, including a logical XOR that guarantees zero deviation in the long run. In the simplest form, the logical XOR compares the random sequence with an alternating 1,0 sequence and registers each match as a "hit," thus eliminating, to first order, any bias of the mean. The design is then empirically tested by thorough device calibration, and finally, resampling procedures are used to examine the distribution of parameters in the actual data. The resampled control data are expected to produce chance results because by hypothesis no engaging event can be specified. See Nelson et al. (1998) for mor e detail and examples of the resampling procedure. We have recently added another type of control analysis, based on a complete clone of the GCP database with all trial values replaced by values created from a high-quality pseudorandom algorithm. Details are beyond the scope of this article, but the control analysis essentially duplicates the formal database results using the pseudorandom database. Thus, although a single comparison of active and pseudo results would not be an adequate control procedure, the overall results combined across all formally defined events will provide a sufficient sample. Although the active data show a highly significant cumulative deviation from expectation, the corresponding analysis using the pseudorandom clone data should not differ from chance expectation. The combined force of these efforts ensures that the GCP data meet rigorous standards and that the active subsets subjected to hypothesis testing are correctly evaluated against expectations established by theory and resam pling of appropriate control and calibration data.