(2019-02-08, 07:29 PM)Chris Wrote: [ -> ]I've been thinking about this a bit more, and it seems to me that the graphs produced by Peter Bancel - showing the averaged time-variation of the data before, during and after events - aren't really the clinching evidence for a psi-mediated selection mechanism that they might appear.
Here are the graphs:
[Image: SelectionGraphs.jpg]
Both graphs show the time-varying cumulative correlation data. The one on the left is for events where there was flexibility in the choice of start and end times (the events have all been stretched to a duration of 24 hours before averaging), while the one on the right is for 24-hour events starting and ending at midnight, where there was no such flexibility. The key point is that the graph on the left shows that the increase in the cumulative signal during the event is almost exactly cancelled out by decreases before and after the event. But the graph on the right shows no systematic change before or after the event.
The interpretation is that for the events with flexibility, psi has allowed the experimenter to choose start and end points so as to produce a positive effect within each event, at the cost of matching negative contributions before and after. The signal itself remains an ideal random walk, but a favourable period of time has been selected. For the 24-hour events this cannot happen. Instead, presumably, psi has allowed the experimenter to choose favourable days for 24-hour events, and to avoid unfavourable days.
One question that might be asked is why there shouldn't also be an element of choosing whether to define events on favourable days in the left-hand graph, as well as just choosing favourable start and end points. If there were such an element, the negative contributions before and after the event would only partially cancel out the positive contribution from the event itself. But as the graph shows, this didn't happen.
Another question is whether we can actually produce a graph that looks like the left-hand one by defining suitable rules for the selection of start and end points. I doubt we can. Perhaps the simplest rule would be to specify a start period and an end period for each event, and to select start and end points according to the location of the minimum and maximum respectively of the cumulative curve during these periods. I reckon that would produce something of the form below, which doesn't look much like the experimental data:
[Image: SelectionGraphTheoretical.jpg]
There's also a more quantitative objection to the psi-mediated selection mechanism. In the simple model just suggested, the selection within the start and end periods produces a contribution to the cumulative statistic that is proportional to the square roots of the durations of those start and end periods. That's because of the fundamental fact that the deviation of a random walk scales like the square root of time. So the same square-root scaling will also apply to more sophisticated models of selection based on the behaviour of the signal within fixed start and end periods.
That means we can estimate how the size of the effect, expressed as a Z value per event, should vary with the duration of the event (call it N). That depends on whether the start and end periods have fixed lengths, or whether they grow in proportion to the duration of the event. If they have fixed lengths, Z is inversely proportional to the square root of N. If they grow in proportion to the duration, Z is independent of N. Those cases are in contrast to a field-type effect, for which Z would be proportional to the square root of N.
It so happens that in 2015 (in "Evidence for Psi", edited by Broderick and Goertzel) Bancel tested the dependence of Z on N for events whose duration was 12 hours or less (thus, fortuitously, excluding the 24-hour events for which he now believes the mechanism of psi-mediated selection is different). He called this a signal-to-noise test. The result was that he rejected what he then described as the "data selection hypothesis", in which Z was independent of N. The result of the statistical test would translate to a (one-tailed) p value of .0037. That rejected hypothesis would be equivalent to the start and end periods growing in proportion to the duration of the event. The alternative, where the start and end periods had fixed lengths, would have been even more strongly rejected. (The 2015 paper was based on 426 events, and therefore represented about 85% of the complete series.)
Peter Bancel's conclusion at that time was that both a simple selection hypothesis and a straightforward global consciousness field hypothesis had to be rejected:
"The analysis of data structure rejects the simple selection hypothesis at a reasonably high level of confidence. The signal-to-noise analysis provides the most clearcut support for this conclusion. ...Tests for a loophole to circumvent the XOR no-go suggest that a straightforward conception of proto-psi global consciousness is also not tenable. ...
The analyses, then, provide good arguments for rejecting both simple models and we are forced to look elsewhere for an explanation."
https://books.google.com/books?id=KVyQBQ...&lpg=PA274
Going back to the discussion earlier this year about Peter Bancel's suggestion that the GCP results were consistent with a selection process, in which the start- and end-points of the events were chosen to increase the value of the test statistic - I've been looking at the question of how the effect size per event, Z, depends on the duration of the event.
To summarise what was said previously, there are three possibilities:
(1) With a selection model of this kind, if the intervals from which the start- and end-points are chosen don't vary with the total duration of the event (for example, if the start- and end-intervals are an hour long, regardless of the whether the event is two hours or two days), then Z will scale as the inverse square root of the event duration.
(2) With a similar selection model, but allowing the start- and end-points to be chosen from intervals that increase in proportion to the total duration of the event, then Z will be independent of the event duration. This is the same scaling that is to be expected for a selection model in which - instead of adjusting the start- and end-points - whole events are either included or excluded according to their Z values (for example, if only the events with Z values in the top 50% are included).
(3) If instead of a selection process, there is a "field" effect, causing some kind of steady perturbation of the statistics for the full duration of each event, then Z will be proportional to the square root of the event duration.
As far as I know, Bancel's most recent conclusion is that the results are owing to start- and end-point selection in most cases, but that for events one day long, starting and ending at midnight, there was selection of whole events. That means that - apart from whole-day events - we should expect Z either to be independent of duration, ot to vary like the inverse square root of duration.
It should be emphasised that Bancel proposed that these selection effects were psi-mediated experimenter effects. However, the same scalings would be expected if the selection were accomplished by conventional means.
Previously I referred to earlier work by Bancel, in which - in contrast - he found statistically significant evidence of a field effect, corresponding to possibility (3) above. A field effect would result in Z growing in proportion to the square root of event duration.
However, Bancel's finding wasn't quite that straightforward, because he had to exclude longer events (in his analysis, longer than 12 hours), for which the effect (viewed as a steady "field" effect) was weaker. The analysis was also complicated by the inclusion of some events for which non-standard statistical measures were used, whose behaviour would be expected to be different. Also, only 426 of the full series of 500 events had taken place when he did the analysis.
I've looked at the variation of Z with the event duration just for the events for which the "standard" statistical analysis was used (that is, for each second the outputs of all the random event generators were added together, and then the squares of these sums were added together over the whole duration). I've also excluded a few events which were made up of several disjoint time intervals, for which the notion of choosing single start- and end-points isn't applicable. (I've also excluded the 13 events identified by Bancel as having been insufficiently specified before the data were examined.)
That leaves 415 events in total. I divided these according to their duration into 5 groups of roughly comparable size - up to and including 2 hours (n=78), 4 hours (n=64), 6 hours (n=101), 20 hours (n=69) and the rest (n=103). These are shown as a scatter plot below. The duration is the average within each group, and the error bars indicate the standard errors of the mean.
[Image: ZvDuration.jpg]
Obviously the dependence of Z on duration is more complicated than Bancel's earlier finding of support for a "field"-type behaviour would suggest. That would correspond to an increase of Z with duration. In fact, for the first three groups there is a decrease of Z with duration, and it appears consistent with the inverse square root dependence predicted by Bancel's start- and end-point selection model number (1) (I've added an inverse square root of duration line passing through the first point, for comparison).
However, for events longer than 6 hours the value of Z is much larger, and clearly must be accounted for by a different mechanism. It's not obvious to me what the explanation for that is.