The Global Consciousness Project

Thanks for this analysis, Chris. Some of the maths is a bit beyond me (i.e. the ratios of effect size to duration) but I can at least ask a question re the above quote:

Do you have any opinion on whether it is reasonable to expect that the matching negative contributions occur immediately before and after the events? That is, why would we expect them to occur there as opposed to, say, anywhere else in the data? More generally, why would we expect them to occur at all, just as we (supposedly) don't expect them to occur for the full-day events?

I realised while I was writing that post that it wasn't really feasible to explain the mathematical details, so it ended up more as a summary of what I'd concluded.

But I'll try to have a go some time at explaining the arguments about the dependence of Z on event duration, as those are essentially straightforward.

I'm sure it is reasonable to expect the matching negative contributions to occur immediately before and after the events. The reason for that is simply that if you adjust the end point (say) so as to increase the average size of the correlation statistic during the event, then by that choice you are necessarily going to decrease the average size of the correlation statistic in the period immediately after the event. It's essentially no different from taking a set of unbiased statistics and selecting the largest values. The ones that aren't selected will tend to be smaller than expectation. The only difference here is that you're constrained to selecting a set of values generated during a continuous period of time. But exactly the same principle applies - if you select a set of larger-than-average values, the ones left will be smaller than average.

If I've got it right, this graph is showing the theoretical expectation - for the average time-dependent cumulative correlation statistic - when the start and end points are chosen by looking for its minimum within a fixed start period, and its maximum within a fixed end period. The negative contributions are reflected by the negative slope of the graph before the first cusp and after the second: