Agape Experiment:  Further Statistical Studies (in progress)

Summary From December 1993 to January 2001, we carried out 240 ESP group sessions with majority vote (27 845 collective tries, that is 250 000 individual tries; 418 participants, with no selection regarding prior psi capabilities; 2/3 of women, 1/3 of men). The size of the transmitter group varied from 0 to 15 persons, the size of the receiver group from 1 to 16. We varied a number of parameters, particularly the target’s type (pictures, words) and the number of possible answers (2, 3 or 5). The redundancy offered by the majority vote, not only didn’t significantly increase the psi-hitting as we expected under the hypothesis of an improvement of the ratio Signal / Noise. On the contrary, it seems that its impact made the results random: the number of individual hits as well as the number of collective hits (result of majority vote) proved to be compatible with the hypothesis of results occurring by chance alone. We especially observed that strong majorities did not get better results than weak ones. Two studies led by M. Campardon and F. Garcia on the variance of the results from the vote are discordant. The variance of success in relation to time, assessed with the method of clusters of collective tries (15, 30 or 60 consecutive tries), does not match expectation for the experiment with 2 possible targets, and is not significant with the two other protocols. If we calculate variance on sliding salvos (tries clustered into a moving frame), data are smoothed out and the variance loses its significance. The variance evaluated with the method of spaces between consecutive successes of the vote was significantly different from sheer chance for two of the three protocols; but this result is very hard to read (the variance is normal, significantly low, or significantly high compared to the expected one, depending on the protocol used). In case the seemingly random data belong to a second kind error, we initiated an analysis of the covariance, carried out for heuristic purpose only, in order to discern the protocol parameters which could have had an impact on the results. We work at the try level. A try is made of each participant’s vote for a word or a picture and for a given emission of a message from the transmitters. We confined ourselves to studying the tries with results either significantly higher or lower than chance expectation. In order to be able to test the influence of each modality of the variables, we resorted to a transformation of the variable "percentage of successes” that enables us to compare percentages of successes obtained with 2 pictures, 3 words or 5 words. We build for each try the percentage of right answers given by the receivers; this will be the variable to be explained. The significant variables have been selected with a step by step procedure, and kept above a threshold of 5%. All this leads to a rather puzzling result since, even though the significant tries are more often successful than not (two and a half successes for one failure), it appears that it’s nearly the same protocol parameters that hold the results away from chance expectation in both cases. These parameters are, in particular: a higher number of transmitters in relation to the number of recipients, the active involvement of the transmitters in the transmission, and their social links (assessed with a sociometric survey) with the receivers. But too big a number of receivers (higher than twice the number of transmitters), or very strong social links between them result in bringing the outcome closer to chance. A subsequent research (SYBIL) will explore the following hypothesis: we can hope for success with groups only if we build sub-groups so that there is more affinity between receivers and transmitters than there is amongst the receivers.

Click here for a slide-show (power point) or click there for a shorter and more synthetic slide-show.

From December 1993 to January 2001, we carried out 240 telepathic ESP group sessions, made up of 27,845 collective tries (that is more than 250 000 individual tries)!  The population of participants, who all volunteered and were recruited without special method (friends, acquaintances, ads in papers), consisted of 274 female individuals and 145 male individuals.  That is a total of 418 persons, with approximately 2/3 of women and 1/3 of men.  The size of the transmitter group varied from 0 to 15 people, the size of the receiver group from 1 to 16. 

We varied a number of parameters, particularly the target’s type (pictures, words), and the possible answers’ number (2, 3 or 5). 

Both the number of individual hits and the number of collective hits (result of the majority vote) proved to be compatible with the hypothesis of results occurring by chance alone. 

Test of comparison with pure chance results for individual answers

For the experiment with 2 pictures (respectively 3 words and 5 words), we looked if the percentage «   » of right answers were equal to p₀=1/2 (respectively 1/3 and 1/5), that is equal to chance.

The hypotheses for this test are:

H₀: p = p₀  versus  H₁: p ¹ p₀

The statistical function used is:  where n is the number of tries associated to each experiment. 

It follows asymptotically a normal standardized distribution.

Results obtained by majority vote

Variance of success for answers got by vote

We could suppose that high percentages (those higher than expected by chance, or Psi-Hitting), and low percentages (Psi-Missing) counterbalanced each other.  Under this hypothesis that there are fluctuations between attitudes in Psi-Hitting and Psi-Missing, it can be interesting to test the variance of success. 

To test this variance, we can proceed in different ways:

• We can group the tries in “salvos” or clusters of 15, 30 or 60 consecutive tries, and check if the number of hits within these groups has a random variance or not.  The Campardon study shows that in the experiment complying with the « two pictures protocol », the observed variance is lower than the expected one.

·        On the other hand, Garcia doesn’t find any of the three variances for the three protocols different than expected by chance. 

[It remains to check if the random choice laid down by Garcia in order to settle the equally placed votes, and Campardon’s choice to discard salvos which are not multiples of 15, are not accountable for the differences between their conclusions.]

·        To reach a better evaluation, we can also note the interval (or space) between two consecutive hits, and check if the variance of these intervals is random or not.  When the people voting have to choose between two possible targets, the results gather around the mean (variance of the spaces significantly lower than chance expectation).  On the contrary, the results are away from the average in the case of three possible targets (variance significantly higher than expected).  This unexpected variance could result from instable attitudes sometimes leading to Psi-Hitting, sometimes to Psi-Missing (Cf. Campardon’s study).  Nonetheless, when receivers have to choose between five possible targets belonging to a same repeated set, the variance is not different from the expected one (possible interaction with a stacking effect)

Targets	Number of successes	Observed variance	Expected variance
2	1463	1.93*	2
3	3512	6.42*	6
5	777	20.05	20

 

Majority strength and success of answers got by vote

We can suppose that, if some answers are not due to chance but to ESP, this should have an impact on the majority: strong majorities could be more linked to success than weak ones.  In fact the calculations carried out on the sessions made us reject this hypothesis: unlike what we expected, strong majorities didn’t get better results than weak ones (Cf. Campardon’s study). 

 

Conclusion of the hypothesis test

The results didn’t fulfil our expectations, especially regarding a possible improvement of the ratio signal to noise linked to the redundancy got from majority vote.  This way of carrying out the experiment, not only didn’t strongly increase the Psi-Hitting as we expected, but seems to have made all the results random, for either individual answers or answers obtained by vote. 

We especially noticed that, unlike what we expected, strong majorities didn’t get better results than weak ones. 

Two different studies about the variance of answers got by vote give discordant results:

The variance of success in relation to time, assessed with the method of clusters of collective tries (15, 30 or 60 consecutive tries), does not match expectations for the experiment with 2 possible targets, and is not significant with the two other protocols.  If we calculate variance on sliding salvos (tries clustered into a moving frame), data are smoothed out and the variance loses its significance.

The variance evaluated with the method of spaces between consecutive hits of the vote significantly departed from chance expectation for two of the three protocols; but this result is very hard to read (the variance is normal, significantly low, or significantly high compared to the expected one, depending on the protocol used).

 

Prospective purpose: covariance analysis

In case our seemingly random data resulted from a Type II error, and under the hypothesis that ESP would be a scarce phenomenon within the frame of our protocol, with a weak impact and a changing sign (sometimes leading to Psi-Hitting, sometimes to Psi-Missing), we decided to carry out a covariance analysis on collective tries which are significantly different from chance (p <0.05), and this for heuristic purpose only.  We are well aware that we can expect 5% of the tries to be different from chance under the threshold p=0.05, but we don’t foresee that a regression on these tries leads to identify the parameters which would increase or decrease the difference from chance (Ho). 

Here, a “stacking effect” can interfere (non-independence of the receivers’ answers).  Indeed, for each collective try, each member of the receiver group chooses from a common set of possible targets.  If one possible target has attractive or repulsive characteristics, there will be a surplus of votes in favour of this possible target or away from it, regardless of any telepathic phenomenon.  If it happens that the real target matches an “attractive possible target”, we’ll have a fake “hit”, conversely, if the real target matches a “repulsive possible target”, we’ll get a fake “miss”.  The Greville method could allow us to control this phenomenon, but our purpose is strictly heuristic and we don’t intend to demonstrate anything.  Furthermore, our results can hardly be put down to a “stacking effect”. 

In order to test the effect of each variables modality, we used a transformation of the « percentage of hits » to be able to compare the results for the protocols with two pictures, three or five words. 

where:- is the percentage of right answers in the try

- p is the expected percentage under the hypothesis of the choice being made at random (0.50 for two pictures, 0.33 for three words and 0.20 for five words). 

If we look into the quality or the tries, we can test if the percentage of hits got for each try is significantly lower than chance, significantly higher than chance, or equal to chance thanks to a test of Khi². 

The statistic of this test, calculated for each try, is

~Khi2 (one df) with previously defined notations.

We get the following results with a threshold of 5%:

We focus on a study of the tries where the target collects either significantly more votes or significantly fewer votes than expected.  The effect of different variables “protocol” on the answers will be outlined with a covariance analysis.  The significant variables will be selected thanks to a step by step procedure and kept under a threshold of 5%.  We took into account the tries significantly lower than chance as well as the tries higher than chance because the former could be a manifestation of “Psi-Missing” and we could hope to single out the factors involved in favouring success from other factors facilitating failure. 

Collective tries significantly departing from chance

We consider the case where the variable « answer » (transformed percentage h) is significantly higher than the expected value under the hypothesis of answers made at random.  We get significant variables with a p-value close to 0.0001.

Parameters linked to getting the results closer to chance:

Parameters linked to the results departing from chance:

Effect of the relations between participants

Before a huge number of sessions, the receivers gave each participant a mark going from 0 to 5, answering the question:

We made two fractions: 

where “Receivers’ mark” is the mean of the marks given by the receivers to the other receivers, and “Transmitters’ Mark” is the mean of the marks given by the receivers to the transmitters.  The « Group’s Mark » is the mean of all the marks. 

For the significant tries (threshold 5%) with higher results than expected (Psi-Hitting), the table had 1,079 observations; for 438 of them, we didn’t have these pieces of information; the study of simple regression was therefore carried out on 641 observations.  The adjusted R² equals 10.8% (« small » effect according to Cohen’s convention).

When the receivers know one another better than they know the transmitters, the results come closer to chance (less success).  When the receivers know the transmitters better than they know one another, we move away from chance (more success) [2] .

We find the same tendency, although not as clearly [3] , if we take into account significant tries towards Psi-Missing (in that case, when the receivers know one another well, the failure is lessened, while when they know the transmitters better, the failure is strengthened).  The effect is very very small !

 

Reading Suggestion

The parameters which seem to promote chance involve all the participants: preliminary choice of possible targets (from a given set); group reward; longer allotted time to answer. 

If we allot the receivers a time to answer depending on the time spent by the first half of them, (competitive factor, source of tensions in the receivers subgroup), we can observe that the results move away from chance. 

The parameters which seem to induce a distance from chance mostly involve the transmitters: number of transmitters; specific instruction to focus; the receivers know the transmitters better than they know one another. 

The parameters we educe can hardly be linked to a form of stacking effect, especially the instruction given to the transmitters to focus in a precise way, the number of transmitters, the familiarity receivers feel among themselves compared with the one they feel towards transmitters.  These parameters seem to instigate unspecified Psi, or Psi-Something, rather than a lack of Psi (Psi-Nothing).

A higher sociometric mark got by the transmitters (TransGr) contributes to moving the results away from chance, counter to the mark got by the receivers.  This can be explained the following way:  when there is a better familiarity among receivers, they tend to focus on the partners in their own subgroup instead of focusing on the message sent by the transmitters.  On the contrary, when the transmitters are well known by the receivers, this contributes to widen the distance from chance, for the receivers take a stronger interest in the transmitters’ group and the message they send. 

In other words, group life tends to give rise to a fusion between the members of each sub-group (transmitters and receivers), and this prevents the members of a sub-group from connecting with the members of the other sub-group (weakened transmission).  This phenomenon is clearer when the receivers know one another beforehand, and when there are no special tensions among them.

If it’s not the case, and if there are strong links between transmitters and receivers, the transmission can be better.  It would be appropriate to change very often the role (transmitter or receiver) of each participant to avoid the « coagulation » of the sub-groups.  We also still have to examine if the tries following right away a “gathering of all participants” (after the breaks), favour a wider distance from chance than the other tries. 

Is Psi-Missing an anti-Psi defence?

If we admit that there is Psi in our experiment, we are forced to observe that we can’t underscore any parameter that would facilitate Psi-Hitting against Psi-Missing.  The fact that there is as much Psi-Missing as Psi-Hitting suggests that there is a strong tendency to reject the right answer coming from the transmitters’ sub-group, as if it was a way of protecting from it as an trespass or intrusion from the transmitters.  Considering the huge variety of targets used, the hypothesis of a Freudian perceptive suppression is unlikely, even if perfectly unconscious.  Couldn’t it be the need for each individual to avoid his own dissolution in order to exist as an individual with a psychic frontier?  This phenomenon could be enhanced if the individual belongs to a group, situation which favours the fusion among the members!  Some subjects, who got significant results within other experiments involving pairs, just had results close to chance in the collective frame defined by Agape’s protocol. 

The attempt by the statisticians from Pr. Aragon’s laboratory to carry out a heuristic study is no proof and can’t hide our discomfiture in relation to the hypothesis tested.  However, it opens the door to a further research; we can devise indeed a protocol to test the following hypothesis:  we can hope for success with groups only if we build sub-groups so that there is more affinity between each receiver and at least one agent than there is affinity among receivers.  The simple sociometric test used for Agape should be enough to achieve this, provided the results before each session help to distribute the roles.  That’s what we plan to do in the protocol SYBIL.