Agapè: Checking the Stacking-Effect

AgapÈ : checking the stacking-effect

Bernard M. Auriol¹, Frédérick Garcia², Laetitia Puech³, Sylvie Lagrange³, Corinne Morer³, Olivier Rabat³, Sophie Valentin³, Eve Leconte³ and Olivier Perrin³

¹Institut Métapsychique International, IMI-Paris, France

²Institut National de la Recherche Agronomique (INRA), Toulouse, France

³Université Toulouse I and Université Toulouse III, France

Abstract

From December 1993 to January 2001, we carried out 240 ESP group sessions with majority vote. Both the number of individual successes and the number of collective successes (result of majority vote) proved to be compatible with the null hypothesis. The variance presented interesting anomalies but their interpretation is awkward.

The redundancy offered by the majority vote, 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.

In case the seemingly random data belong to a second kind error, we initiated an analysis of the covariance, carried out for exploratory purpose only, in order to discern the protocol parameters which could have had an impact on the results. We work at the trial level. A trial 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 trials 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 trial 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, it appears that it’s nearly the same protocol parameters that hold the results away from chance expectation in both cases (hits and misses). 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 strong social links between the transmitters result in bringing the outcome closer to chance.

But because these interesting results could be linked to a "stacking effect" (Caroline Watt, 2003), we used a resampling method to control that "stacking effect". Indeed, the replacements of the genuine targets by fake targets does not fundamentally change the results of the covariance analysis: The creation of faked targets allowed us to select new significant collective trials. The regression conducted on these gathered results very similar to those excerpted from the genuine data. We observe the same thing about the sociometric data.

Thus, we are most probably facing a stacking effect.

Introduction

The Agapè project, ESP group sessions with majority vote (Auriol, 2003) gave puzzling results: Both the number of individual successes and the number of collective successes (result of majority vote) proved to be compatible with the null hypothesis but the variance presented interesting (though awkward) anomalies.

The seemingly randomness of our data could belong to the second kind error. This is why, on a purely exploratory basis, and under the assumption that ESP would be (within the framework of our protocol) a scarce phenomenon with a weak impact and/or unspecified sign (sometimes towards Psi-Hitting, sometimes towards Psi-Missing) we undertook a covariance analysis on the collective trials which deviated significantly from expectation (p < .05). We are well aware that we can expect 5% of the trials to be different from chance under the threshold p = 0.05, but we don’t foresee (H_o) that a regression on these trials leads to identify parameters which would increase or decrease the difference from chance (H₁) .

If any interesting results were released they could be due to a stacking effect. An available parade would be to use the Greville correction (1944). However, this tool, in the context of our study, is very laborious (Cf. Thouless & Brier, 1970), nearly impossible to deal with. We thus decided to use a resampling technic.

Methods

Protocol structure

The main steps were :

1. A Personal Computer selects a target (word or picture) randomly and displays it in the room of the transmitters.

2. This target is also displayed with decoys in the room of the receivers. Each receiver has a keypad and selects a number corresponding to one of the possible targets.

3. Then, results are recorded and the PC gives (or not) a collective and/or individual feedback.

4. Then, there is a new trial. After a certain number of trials, there is a break and the next series starts. And so forth until the participants are tired or the time is over.

Several sub-protocols

Three main sub-protocols have been tested:

- Two pictures: A picture which is randomly picked by a computer among a directory of 1 500 pictures is proposed with a decoy to the transmitting group. The members of the receiving group must choose between the two pictures which are displayed randomly on two screens (one is the emitted picture, the other one is a decoy).

- Three words: A very common word is randomly picked among a large list and is proposed to the transmitting group. It is proposed to the receiving group with two decoys.

- Five words: The participants brainstorm a list of five words repeatedly used during the whole session. The transmitting group sends one of the five words, randomly selected by the PC, and the receivers make their choice among the words of the list.

In order to determinate if there are conditions favoring ESP results we varied some other details in the protocol (Auriol, 2001) :

The «white screen latency» : that is a period between the beginning of the transmission by the transmitters and the display of the list of possible targets on the screens of the receiving group. This period of time can last during 0, 3, 5, 9, 10, 18, 20 or 60 seconds. The instruction given to the receiving group was to let all sensations, words or pictures come to their consciousness. The members of the receiving group were encouraged to use this material afterwards for guessing the target.

The «maximum deadline left» to the receiving group to answer can vary between 18, 20, 25, 30, 60 or 120 seconds.

This period can be cut short: When 50% of the receiving group has answered, the software leaves to the rest of the group only the elapsed time (x2=x1) or twice the elapsed time (x2+x3=2x1) to give their answer. If the total time exceeds the maximum deadline, then, the answers done after the deadline are not taken into account (Fig. 1).

Fig. 1

After the judging is closed a feedback is given.

- Individual feedback: each receiver is informed of his/her personal hit or miss, by displaying on the screen either his/her name or the target.

- Feedback for the group: when the trial is over, if the vote gives a hit, the lights are switched on (traffic lights’ style: see on the right of the displays, fig 1, 2 and 3) in the transmitters’ room and the receivers’. For some sessions, one light is switched on even if the majority gives a miss provided that the number of right individual answers be above the mean chance expectation. The number of lights on depends on the strength of the majority.

- Instructions may be given to the transmitters, or they may be free to send the message their own way. When there were instructions, they consisted of: for some sessions, to focus on the target to transmit, for others, to focus especially on one (or several) receiver(s) chosen, as much as possible by each transmitter.

Sociometric questionnaire

Before many sessions, the receivers had to answer on their keypad to the following question about each of the other participants (either transmitter or receiver): “Do you know this person?” [mark from «not at all» (1) to «very well» (5)].

The participating groups were "open" groups: each individual joins in as he/she wishes. Each participant chooses to be transmitter or receiver at the beginning of session and he/she keeps doing until at the end of this session. The number of the transmitters varied from 0 to 15 people and the number of receivers from 1 to 16 people.

Results

Collective trials significantly departing from chance

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 trial

- p is the expected percentage (0.50 for two pictures, 0.33 for three words and 0.20 for five words).

If we look into the quality of the trials, we can test if the percentage of hits got for each trial 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 trial, is

~Khi² (one df)

	Number of trials	Percentage of trials
Higher than chance	1079	3.87%
Lower than chance	413	1.48%
Equal to chance	26 353	94.64%

Table 1 : Collective trials selected with a threshold of 5%

We focus on the trials where the target collects either significantly more votes or significantly fewer votes than expected. The effect of different variables of “protocol” on the answers will be outlined with a covariance analysis. The significant variables will be selected thanks to a stepwise procedure and kept under a threshold of 5%. We took into account the trials significantly lower than chance as well as the trials 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.

To check the stability of the selected variables we carried out, with comparable results (Auriol et al., 2004b), the same covariance analysis regarding the collective trials tendencially significant (p<0.10 and p<0.20).

We consider the case where the variable « answer » (transformed percentage h) is significantly higher or lower than the expected value under the null hypothesis. We get significant variables with a p-value close to 0.0001 (Table 2).

	Variable	Estimate
	Collective trials	Higher than chance		Lower than chance
	Constant	+1.06		-1.12
Qualitative Variables	The transmitters were given an instruction		+0.10		…
	The participants chose the targets’ list		-0.34		+0.26
	There was some kind of group reward		-0.13		…
	The time left once half the receivers answered = the time already spent		+0.27		-0.02
	The time left once half the receivers answered = twice the time already spent		+0.30		-0.12
Quantitative Variables	Time to answer		-0.01		+0.01
	Ratio {nb of transmitters / nb of participants}		-1.46		…
	Ratio {nb of transmitters / nb of receivers}		+0.96		…

Table 2: significant variables- (calculated on the genuine data)

Fig. 2

Parameters linked to getting the results closer to chance (Fig.2):

The participants could choose the potential targets’ list (-0.34)(+0.26)

The session included some kind of readable group feedback (-0.13) (…)

A longer time granted to answer (-0.01) (+0.01).

Parameters linked to the results departing from chance (Fig.2):

When 50% of the receiving group has answered, the software leaves to the rest of the group only the elapsed time (x2=x1) or twice the elapsed time (x2+x3=2x1) to give their answer. (+ 0.27 & +0.30) (-0.02 & -0.12)

Protocol in which the transmitters received an instruction (to focus either on the receivers, either on the target) (+ 0.10) (…).

· Number of transmitters and receivers: The two ratios { number of transmitters / number of participants } [(k*NbT)/(NbT+NbR)] (-1.46) (…) {closer to chance} and { number of transmitters / number of receivers } [(g*NbT)/NbR] (+0.96)(…) {away from chance} must be interpreted together because the same variables are involved in both..

Effect of the relations between participants

We made two ratio based on the data from the sociometric questionnaire:

	Receivers’ Mark		Transmitters’ Mark
RecGr =	----------------------------	TransGr =	--------------------------
	Group’s Mark		Group’s Mark

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 trials (p<0.05) with higher results than expected (Psi-Hitting), the table had 1,079 observations with 438 missing data; 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).

Variable	Estimate	Success	Distance from chance	P-value
RecGr	-1,54	-	-	<0.0001
TransGr	+0,58	+	+	0.0003

Table 3

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) (Table 3).

We find the same tendency, although not as clearly (effect very small), if we take into account significant trials 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 variable linked to better results are also linked to worse results. In that way we could conclude «the significance is increasing only because the receivers give more similar answers, independently of the hypothetical transmission process originated by senders».

Checking the stacking effect

Covariance analysis is valid only if one admits independence of the answers of the subjects; this condition was partially met because each subject had an individual keyboard. However occurrence of a "stacking effect" it cannot be cleared out insofar as somebody could have been "copying". A telepathic influence of a leader on the choice of other receivers cannot be drawn aside; when this leader misses the target; he/she could transmit to some of the other receivers the decoy he believes the right answer (Auriol, 2004a). Mostly, the receivers can have collective preferences / dislikes for some possible targets.

In addition, the subjects could have adopted more or less common strategies (Krugel, 1978), based on the feedback: to play back a guess which succeeded at the preceding trial, or on the contrary to avoid it. In fact, this phenomenon had significant effects on the protocols with three and five words (Garcia, 2003).

A stacking effect could meet the same results as our covariance analysis. In such a case, the selection of the variables would depend only on the answers of the percipients. This selection should be about the same one if we replace the genuine targets by faked target ones. We thus have remake calculations by carrying out a permutation of the targets:

Permutation 1 consists to replacing the genuine target by a target shifted of one row.

Permutation 2 consists to replacing the genuine target by a target shifted of two rows. And so on for permutations 3 and 4.

Permutation 5 consists to replacing the genuine target (target number i) by the fictitious target (target number i+1). If i is maximum, we replaced i by 1.

	Genuine data	First permutation	Second permutation	Third permutation	Fourth permutation	Fifth permutation
	Number of trials	Number of trials	Number of trials	Number of trials	Number of trials	Number of trials
Higher than chance	1079	1047	1028	1052	1011	1073
Lower than chance	410	426	423	435	454	460

Table 4 : Collective trials selected with a threshold of 5%

1.1 Analysis of the collective trials significantly higher than expected :

	Names	Abbrev.
Qual. Variables	The transmitting group has had an instruction	Instruction
	The participants (agents and percipients together) have chosen the list of potential targets	Choice
	There was a group feedback	G feedback
	There was an individual feedback	I feedback
	Maximum time for the vote = 20 seconds	20Max
	Maximum time for the vote = 60 seconds	60Max
	Maximum time for the vote = 120 seconds	120Max
	The time left to vote was shorted when the half of the percipients had voted	TimeLeft
Quant.Var.	Ratio : number of agents / number of participants	A/(A+P)
Quant.Var.	Ratio : number of agents / number of percipients	A/P

Table 5 : names of variables and abbreviations

		Genuine data	First permutation	Second permutation	Third permutation	Fourth permutation	Fifth permutation
	Variable	Estimate	Estimate	Estimate	Estimate	Estimate	Estimate
	Intercept	+ 0.92	+ 0.91	+ 0.82	+ 0.78	+ 0.78	+ 0.93
Qualitative Variables	Instruction	+ 0.10	+ 0.06			+ 0.10
	Choice	- 0.29	- 0.32	- 0.30	- 0.32	- 0.30	- 0.32
	G feedback	- 0.11	- 0.08	- 0.09	- 0.11	- 0.10	- 0.06
	I feedback	+ 0.04		+ 0.06
	20Max	+ 0.13	+ 0.20	+ 0.19	+ 0.21	+ 0.19	+ 0.15
	60Max	+ 0.19	+ 0.21	+ 0.24			+0.17
	120Max	+ 1.08	+ 1.04	+ 1.05			+ 0.98
	TimeLeft	+ 0.07	+ 0.13	+ 0.07	+ 0.12	+ 0.09	+ 0.13
Quantitative Variables	A/(A+P)	- 1.06	- 1.31	- 0.81	- 1.16	- 1.50	- 1.58
Quantitative Variables	A/P	+ 0.86	+ 1.02	+ 0.82	+ 0.93	+ 1.13	+ 1.13

Table 6 : Analysis of the collective trials significantly higher than expected

1.2 Analysis of the collective trials significantly lower than expected

		Genuine data	First permutation	Second permutation	Third permutation	Fourth permutation	Fifth permutation
	Variable	Estimate	Estimate	Estimate	Estimate	Estimate	Estimate
	Intercept	- 1.21	- 1.43	- 1.43	- 1.42	- 1.24	- 1.45
Qualitative Variables	Instruction	- 0.10	- 0.12	- 0.15	- 0.15	- 0.09	- 0.15
	Choice	+ 0.22	+ 0.24	+ 0.31	+ 0.31	+ 0.26	+ 0.34
	G feedback		+ 0.12	+ 0.06	+ 0.07		+ 0.07
	I feedback	+ 0.10	+ 0.10
	20Max
	60Max		- 0.14
	120Max
	TimeLeft	- 0.08				- 0.0433
Quantitative Variables	A/(A+P)			+ 1.37	+ 1.06	+ 1.02	+ 1.16
Quantitative Variables	A/P	- 0.13	- 0.15	- 0.65	- 0.49	- 0.49	- 0.49

Table 7: Analysis of the collective trials significantly lower than expected

2. Effect of the reciprocal knowledge between participants

We asked to the percipients, „do you know this people ?“ (ranked from „not at all“ to „very well“) and we calculated two ratios :

Resgr =

Emetsgr =

(“Receiver score“ = mean of the marks that the receivers have allocated to the other receivers; “Transmitter score” = mean of the marks that the receivers have allocated to the transmitters; “Group score” = mean of all the marks)

2.1 Analysis of the collective trials significantly higher than expected (p <.05):

	Genuine data	First permutation	Second permutation	Third permutation	Fourth permutation	Fifth permutation
Total number of observations	1079	1047	1028	1052	1011	1073
Usables observations	662	624	620	644	616	654

Table 8

	Genuine data	First permutation	Second permutation	Third permutation	Fourth permutation	Fifth permutation
Variable	Estimate	Estimate	Estimate	Estimate	Estimate	Estimate
Resgr	- 1.48	- 1.49	- 1.32	- 1.86	- 1.34	- 1.39
Emesgr	+ 0.59	+ 0.38	+ 0.36	+ 0.35	+ 0.41	+ 0.40
R²	0.11	0.11	0.07	0.13	0.09	0.09

Table 9

2.2 Analysis of the collective trials significantly lower than expected (p<.05):

	Genuine data	First permutation	Second permutation	Third permutation	Fourth permutation	Fifth permutation
Total number of observations	410	426	423	435	454	460
Usables observations	352	363	369	373	383	387

Table 10

Results

	Genuine data	First permutation	Second permutation	Third permutation	Fourth permutation	Fifth permutation
Variable	Estimate	Estimate	Estimate	Estimate	Estimate	Estimate
Resgr	+ 1.77	+ 2.18	+ 1.93	+ 1.91	+ 2.04	+ 1.62
R²	0.12	0.13	0.15	0.13	0.13	0.11

Table 11

Indeed, the replacements of the genuine targets by fake targets does not fundamentally change the results of the covariance analysis: The creation of faked targets allowed us to select new significant collective trials. The regression conducted on these gathered results very similar to those excerpted from the genuine data. We observe the same thing about the sociometric data.

Thus, we are most probably facing a stacking effect.

Discussion

Every association of variable levels was not present. Consequently, confusional effects could have been at work. For example, participants can have chosen the list of possible targets only during the first sessions (5 words protocol), the maximum deadline “120 seconds” was tested only for the 3 words protocol …

Is Psi-Missing an anti-Psi defence?

Yet, if we assume that there is Psi in our experiment, we are forced to acknowledge that we have not been able to find any variable that would facilitate Psi-Hitting against Psi-Missing. 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? Some subjects, who got significant results within other experiments involving pairs, just had results close to chance in the collective frame defined by Agapè’s protocol. This phenomenon could be enhanced if the individual belongs to a group, situation which favors the fusion among the members!

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Softwares : Excel, S-Plus (MathSoft) and SAS.

Acknowledgments

Grant : Fondation Odier de Psycho-Physique

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