A rejected manuscript

As the reviewing process reveals, there have been some misunderstandings regarding the ideas in my paper, The Balancing Effect in brain-machine interaction. These misconceptions refer to the role of the funnel plot of MicroPK data, the use of the Markovian model to successfully replicate it, the Rescaled Range Analysis of MicroPK data sequences, and the interpretation of the analysis results.

In this text, I aim to clarify the misunderstood concepts by directly responding to the more relevant comments of the two anonymous reviewers.

My response: Assuming that the comment indicates by p(1,0) the probability (or frequency) of dyad sequences of the kind: '10' and likewise '01', the statement p(1,0) = p(0,1) > 0.5 is wrong. This frequency, estimated by the Markovian model for the MicroPK database, is approximately 17%. It is below and not above 0.5, as this reviewer concludes. So, if "we mapped (0,1) and (1,0) on 1", then there will be fewer '1' than '0' digits. That's a clear imbalance of bits, not a non-existent MicroPK as the reviewer assumed. Yet, my paper shows quite the opposite to be the case.

The error seems to be the confusion about what digits '1' and '0' represent in the Markovian model of MicroPK data. Each MicroPK '1' involved in the funnel plot implies 'hit'; a successful trial in a study. Each MicroPK '0' is a 'failure' (a 'miss'), not bits generated by RNGs. [Bösch et al., (2006)] have carefully converted (from 'z-scores', or 'es') all records of MicroPK tests with true RNGs into the proportion of hits, 'pi'. The funnel plot presents the size of the study, N, against this proportion of hits, 'pi', i.e., the proportion of 1's.

Therefore, in the Markovian model, a dyad sequence {(0,1) or (1,0)}, i.e., 'hit after miss' or 'miss after hit' cannot be mapped by a 'hit'; by '1'! Similarly, a 'hit after hit' and 'miss after miss', i.e. (1,1), (0,0), cannot be mapped by a 'miss', by '0'. As these digits are not RNG-generated bits, they cannot be manipulated by software or hardware. If such replacement were introduced in MicroPK data sequences, as suggested, this would be condemned as data manipulation! Neither can such mapping be implemented in the Markovian model, as equally forbidden.

My response: This paper was written specifically to show no discrepancy between my early test results that indicated the "balancing effect" and my recent results that indicate no evidence for the MicroPK hypothesis. Naturally, all related previously published results had to be invoked in this paper. As such, my paper maintains its originality.

My response: The convergence of the funnel plot of MicroPK data is not close, but equal to 0.5. Also, the funnel plot refers to one whole database; it's not a funnel plot for large N or a funnel plot for small N. Therefore, the funnel plot converges to 0.5 for the whole MicroPK database. Said differently, the most representative effect size for the MicroPK database is 0.5: The chance result of a random process that true RNGs exhibit!

The Markovian model can successfully simulate the broadening of the funnel plot and its convergence to 0.5. It is wrong to include the asymmetry in its successes. The asymmetry in the spread of data on the funnel plot is caused by publication bias driven by the attitude of experimenters to neglect reporting data or to err during data collection. Once data points on the funnel plot are generated via the Markovian model, one should randomly remove some from sections that align with the experimenters' attitudes, introducing publication bias to account for the asymmetry.

My response: The reviewer of my paper implies, as it was argued in the debate [1], that the body of MicroPK data with pure RNGs be truncated into smaller parts, which are conveniently tagged according to a property of the database (the size of the study), and to separately analyze smaller parts of the database. In that sense, a selection of data will be introduced, and many interpretations will be individually offered for the MicroPK hypothesis for each subdivision of the database as if it wasn't the only hypothesis to be tested.

As discussed in my paper, in studies of smaller size (often generating bits at a slower rate), there is a higher risk of introducing biases during the collection of data (often to satisfy the expectations of the experimenters [2]). Those who adhere to such database fragmentation instinctively understand or have first-hand experience with the stronger effects expected in small-size MicroPK studies. So, they emphasize the need to treat small-size studies separately. Yes, small studies tend to show higher MicroPK scores, but this is not because some direct Mind-Matter Interaction manifests better in such small studies [3].

My paper presents the analysis of MicroPK data with pure RNGs as a whole, as the question under the microscope is only to investigate "the MicroPK effect with true Random Number Generators". Fragmentation of the database is equivalent to data manipulation, and this is my answer to why such 'alternative approaches' are not viable.

My response: I have suggested that "there most likely exist real psi effects, e.g. telepathy and clairvoyance" worth of investigation, which is far from my stating that I have accepted them as real psi effects.

Furthermore, the reviewer prompts to adopt the following non-scientific task: to explain away a purported effect (MicroPK) by invoking another unsubstantiated effect (clairvoyance).

Finally, many scientists introduce the R/S analysis and Markovian processes in their research, who do not consider them as complicated.

My response: Using the label "PK-MP correlations" (MP for Markovian process) that the reviewer adopts is misleading for a couple of reasons. First and foremost, my paper shows that there is no evidence for a MicroPK effect.

Furthermore, the Rescaled Range analysis, R/S (or RSA as the reviewer labels it) does not provide evidence of a Markovian process (the 'PK-MP', according to the reviewer's tagging), but of possible long-range correlations present in the data sequences, not caused by Mind-Matter Interaction (MicroPK).

The Markovian model was only implemented to introduce a magnifying glass into the inner machinery of the 'MicroPK process', at the level of single trials. The model has successfully simulated the main features of the database, i.e. the broadening of data (indicating the presence of Markovian correlations between trials) and its convergence to 50% (indicating that the MicroPK hypothesis is refuted).

The collective evidence, considering the R/S analysis too, suggests that those long-range correlations present in the data sequences are introduced by "data handling", i.e. conscious or unconscious errors during the collection and reporting of data and not a mind-matter interaction.

My response: My analysis does not suggest the presence of a PK effect; Quite to the contrary. It shows that there is no MicroPK effect.

Regarding the MP part of the same label, the Markovian model can simulate the funnel plot of a database comprised of the proportion of hits generated by a binary process. Such funnel plots can exhibit either larger or narrower dispersion than expected or no deviation from the normal (see Fig. 5).

The dispersion of data in the MicroPK funnel plot is more extensive than expected from random data, indicating data correlation between hits or misses in separate studies due to introduced errors during experiments.

My response: There are two R/S analyses discussed in my paper, not only one. They were performed on two separate occasions and with different data, yielding different results.

1. The first analysis refers to the FAMMI MicroPK, control, and calibration data [Pallikari, (1998); Pallikari (2001)]. It indicated the presence of weak persistent long-range correlations in sequences of MicroPK data; even weaker correlations were present in control data and none in calibration data generated by RNGs that have passed the test for proper performance.

2. The second was applied [Pallikari, (2015)] on the time series of MicroPK data taken from the funnel plot, i.e., on the sequences of MicroPK test records specifically arranged per date of publication as accurately as possible.

The second analysis showed that the reported effect sizes in MicroPK tests by 62 principal experimenters over 35 years were not independent. There were persistent long-range correlations in the arranged per-date sequence of their reported data, indicating a mimicking aspect in the attitude of experimenters.

My response:

1. The Rescaled Range Analysis, R/S, did not produce these Markovian transition probabilities. The fitting of the Markovian model on the funnel plot of MicroPK data has produced them.

2. The Markovian transition probabilities, p00, and p11 represent the average frequency of runs of size 2 of the same bits (bit = a hit or a miss trial). They are probabilities that a 'hit' follows a 'hit' and a 'miss' follows a 'miss' in a sequence of all MicroPK records in the meta-analysis. True, such information cannot be available for practical reasons. Yet, such high frequency is expected due to the longer runs of MicroPK 'successes' or 'failures' being generated on average due to errors introduced during tests.

3. What exactly are these "simpler analyses" the reviewer refers to? And can these analyses estimate the frequency of runs of the same score of size = 2, (hit-hit & miss-miss), as in #2 above, across all MicroPK test results?

4. Unlike what the reviewer maintains, these transition probabilities do not indicate PsychoKinesis, PK.

5. An average frequency of two 'hit' or 'miss' trials in a row across all MicroPK experiments as high as 83% corresponds to a correlation coefficient between the adjacent MicroPK records of 66% [see Table 2 in Fotini Pallikari, Investigating the Nature of Intangible Brain-Machine Interaction, Journal of Social Sciences and Humanities, 1(5), 499-508, (2015)].  Unlike what this reviewer believes, this is a moderate, not "a fantastically large" degree of correlation. Not a 'PK effect'.

If all experimenters carried out their MicroPK tests religiously in the same (unnatural) manner, so that the correlation coefficient between adjacent trial scores was 66% (instead of 50%) due to a fixed 83% persistence to yield a 'hit' after a 'hit' and a 'miss' after a 'miss' (instead of 50%) and their average scores were presented on a funnel plot, then this plot would share the same characteristics as the funnel plot of MicroPK data (lacking the publication bias). To account for the publication bias, some experimenters, especially of small-size studies where the proportion of hits may have, by natural causes, fallen below 50%, should remove their data from the funnel plot. Then, the observed asymmetry will be reproduced, too.

Yet, a universal mechanism of direct mind-matter Interaction, where the MicroPK test participants affect the random process through direct mental interference, does not exist (as the database's funnel plot confirms converging to 50%).

In conclusion, these proclaimed by the reviewer as "high" transition probabilities stand only as an equivalent average of a model mechanism, operating deep at the level of trials, being introduced by the mishandling of MicroPK data.

My response: The broadening of variance my paper mathematically treats refers to all the MicroPK test scores with pure RNGs. That is the unnaturally broadened dispersion of MicroPK scores in the extensive MicroPK database. It is the dispersion of data points (separate MicroPK test records) in the funnel plot and not just the dispersion of trial scores in one experiment, i.e., of trials inside one data point (one study) on the funnel plot, such as the one referring to the consortium data.

It is well known that the consortium data have all yielded zero mean shifts (refuting the MicroPK hypothesis). They may have also produced variance at the null expectation concerning random data. Such null deviation from chance in variance implies that the data are randomly distributed (see Fig. 5) and that there is an absence of correlations in the data sequences. However, this is doubtful as my analysis [Pallikari, (1998); Pallikari (2001)] has identified persistent correlations in these data sequences, which should affect their variance. This reviewer seems to be well-informed about the details of the consortium experimental results. But I also have direct knowledge of them regarding the FAMMI data (of the Freiburg, IGPP branch).

The broadening of the funnel plot, though, is not brought about by data in only one experiment, i.e., not due to one "star system" but to the whole "galaxy" of MicroPK data. All these data collectively exhibit a broadening of variance, i.e., correlations binding data points on the funnel plot, whereas these should be independent.

Therefore, even if there was no variance deviation from expectation in one MicroPK experiment only (which my previous analyses challenge), this does not refute the successful application of the Markovian model (which indicates an increase of variance across all experiments). Moreover, the Markovian behavior of MicroPK data is not itself PK, according to the reviewer's comment.

My response: The R/S analysis identifies long-range correlations, not short-range ones. These long-range correlations identify an overall trend in MicroPK test results that binds the data regardless of their separation.

Perhaps the reviewer refers to the shorter MicroPK sequences as those generated by one group (FAMMI). The different ways of assembling experimental, control, and calibration data may be the source of introducing long-range correlations.

My response:  The analysis of MicroPK data presented in my paper considers the database generated in the associated meta-analysis [Bösch et al., (2006)] (tagged as BSB by the reviewer) as the product of careful and honest data selection [4], one that provides valuable information about the MicroPK hypothesis with true RNGs.

If data are removed from this database (accusing experimenters of having published the wrong data or some unreliable effect sizes), it destroys/manipulates the database formed under a precise question. The question is to investigate the hypothesis on direct mind-matter interaction with true RNGs. One cannot apply their unjustified beliefs to dismantle a database to explain away their expectation. With their comment, the reviewer demonstrates the argument in my paper, which is how easily experimenters introduce data manipulation when contributing to or analyzing a database.

My response:  I am not using PK-MP because the evidence indicates no micro-PK effect. As for the MP tag, the Markovian model (Process) successfully simulates the main characteristics of the MicroPK database: its broadened scatter and its convergence to 50%.

The database asymmetry, on the other hand, could be introduced a posteriori by removing data from the already simulated database (corresponding to data that some experimenters decided not to report, thus introducing publication bias) and not because these data could already exist in the database simulated by the Markovian model. Removing some data points from the simulated funnel plot of Fig. 5c reproduces the asymmetry.

My response: The reviewer accuses the authors of the already published MicroPK meta-analysis [Bösch et al., (2006)] without providing precise and concrete evidence to support these accusations other than to 'strongly suspect' the hypothetical misconduct.

Still, this asymmetry in the funnel plot of control data is not limited to regions where the reviewer focuses having size just above N=100, but confirmed by the spread of data in other areas of the funnel plot, e.g., above N=1000.

My response: The statistical balancing in the MicroPK database is due to accidental statistical data formation. It may be observed as the consequence of the law of large numbers in large enough databases whose statistical average converges to a null mean shift [5]. The statistical balancing observed in unweighted experimental and control MicroPK scores is not a hypothesis under verification. It happened to appear in the extensive MicroPK database despite the publication bias in it.

Before the publication of the MicroPK meta-analysis [Bösch et al., (2006)], there was a period of debate between a circle of researchers against its results [1] during which the reviewer, who seems to be well-informed about the details of this meta-analysis, should have addressed such concerns regarding the validity of data. If such an objection had been raised, I understand that [Bösch et al. (2006)], fluent in German, could have easily spotted such possible errors and would have duly corrected their database. As [Bösch et al. (2006)] have improved their meta-analysis following the debates and thus considered it correct for publication, such belated critique addressed here is totally out of place.

My response: The term 'expectancy MP' must refer to the 'experimenter expectancy effect' mentioned in my paper. The unintended and well-documented influence of the experimenters' hypotheses or expectations on the results of their research [Rosenthal (2004); Bakker et al. (2011)]. My analysis shows that previous similar publications influenced the report of experimenters  (Hurst exponent of the arranged MicroPK data being above 0.5).

a. My paper does not propose, as the reviewer labels it, an 'expectancy Markovian process' (an 'expectancy MP').

b. The 'experimenter expectancy effect' does not introduce a 'statistical balancing' of data.

c. The 'experimenter expectancy effect' is not only present in the MicroPK studies but is common in almost all areas of scientific inquiry [Rosenthal (2004); Bakker et al. (2011); R. Nuzzo, Nature, vol. 526, pp. 182-185, (2015)]. It is, therefore, not used ad hoc in my paper.

d. The 'experimenter expectancy effect' is well reviewed within psychology, too [R. Nuzzo, Nature, vol. 526, pp. 182-185, (2015), see page 184].

e. The suggestion that experimenters are influenced by previously published studies in the same field when reporting their results describes a trend. It does not imply that every experimenter has done so. That would be impossible anyway for MicroPK studies presented at a conference. That this tendency of experimenters is present in MicroPK tests is confirmed by the R/S analysis of the MicroPK time series, which yielded a Hurst exponent above 0.5.

My response:

(A). Regarding the sentence 'Accepting Yu et al. position without rejecting PK': The reviewer asserts that although consciousness may not be needed to collapse the wavefunction, it can perform the task, nevertheless. This assertion is fallacious as will be explained in (B) below. In any case, the MicroPK (and PK) hypothesis is not rejected by the paper of Yu et al., but by the strong evidence against it, as presented in my paper.

(B). Suggesting that consciousness can collapse the wave function (that the mind can directly affect the physical process) is equivalent to suggesting that the mind-matter MicroPK hypothesis is valid. But, there is no evidence in support of MicroPK. So, neither is consciousness needed to collapse the wavefunction nor can it perform such a feat.

(C). To formulate a (quantum) theory of a phenomenon, there must pre-exist evidence to support it. Yet, there is no evidence for MicroPK, and there can be no theory (or extension of a theory). 

Furthermore, the discussion is limited to MicroPK data and not to any 'psi phenomena', as the reviewer chooses to generalize.

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