Mind–Matter Entanglement Correlations: Blind Analysis of a New Correlation Matrix Experiment

Grote, H. (2021). Mind–Matter Entanglement Correlations: Blind Analysis of a New Correlation Matrix Experiment. Journal of Scientific Exploration, 35(2), 287–310. https://doi.org/10.31275/20211931

AI Assessment

A pre-registered blind-analysis replication whose main pre-specified result was null and is reported as such. Two hundred participants spent about half an hour each trying to influence a hardware random process, and the pre-registered correlation-matrix analysis, unblinded live at the 2019 Parapsychological Association convention, returned p = .76. A second blind-analysis experiment correlating questionnaires with the psi task returned p = .064, and a post hoc count of raw hits returned p = .064 as well, a numerical coincidence the author flags himself. The analysis code and the full experimental data are publicly accessible on the Open Science Framework.

Provenance

DOI. 10.31275/20211931 · Open access, Creative Commons License CC-BY-NC.

Author. Hartmut Grote (Max Planck Institute for Gravitational Physics, Hannover, Germany), a gravitational-wave physicist writing as sole author and sole experimenter. Submitted August 6, 2020; accepted January 4, 2021; published June 15, 2021.

Study type. Conceptual replication of the correlation matrix micro-psychokinesis experiment of von Lucadou, run under a blind analysis protocol in which the complete analysis software was written and tested before the data were analyzed for the effect under study.

Funding. BIAL Foundation, grant number 161/19. The study was approved by the ethics committee of the Max Planck Society; the author states that no other resources of the Max Planck Society were used.

Data availability. The apparatus code, feedback audio files, test random data, consent form, and questionnaire were pre-registered before data-taking at osf.io/cgf4k; the analysis code and all experimental data are accessible at osf.io/xwhn6 (Experiment 1) and osf.io/cj8kd (Experiment 2).

Source basis. Figures confirmed against the primary article (publisher PDF, Journal of Scientific Exploration, 35(2), 287–310).

What the paper reports

Two hundred participants, the pre-planned number, each spent about half an hour with a purpose-built device, pressing buttons to try to influence the direction of an arrow on a screen that was driven by a hardware random number generator.¹ Experiment 1, the pre-registered correlation matrix analysis in the tradition of von Lucadou,² correlated 45 psychological variables against 45 physical variables and evaluated the 900 time-forward correlation factors as a single ensemble. Its unblinding, performed live at the Parapsychological Association convention in Paris on July 6, 2019, showed the result falling well within the permutation background distribution, p = .76, with no evidence of anomalous correlations. Experiment 2 correlated a 50-item questionnaire with each participant’s performance on the psi task and returned p = .064, marginal and on the same order as the result of Jolij and Bierman that it conceptually replicated.³ A post hoc analysis of the raw psi task found a surplus of 138 hits out of 96,000 trials, p = .064 one-sided, the same numerical value by what the author calls pure coincidence. The paper closes with three anecdotal incidents the author found remarkable, including an 8-year-old boy, the only person tested outside the regular cohort, whose excluded session produced the most extreme psi-task score of anyone, a total of −19 with a two-sided p = .0038.

The pre-registered main analysis returned a null result. Both p = .064 findings sit above the conventional significance threshold, one of them is post hoc, and the author notes that their identical numerical value is pure coincidence.

How it was run

• A total of 200 participants completed the experiment between December 2017 and May 2019 at four locations: 75 from the general population of the Santa Fe area (tested at Mountain Cloud Zen Center), 48 students in Freiburg im Breisgau (tested at the IGPP institute), 56 recruited and tested in Berlin and Hannover, and 21 in Oxford and Cardiff. Average age was 45.6 years (SD 17.5); 78 reported as male and 122 as female.
• The apparatus was a dedicated device of wood and metal built by the author, with a 7-inch video screen and four push buttons. Its new hardware random number generator drew on the thermal noise of two electrical resistors in a differential, shielded configuration; 16-bit random Words passed Marsaglia’s diehard test suite with no suspicious deviation from randomness, and successive Words were compared to yield binary random events.
• Each session comprised 9 runs of 80 button presses. In each run the participant tried to move the displayed arrow in an instructed direction (right, middle, or left, each condition occurring 3 times), with each button press triggering one random event that stepped the arrow right or left. Auditory feedback, cheering sounds for hits and a less pleasant sound for misses, was novel in this experiment.
• For about half of the participants the random events were generated in real time (RT-bits); for the other half the full bit sequence was XOR’d with a Mersenne Twister pseudo-random stream and pre-recorded at the start of the session (XPR-bits), read from memory 15 to 30 minutes later. The control computer assigned the bit type randomly per participant; participants did not know of the two modalities, and the experimenter remained blind to each assignment until the unblinding.
• Five psychological variables (button-press patterns and timing) and five physical variables (hit counts and randomness statistics) were computed for each of the 9 runs, giving 45 of each and a 45 x 45 matrix of 2,025 correlation factors; the pre-registered main analysis used only the 900 time-forward factors, correlating psychological variables with physical variables from later runs, to exclude feedback-induced causal correlations.
• Under the blind analysis protocol the complete analysis software was written, debugged, and tested before the data were analyzed, with the real data disguised by permuting the association of psychological to physical variables between participants. The test statistic, the mean of cubed absolute correlation factors, was compared against a background distribution from 10,000 permutations, one-sided.⁴

Results, as reported

The paper reports one-sided p-values from empirically estimated permutation backgrounds and the raw hit surplus; it reports no standardized effect sizes and no confidence intervals, so none are stated here. For the hit-rate analysis the author notes that the standard deviation of the underlying Markov chain is sqrt(N/12) rather than the sqrt(N/4) of independent random bits.

Eleven-dimension audit

Pre-registration

The apparatus code, feedback audio files, test random data, consent form, and questionnaire were pre-registered on the Open Science Framework before data-taking, and the complete analysis code for both experiments was registered before the data were analyzed, at the three OSF addresses the paper prints. The blind analysis protocol goes beyond a written pre-registration: the analysis software was fully written, debugged, and tested before the unblinding, with the data not looked at or analyzed in any way beforehand. One secondary analysis, the split by RNG type, was performed blind but was not publicly pre-registered, and the paper says so explicitly.

Randomization

The random source was a hardware generator built on the thermal noise of two electrical resistors in a differential, shielded configuration designed to minimize coupling of environmental fluctuations. The 16-bit random Words were scrutinized with Marsaglia’s diehard suite of tests with no suspicious deviation from randomness found, and random events were derived by comparing successive Words, the same 1-step Markov procedure used by von Lucadou (2006) and Walach et al. (2020).⁵ The assignment of each participant to RT-bits or XPR-bits was itself decided randomly by the control computer.

Sensory leakage

As a micro-psychokinesis design, the experiment has no target for a participant to perceive, so sensory leakage in the receptive sense does not arise; the analogous concern is ordinary causal pathways into the correlation structure. The paper addresses these directly: the main analysis used only time-forward correlations, in which the psychological variables were obtained before the physical ones, precisely to exclude feedback-induced causal correlations, and the elevated correlations visible near the matrix diagonal, which the author judges very likely causal (longer button-press times when cheering sounds play), were excluded from the pre-planned analysis.

Blinding

Blinding here is analyst blinding. The analysis code was developed and tested against disguised data, with the association of psychological to physical variables permuted between participants, and the experimental data were not analyzed for the effect under study until the unblinding. The unblinding of Experiment 1 was performed live during a presentation at the Parapsychological Association convention in Paris on July 6, 2019; the unblinding of Experiment 2 was performed in the sole presence of the author on September 15, 2019. The author also remained blind to which participants received RT-bits versus XPR-bits until the blind condition was removed.

Optional stopping

The paper states that 200 participants was the pre-planned number, and the session structure was fixed at 9 runs of 80 button presses for every participant. Under the blind analysis protocol the data had not been looked at or analyzed in any way before the unblinding, which forecloses outcome-dependent stopping of data collection. No interim analyses are reported.

Outcome measure

The pre-specified outcome was a single test statistic for the whole matrix: the mean of the cubed absolute values of the 900 time-forward correlation factors, evaluated against an empirically estimated permutation background. This differs from von Lucadou’s practice of counting significant correlations, which the author notes has the disadvantage that not all matrix elements contribute; he reports having tested both statistics on the Walach et al. (2020) data. Experiment 2 used the mean of 50 squared correlation factors, and a post hoc re-run with cubed factors returned exactly the same p = .064.

Effect size

The paper reports one-sided p-values for the matrix analyses and, for the post hoc hit-rate analysis, the raw deviation: a surplus of 138 hits out of 96,000 trials. It reports no standardized effect sizes and no confidence intervals for any of the analyses. The author does correct the variance assumption for the dependent Markov-chain bits, using a standard deviation of sqrt(N/12) rather than sqrt(N/4).

Multiple comparisons

The correlation matrix method is, in the paper’s own words, in essence a multiple-analysis technique, and the design answer to that multiplicity is to evaluate all correlation factors together as a single ensemble statistic rather than to test 900 correlations separately. The blind analysis protocol draws a clear line between the pre-planned analyses (Experiment 1 and Experiment 2, one test each) and the post hoc analyses, each of which the paper labels as such. No corrections across the several post hoc tests are reported.

Internal replication

The study contains two pre-planned experiments on the same 200 participants, and they diverged: the correlation matrix analysis was null (p = .76) while the questionnaire correlation was marginal (p = .064). Three control datasets recorded around each experiment’s data all fell within the background distribution (p = .22, .74, .08 for Experiment 1; p = .61, .53, .19 for Experiment 2). The split by random-event type showed no meaningful difference in either experiment, which the author reads as the result being independent of RNG complexity and of pre-recording.

External replication

Experiment 1 is a conceptual replication of the correlation matrix experiments of von Lucadou (1986, 1991, 2006), all three of which reported statistical significance, and of the independent replication by Walach et al. (2020), which obtained less significant results; this experiment, built from scratch with new hardware and software, found no evidence of anomalous correlations. Experiment 2 is the first replication of Jolij and Bierman (2019) and returned marginal evidence of the same order of magnitude. The author’s stated main conclusion is the suspicion that the correlation matrix idea will not escape the replication problem in parapsychology.

Transparency

The article is open access under CC-BY-NC, and the registration trail is unusually complete: apparatus code, audio files, test data, consent form, and questionnaire registered before data-taking, and analysis code plus all experimental data publicly accessible on the OSF. The main unblinding was performed in front of a convention audience. The paper reports its null main result without hedging, prints the control p-values, discloses that the RNG-split analysis was not publicly pre-registered, reports funding (BIAL Foundation grant 161/19) and ethics approval, and recounts three anecdotal incidents, labeled as observations rather than analyses, that most researchers would have left out.

The adversarial record

• The lineage is contested ground. Von Lucadou’s three correlation matrix experiments (1986, 1991, 2006) reported significance, but the paper’s first endnote states that they had not taken internal correlations between psychological variables into account and thus overestimated the statistical significance of the results; the independent replication by Walach et al. (2020), using the empirical background estimation this author proposed in earlier work (Grote 2015, 2017), obtained less significant results than von Lucadou reported.
• The statistics themselves are debated. The paper argues that strong correlations among psychological variables render the usual analytical significance methods invalid, leaving permutation and simulation approaches as the only viable method; Walach et al. (2020) had called that approach conservative, citing Calude and Longo (2017), a citation this author says misses the point. A separate controversy over possibly causal correlations from same-run and earlier-run feedback is the reason this study restricted its main analysis to time-forward correlations.
• Reading against the study: the author was the sole experimenter for all 200 participants and the sole witness of Experiment 2’s unblinding; the RNG-split analysis, while blind, was not publicly pre-registered; the abstract gives prominence to two p = .06 values that do not reach conventional significance, one of them post hoc; the trickster incidents are anecdotes by the author’s own framing; and the offered interpretations of the null result, a decline effect or the author not being a psi-conducive experimenter, are not testable within this experiment.