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Studies of the I Ching: II. Additional analysis.

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The Chinese book of divination, the I Ching, or "Book of Changes," contains 64 so-called hexagrams (six-line structures) and associated readings that are accessed in modem times by six throws of three coins. The user poses a question and then throws the coins to generate a hexagram and associated reading, which is ostensibly an answer or forecast to that question, thus suggesting that a paranormal ("future-telling") component may be involved in the I Ching process. Throwing three heads (or three tails) is regarded as propitious because they produce "changing lines" with their own unique readings (up to six changing lines can be thrown per hexagram). Changing lines produce a second hexagram and its associated reading, which thus furnishes additional information for the user.

The I Ching has occasionally been used in parapsychological experimentation (e.g., Rubin & Honorton, 1971, 1972; Thalbourne, 1994; Thalbourne, Delin, Barlow, & Steen, 1992-1993). We also used the I Ching, but in a somewhat unorthodox way (see Storm & Thalbourne, 1998-1999), using a sample of 93 participants collected in 1998 (referred to in this article as "Sample 1998"). The purpose of that study was to find evidence in the I Ching process of a putative paranormal effect. To establish whether certain personality types were more successful than others at generating predesignated hexagrams and changing lines, we looked for relationships between these two variables and factors on the 16 Personality Factor Questionnaire, orl6PF (Cattell, Eber, & Tatsuoka, 1970), and transliminality, the "hypothesised tendency for psychological material to cross (trans) thresholds (limines) into or out of consciousness" (Thalbourne & Houran, 2000, p. 853). Regarding transliminality, we hypothesized that paranormal information mig ht, in highly transliminal individuals, cross the "threshold" into consciousness.

Participants in Sample 1998 preselected 16 of the 64 hexagram-descriptor pairs, bearing in mind the statement "Lately, or right now, I feel..." Coins were thrown to generate a hexagram, and it was found that outcome hexagrams matched designated hexagrams to a marginally significant degree: proportion of matches [P.sub.obs.] = .32 (p = .067), where [P.sub.MCE] = .25 (the binomial test was used, where hit = 1 and miss = 0). When expressed as an effect size [pi] the proportion of matches was in excess of chance, [pi] = .59, p = .048, where [[pi].sub.MCE] = .50 (see Storm & Thalbourne, in press).

Thalbourne (1996) hypothesized that transliminality scores would correlate with scores on a precognition task, but his result was not significant. However, Sanders, Thalbourne, and Delin (in press) showed that, for senders, telepathic transmission of emotional states correlated significantly with transliminality. In Storm and Thalbourne (1998-1999), we found a significant correlation between hitting and transliminality and a weak but marginally significant correlation between transliminality and changing lines. We concluded from these findings, as suggested in Thalbourne and Delin (1994, p. 24), that transliminality might be related to an anomalous dimension of human behavior underlying paranormal belief and ostensible paranormal ability (Storm & Thalbourne, 1998-1999, p. 113). More recently, however, Parker (2000) failed to demonstrate any correlation with paranormal ability and an earlier version of the transliminality scale.

In regard to ESP-personality research, previous researchers have shown that factors on the 16PF, including Factor A (Warmth), Factor C (Emotional Stability), Factor E (Dominance), Factor F (Liveliness), Factor I (Sensitivity), Factor O (Apprehension), Factor [Q.sub.4] (Tension), and Factor EX (Extraversion), correlated with paranormal performance (see Kanthamani & K. R. Rao, 1971, 1972, 1973; Nicol & Humphrey, 1953, 1955; K R. Rio, 1974; Sudhaker & P. K Rao, 1986).

Using the 16PF, we (Storm & Thalbourne, 1998-1999) found significant correlations between the following:

* Hexagram hitting and six 16PF factors: Factors F (Liveliness), H (Social Boldness), [Q.sub.2] (Self-Reliance), [Q.sub.4] (Tension), EX (Extraversion), and IN (Independence). All correlations were positive except [Q.sub.2] and [Q.sub.4].

* Number of changing lines and five factors: Factor A (Warmth), C (Emotional Stability), M (Abstractedness), [Q.sub.2] (Self-Reliance), and EX (Extraversion). All correlations were negative except Factors M and [Q.sub.2].

* Transliminality and five factors: Factor A (Warmth), G (Rule-Consciousness), M (Abstractedness), TM (Tough-Mindedness), and SC (Self-Control). All correlations were negative except Factors A and M.

In a second study (Storm & Thalbourne, 2001), which incorporated some methodological improvements, we attempted to replicate the significant findings found in Sample 1998, this time with a sample of 107 participants (referred to in this study as "Sample 1999"). Again hitting was significantly above chance ([P.sub.obs.] = .35, p = .015; [pi] = .62, p = .006). Also, number of changing lines correlated with answers to the sheep question: "Do you think it is possible for at least some people to exhibit paranormal effects in this experiment?" Although none of the predicted parapsychological correlations with transliminality or the 16PF variables replicated, four of the original five significant correlations between transliminality and factors on the 16PF did replicate.

The results of post hoc analyses are also presented in this article, with the aim of detecting possible reasons for the failures of various hypotheses in the 1999 study to be confirmed. These include bivariate correlation analyses, multiple regression analyses (MRAs), and median-split analyses. Where feasible, the two samples are pooled, thus yielding the combined sample (N = 200), with the aim of calculating more accurate estimates of the relevant population parameters.

Post Hoc Analyses

In this section, bivariate correlation analyses are performed with the aim of determining possible reasons for the failures of various hypotheses to be confirmed. MRAs are performed on Sample 1999 in an attempt to replicate the regression results in our initial study (Storm & Thalbourne, 1998-1999, p. 112). Finally, median-split analyses, as originally performed in our study (Storm & Thalbourne, 1998-1999, p. 114), are performed on Sample 1999 to ascertain the success rates of hexagram hitting for low-and high-scoring participants on the Transliminality Scale (Thalbourne, 1998). For convenience, the results of three performance comparisons between Sample 1998 and Sample 1999 (on hitting, transliminality, and number of changing lines) are given in advance of the REMAINING ANALYSES section below, so that the combined sample can also be subjected to multiple regression and median-split analyses in this section.

Bivariate Correlation Analyses

Transliminality and hitting In Sample 1999, and in contrast with Sample 1998, a significant correlation was not found between hitting and transliminality. Although the correlation in Sample 1998 was significant, we (Storm & Thalbourne, 1998-1999, p. 114) tested (post hoc) for a decline effect in this correlation across the sample because there seemed to be evidence, to the naked eye, of a decline in effect size over time (viz., high transliminals were not hitting as often as might be expected). We subdivided Sample 1998 into four groups of 20 and one residual group of 13. These groups were then ranked first to fifth (first being the earliest tested group and fifth being the last). In the event, using Spearman's test, a nonsignificant decline over the course of the experiment in size and direction of the five hitting-transliminality correlations was found, [r.sub.s] (3) = -.50, p = .196, one-tailed. The failure of this decline to reach significance may have come about as a result of the small number of groups (viz., five).

If there was a similar decline in Sample 1999, then this decline might also have severe effects on the size and significance of the transliminality-hitting correlation, even to the degree that the failure of the correlation to replicate might be explained by that decline. Thus, Sample 1999 was broken down into four groups of 20 participants and one residual group of 27 participants. The resultant five correlations between hitting and transliminality were also ranked chronologically (first through fifth). A weak and nonsignificant decline was indicated, [r.sub.s] (3) = -.10, p = .436, one-tailed. However, when we plotted the individual group correlations of the combined sample (1) (see Figure 1), we happened to notice at the eighth group that there was a decline in the transliminality-hitting correlation, which turned out to be significant, [r.sub.s] (6) = -.88, p = .004, one-tailed. We expected the decline to continue, but the remaining two groups when collected went against the linear trend, to produce in fa ct an overall significant quadratic trend, [r.sub.s] (8) = .57, p = .044, one-tailed. A U-shaped trend might appear if the experimenter was having an effect on the correlations and enthusiasm and motivation picked up toward the end of the experiment (see Broughton & Alexander, 1997, p. 223). (Note that the two significant correlations in Figure 1 are probably nonsignificant when adjusted for multiple analyses.)

In conclusion, neither Sample 1998 nor Sample 1999 nor the combined sample produced significant declines. However, the overall transliminality-hitting correlation was significant for the combined sample, r(198) = .13, p = .038, one-tailed, but this very weak correlation may well have been stronger had it not been for the position effect. (2)

Transliminality and number of changing lines. The transliminality-changing lines correlation failed to reach significance in the 1999 sample. Suspecting that decline effects may have played a part in this failure to replicate, we followed the same procedure outlined in the section above: Decline effects were again hypothesized for Sample 1998, Sample 1999, and the combined sample.

For Sample 1998, there was a nonsignificant incline, [r.sub.s](3) = .70, p = .094, one-tailed. For Sample 1999, the rank-order correlation was also not significant, [r.sub.s](3) = 0.00, p = .500, one-tailed. Nor was there a significant decline for the combined sample, (3) [r.sub.s](8) = -.176, p= .313, one-tailed. A test for quadratic trend yielded entirely null results. Thus, we were not able to find evidence that an ostensible position effect might account for the failure to replicate the transliminality--changing lines correlation in Sample 1999.

Hitting and the 16PF correlations. Not one of the six hitting--16PF correlations that were significant in Sample 1998 was significant in Sample 1999. It was considered highly likely that the two samples were not homogeneous on the following six relevant 16PF factors: Factor F (Liveliness), Factor H (Social Boldness), Factor [Q.sub.2] (Self-Reliance), Factor [Q.sub.4] (Tension), Factor EX (Extraversion), and Factor IN (Independence). This assumption came from an earlier observation (see Storm & Thalbourne, 1998-1999, p. 116) that there was a preponderance of female and psychology students in Sample 1998. Conducting tests on one sample with a view to replicating the results of an earlier sample is unwarranted if there happen to be fundamental differences between the two samples due to biases of one form or another. (4) Therefore, both samples were investigated for biases in sex composition (because sampling procedures in the 1998 study were different from those of the 1999 study (5)), and for the same reasons, it was decided that the number of participants studying psychology should also be investigated.

There was a drop in female participants from 72% to 54% across the two samples (i.e., 9 fewer female participants in Sample 1999), which proved to be significant using the Pearson chi-square test, [chi square] (1, N=200) = 6.75, p = .009, two-tailed. Another bias exists in the form of a significant drop in the number of psychology students: 50.5% in 1998 to 29% in 1999 (i.e., 16 fewer psychology students in Sample 1999), [chi square] (1, N= 200) = 9.73, p= .002, two-tailed. One final chi-square test was conducted, this time comparing four nonoverlapping groups (female psychology students, female nonpsychology participants, male psychology students, and male nonpsychology participants). The result was significant, [chi square] (3, N= 200) = 12.90, p = .005, two-tailed. We hypothesized that the original hitting-16PF correlations may have been specific to groups only and not the whole of Sample 1998. We decided to conduct Pearson r tests on each of the four nonoverlapping groups in Sample 1998 between hitting an d the six relevant 16PF factors.

Prior to running the Pearson r tests, we ran five one-way analyses of variance (ANOVAs) to determine possible differences between groups on mean scores for the five 16PF factors. Only the mean scores on Factor EX scores were heterogeneous across groups, but a post hoc Tukey's test showed that there was only a marginally significant difference on Factor EX scores between male nonpsychology participants and female psychology students (p= .087). Consequently, all the relevant Pearson tests were run for the four groups. Only one of the four groups produced significant correlations, and that was the female psychology students (n = 39; see Table 1). They produced five of the six significant correlations originally found for the whole of Sample 1998; the hitting-Factor IN (Independence) correlation was not significant.

It may be possible that female psychology students disproportionately contributed to those same five correlations originally reported for Sample 1998. In support of this claim, we found that the three remaining groups, when recombined (n = 54; which excludes the female psychology students), produced only one significant correlation: hitting-Factor H (Social Boldness), r(52) = .28, p = .043, two-tailed.

To test for replication of the five significant hitting-16PF correlations given in Table 1 (for female psychology students only), we performed five Pearson r tests on Sample 1999 (female psychology students only). (Note that prior to the Pearson r tests, the two groups of female psychology students, Sample 1998 and Sample 1999, were compared using independent-samples t tests. There were no significant differences between respective groups on Factors F, H, [Q.sub.2], [Q.sub.4] and EX.) Only the hitting-Factor H correlation among female psychology students replicated, r(22) = .44, p = .016, one-tailed. For the remaining subsample of all participants (n = 83), which excludes the female psychology students, we found that the hitting-Factor H correlation was not significant, r(81) = -.08, p = .224, one-tailed.

Given these results, sex and academic affiliation alone do not explain the lack of replication of four correlations that were found in 1998 (viz., hitting with Factors F, [Q.sub.9], [Q.sub.4], and EX). Nevertheless, one correlation (hitting-Factor H) replicated for female psychology students, so that, once again, those participants appeared to have disproportionately contributed to that correlation.

Number of changing lines and the 16PF correlations. Given the above rationale regarding sex and academic affiliation, we ran five one-way ANOVAs to determine possible differences between the same nonoverlapping groups on mean scores for the five 16PF factors. Factor M scores were heterogeneous across groups. A post hoc Tukey's test showed that there was a significant difference on Factor M scores between the female psychology students and the male nonpsychology participants (p = .040; note that Factor EX scores were tested in the previous subsection above). Consequently, Pearson r tests were run for the four groups using only four factors: Factors A, C, [Q.sub.9], and EX. For Sample 1998, the four different groups produced a number of significant correlations (see Table 2).

On the basis of five significant correlations (see Table 2), five respective Pearson r tests were run to see if these correlations might replicate in the Sample 1999 data. (Note again that prior to the Pearson r tests, all four groups, Sample 1998 and Sample 1999, were compared using independent-samples t tests. There were no significant differences between respective groups on the relevant factors.) Only one significant correlation replicated, and this was for the male nonpsychology participants: Factor EX (Extraversion), r(40) = -.33, p = .017, one-tailed. For Sample 1999, no other groups or the remaining subsample (n = 65), which excluded male nonpsychology participants, produced significant correlations with changing lines and the relevant factors.

Multiple Regression Analyses

Belief and 16PF factors as predictors of transliminality. Storm and Thalbourne (1998-1999, p. 112) found that Factor M (Abstractedness), Factor A (Warmth), and answers to the question "Do you believe in your own ability to cast coins for a hexagram which matches one of your sixteen choices?" were significant predictors of transliminality, R = .52 (adjusted [R.sup.2] = .25). These three factors together explained 25% of the variance in transliminality scores. An MRA of Sample 1999 using the forward selection method was run to test whether ability and Factor M (but not Factor A, which failed to correlate significantly) might replicate as predictors of transliminality

Factor M and ability both entered the model summary (Sample 1999). Ability made a moderate contribution as a predictor, R= .35 ([R.sup.2] = .12, adjusted [R.sup.2] = .11), followed by Factor M, which raised the R value to a moderate .41 ([R.sup.2] = .17, adjusted [R.sup.2] = .15). Thus, 15% of the variance of the dependent variable (transliminality) was explained by the two predictor variables. Two of our three findings were thereby replicated (Storm & Thalbourne, 1998-1999, p. 112).

The multiple R was significant, F(2, 104) = 10.41, p < .001. The standardized beta coefficients were as follows: ability, [beta] = .34; and Factor M, [beta] = .21. Ability made the greater contribution as a predictor, but only a little more than Factor M.

Given these results, it was deemed a possibility that the same predictors might replicate for the combined sample. A chi-square test on the two samples found that answers to the ability question were significantly different, [chi square] (1, N= 200) = 11.62, p= .001, two-tailed ([phi] = .24; [[phi].sup.2] = .06), with 52% of Sample 1998 saying yes to the ability question but only 28% of Sample 1999 saying yes to the same question. Nevertheless, the two samples were regarded as homogeneous because the phi-squared value was less than the critical 9% (see footnote 1).

A t test was performed on Factor M scores for the two samples, and the result was also significant, t(198) = -2.69, p = .008, two-tailed ([[omega].sup.2] = .03). However, the omega-squared value also did not reach the critical level. The differences between the two samples on ability and Factor M scores were deemed not important, so they were combined. The two variables (ability and Factor M) were both entered into an MRA for the combined sample.

Ability and Factor M both entered the model, with Factor M entering first and making a moderate contribution as a predictor, R = .33 ([R.sup.2] = .11, adjusted [R.sup.2] = .10). Ability followed, raising the R value to a moderate .42 ([R.sup.2] = .18, adjusted [R.sup.2] = .17). Thus 17% of the variance of the dependent variable (transliminality) was explained by the two predictor variables. Once again, two of our three findings were replicated (Storm & Thalbourne, 1998-1999, p. 112). The multiple R was significant, F(2, 197) = 21.20, p<.001. The beta coefficients were as follows: ability, [beta] = .27, and Factor M, [beta] = .30. Factor M made the greater contribution as a predictor, but only a little more than ability.

Transliminality as a predictor of hitting Transliminality was found to be a predictor of hitting in our 1998 study (Storm & Thalbourne, 1998-1999, p. 112). Conducting an MRA on these two variables for Sample 1999 was academic because transliminality failed to correlate significantly with hitting in Sample 1999. Transliminality also failed to enter an MRA for the combined sample.

Median-Split Analyses

Storm and Thalbourne (1998-1999) performed median-split analyses on transliminality scores to "ascertain the locus and form of the psi effect (psi-hitting or psi-missing)" (p. 114). The median transliminality score was 16 for Sample 1998. The binomial test (two-tailed) was used to assess hexagram hit rates as a proportion of hits P, where [P.sub.MCE] = .25. There were 43 low scorers ([less than or equal to]15), where [P.sub.obs.] = .23 (p = .47), and 45 high scorers ([greater than or equal to]17), where [P.sub.obs.] = .40 (p = .016). Thus, highly transliminal participants scored significantly above MCE on hitting.

Sample 1999 had a median transliminality score of 17, and, paradoxically, a near reversal of effect was found. There were 51 low scorers ([less than or equal to]16), where [P.sub.obs.] = .35 (p = .062), and 50 high scorers ([greater than or equal to]18), where [P.sub.obs.] .32 (p = .164). Hit rates for low-scoring transliminals approached significance.

The combined sample had a median transliminality score of 17. There were 99 low scorers ([less than or equal to]16), where [P.sub.obs.] = .30 (p= .135), and 88 high scorers ([greater than or equal to]l8), where [P.sub.obs.] = .36 (p = .010). Thus, there was a return to a significant hit rate for highly transliminal participants.

Remaining Analyses

By conducting performance comparisons (i.e., tests of homogeneity) between Sample 1998 and Sample 1999, we can determine whether the two samples are drawn from the same population. Should these tests fail to show significant (and relatively substantial) differences between the two samples (i.e., the samples are drawn from the same population), they can be combined, so that better estimates of the corresponding population parameters can be calculated. New descriptive statistics for the combined sample are presented here, along with inferential statistics.

(We point out that there were methodological flaws in Sample 1998, pertinent only to cheating and coin bias, which the journal editor regarded as necessary to investigate [see Storm & Thalbourne, 2001, Appendix B]. We tested both samples and failed to find evidence of cheating or coin bias. For Sample 1998, task feedback before questionnaires were completed raised concern among referees, but we showed that feedback had no measurable effect on responses to the relevant items in those questionnaires. We regard the Sample 1998 data as reliable.)

Hitting Rates

The hitting rates for Samples 1998 and 1999 were compared using Rosenthal and Rubin's (1989) procedure for testing the statistical significance of the "heterogeneity" (p. 334) of the obtained [pi] values, by means of a chi-square test using the two independent samples. This comparison was made in part because it was considered likely that the paranormal task was somewhat "harder" for participants in Sample 1999 than it was for participants in Sample 1998 because the hexagram descriptor form (two descriptors were given for each hexagram) in 1999 did not contain the actual hexagrams (six-line symbols). However, although the hit rate for Sample 1999 was actually higher than that of Sample 1998, there was no significant difference between the two, [chi square] (1, N = 200) = .169, p = .681.

When the binomial test was performed for the combined sample, the hit rate was [P.sub.obs.] = .335 (33.5%; p = .004), where [P.sub.MCE] = .25. The effect size [pi] was .60, where [[pi].sub.MCE] = .50. Of 200 participants, 67 obtained a hit, as opposed to 50 by chance. The 95% confidence interval for the proportion of hits obtained is .27 to .40. Those 200 participants were drawn from a population with a hit rate between 27% and 40%. These rates correspond to [pi] values for the population of between .53 and .67, which does not include [[pi].sub.MCE] = .50.

Number of Changing Lines

The t test showed no significant difference between the two samples on the number of changing lines (see footnote 3). The two samples were combined (see footnote 1 for criteria for combining samples). The mean number of changing lines was 1.46 (SD = 1.07), where MCE = 1.5. The 95% confidence interval for number of changing lines for the population from which the two samples were drawn rests somewhere between 1.3 and 1.6 changing lines, which includes the chance level.

Using the single-sample t test, we found that the mean number of changing lines (1.46) was not significantly different from chance, t(199) = -.527, p = .599, two-tailed. We suggest that some unrecognized factor (e.g., relative task difficulty) may account for the failure of participants to throw five or six changing lines. Specifically, the odds of generating at least four changing lines are up to 10 times more difficult ([P.sub.MCE] = .037) than the relatively easier task of matching a hexagram ([P.sub.MCE] = .250). It is possible that participants were intuitively aware of this increased difficulty and, as a consequence, may have been intimidated by the difficulty of the task (see Storm &Thalbourne, 2000, for a discussion of the hypothesized effects of perceived difficulty).

Added to the difficulty of throwing three-of-a-kind is the fact that participants were required to perform two paranormal tasks simultaneously. Expectation of significant performances in both tasks is perhaps analogous to expecting someone to demonstrate a full comprehension of a text or television program while simultaneously holding a coherent and uninterrupted conversation with a friend. Future I Ching experiments might yield significant performances on changing line generation if hexagram targeting is irrelevant.

The Transliminality-Hitting Correlation

The transliminality-hitting correlation did not replicate in Sample 1999. Given the nonsignificant differences between Sample 1998 and Sample 1999 on transliminality and hitting (see footnote 1 for results), the transliminality-hitting correlation was calculated for the combined sample. As reported above in the POST HOC ANALYSES section, the correlation was significant, r(198) = .12, p = .040, one-tailed. Although weak, the nonchance relationship between the two variables suggests that highly transliminal participants showed a slight tendency to be more successful at hexagram hitting than the other participants. Therefore, transliminality was, overall, shown to be a condition conducive to "exosomatic psychopraxia"--the self manifesting paranormal effects outside the body (see Storm & Thalbourne, 2000, and Thalbourne, in press, for an extended discussion of the theory of psychopraxia)--even though this relationship was not replicated in Sample 1999.

The Transliminality-Changing Lines Correlation

In Sample 1999, the transliminality-changing lines correlation was not significant. Thus, our previous finding of a significant correlation between transliminality and changing lines did not replicate (Storm & Thalbourne, 1998-1999, p. 110). Nor was the correlation significant for the combined sample, r(198) = .08, p= .120, one-tailed. On this occasion, transliminality was not shown to be a condition conducive to exosomatic psychopraxia.

The Hitting-16PF Correlations

Independent-samples t tests were performed on the two samples to test the mean differences on the six relevant personality factors (Factors F, H, [Q.sub.2], [Q.sub.4], EX, and IN). The results were not significant. Therefore, the two samples were combined, and only one out of six correlations failed to reproduce (hitting-Factor [Q.sub.2]), although it was in the right direction (i.e., negative), r( 198) = -.08, p = .128, one-tailed (see Table 3 for other results).

These five significant correlations reproduce our earlier significant findings (Storm & Thalbourne, 1998-1999, p. 110), suggesting that participants who were successful at hexagram hitting tended to be lively (Factor F), socially bold (Factor H), free of tension (Factor [Q.sub.4), extraverted (Factor EX), and independent (Factor IN).

The Changing Lines--16PF Correlations

Independent-samples t tests were performed on the two samples for each of the five relevant factors (Factors A, C, M, [Q.sub.2], and EX). No significant differences were found. The two samples were therefore combined. However, none of our original correlations reproduced for the combined sample (Storm & Thalbourne, 1998-1999, p. 111).

The Changing Lines--Possibility Correlation

In Sample 1999, the number of changing lines correlated with answers to the sheep-goat question concerning the "possibility" of a paranormal effect among participants. For the combined sample, the correlation was significant, r(198) = .18, p = .006, one-tailed. Therefore, participants who believed that it was possible for other participants to exhibit paranormal effects in the I Ching experiment tended themselves to generate significantly more changing lines than those who did not believe in the possibility of paranormal effects.

The Transliminality--Possibility Correlation

Sample 1999 replicated our significant correlation between transliminality and answers to the possibility question (Storm & Thalbourne, 2001). For the combined sample, the correlation was reproduced, r(198) = .37, p <.001, one-tailed. High scorers on transliminality tended to believe in the possibility that participants other than themselves could achieve paranormal effects.

The Transliminality--Ability Correlation

For the combined sample, the transliminality--ability correlation was significant, r(198) = .30, p < .001, one-tailed. High scorers on transliminality tended to believe that their own paranormal abilities would directly contribute to a successful outcome on the paranormal task.

The Possibility--Ability Correlation

In Sample 1999, a significant correlation between possibility and ability was found. The correlation was also significant for the combined sample, r(198) = .37, p < .001, one-tailed. Those participants who believed that other participants had paranormal abilities tended to believe that they too had paranormal abilities.

The Transliminality--16PF Correlations

In Sample 1999, we replicated significant correlations between transliminality and each of five factors on the 16FF (Storm & Thalbourne, 2001). When the two samples were compared on Factors A, G, M, TM, and SC using the independent-samples t test, it was found that there were significant differences on all but two factors: Factor A and Factor G. However, the omega-squared values calculated from the tvalues for the other three factors (M, TM, and SC) did not reach the critical level (all three values were less than 4%). Therefore, the two samples were pooled and the results of the correlations are presented in Table 4.

Note that it may be possible, as we previously stated (Storm & Thalbourne, 2001), that the transliminality--Factor A correlation is an artifact of multiple analyses since at least one significant correlation, which is 5% of 21 correlations (there are 21 16PF factors, and therefore 21 Pearson r tests were originally performed on Sample 1998 data) could be the result of chance alone. Nevertheless, the combined results indicate that highly transliminal participants in the combined sample tended to be warm and outgoing (Factor A) and idea-oriented (Factor M). They also tended not to follow rules (Factor G), were not tough-minded (Factor TM), and were lacking in self-control (Factor SC).

Success Rates

In the POST HOC ANALYSES section above, four nonoverlapping groups were individually tested for significant correlations between 16PF factors and the two paranormal tasks (hitting and changing lines), but only 2 tests for replication were successful out of a total of 10 relevant tests: That is, the hitting-Factor H (Social Boldness) correlation for female psychology students in Sample 1999 was significant, and the changing lines-Factor EX (Extraversion) correlation for male nonpsychology participants in Sample 1999 was also significant. We acknowledge the possibility that these replications may have been the result of chance due to multiple analyses.

In the REMAINING ANALYSES section, 24 specific statistical tests were performed to test 11 hypotheses. Of these tests, 16 produced significant results that confirmed or partially confirmed 8 of those 11 hypotheses (i.e., 67% of all tests were successful, resulting in the confirmation of 73% of all hypotheses tested).

More specifically, for the parapsychological hypotheses, there were 8 successful tests out of 16 (50%), and for the psychological hypotheses, there were 8 successful tests outof8 (100%). (Note that all these percentages are greater than 5% and therefore are unlikely to be explained by chance alone.)

Conclusion

In our initial study with the I Ching (Storm & Thalbourne, 1998-1999), we sought to find evidence in the I Ching process of ostensible paranormal effects. In the tradition of ESP-personality research, we also attempted to find relationships between (a) 16PF factors and success at two I Ching tasks (i.e., hexagram hitting and number of changing lines) and (b) transliminality and success at the two I Ching tasks. There were a number of significant findings (see Storm & Thalbourne, 1998-1999, pp. 108-112).

In a follow-up study (Storm & Thalbourne, 2001), we concluded that the ESP-PK dichotomy was in this case unworkable in practice because the main paranormal effect (i.e., hexagram hitting) could not be categorized exclusively as ESP or PK We explained this effect as an example of psychopraxia (the self bringing about goals in the mind-body complex or in the wider world). However, in the same study, we found that little light was thrown on the necessary mediating conditions that must theoretically be involved in the psychopractic process, although answering yes to a paranormal belief question ("Do you think it is possible for at least some people to exhibit paranormal effects?") was suggestively conducive of a psychopractic effect (specifically, the generation of changing lines). In the same study, transliminality and nine factors on the 16PF (Factors A, C, F, H, M, [Q.sub.2], [Q.sub.4], EX, and IN), each of which previously correlated with paranormal performance of one form or another (see Storm & Thalbourne, 1998-1999), failed to replicate as necessary conditions of exosomatic psychopraxia. The present article sought to unearth some possible reasons why many previously significant findings in our initial study (Storm & Thalbourne, 1998-1999) failed to be confirmed in the corresponding hypotheses in our follow-up study (Storm & Thalbourne, 2001).

This article also sought to combine, where possible, the relevant variables in the two samples. Overall, the binomial test yielded significant hitting on designated hexagrams: The official pro attitude (6) asked of participants (a disposition toward hitting 1 of these 16 preselected hexagrams) was fulfilled to a significant extent for Sample 1998, Sample 1999, and the combined sample.

For the combined sample, the fluctuations of the transliminality-hitting correlations for 10 groups of 20 participants were first shown to conform at the 8th-group mark to a decline effect, which was hypothesized at that point, but later, when all data were collected, the correlations of the 10 groups conformed to a U-shaped trend. Thus, high scores on transliminality were associated with hitting at the beginning and the end of the experiment, whereas low scores on transliminality were associated with hitting at the middle of the experiment. The fact that the decline did not continue may be related to the experimenters focusing on that effect or extraneous influences coming into play (see Broughton & Alexander, 1997, p. 223). Nevertheless, transliminality was repeatedly confirmed (at least suggestively) as being a necessary condition that might help to bring about psychopractic effects.

The alternative paranormal measure, number of changing lines, did not replicate in Sample 1999 as a significant correlation with transliminality, and no evidence of a decline effect or U-shape trend in 10 transliminality-changing lines correlations across 10 groups was present that might otherwise help explain the failure to replicate. Nor did changing lines correlate with five relevant 16PF factors in Sample 1999 or the combined sample.

For Sample 1999, six factors on the 16PF did not replicate as significant correlates with hitting, contrary to previous findings (Storm & Thalbourne, 1998-1999, p. 109), although a replicated hitting-Factor H (Social Boldness) correlation for female psychology students was found (seep. 297). For the combined sample, however, five of the six significant hitting-16PF correlations reappeared (see Table 3).

Likewise for Sample 1999, five factors on the 16PF did not replicate as significant correlates with changing lines, contrary to previous findings (Storm & Thalbourne, 1998-1999, p. 111), although a replicated Factor EX (Extraversion)-changing lines correlation for male nonpsychology participants was found (see Table 2). For the combined sample, there were no significant changing lines-16PF correlations.

Finally, all five 16PF correlates of transliminality (four of which replicated in 1999) were significant in the combined sample (see Table 4).

Despite the poor level of replication of correlations in Sample 1999 (especially of psychopraxia-personality correlates), reproduction of many significant correlations was obtained in the combined sample for (a) parapsychological effects, particularly, the overall hexagram hitting rates and hitting-16PF correlations, and (b) psychological effects, namely, the 1 6PF correlates of transliminality and various belief correlations. Thus, regarding (a), the effects of hitting and its correlates are at least consistent with the notion that exosomatic psychopraxia was operating and that necessary conditions may apply (i.e., some personality types tend to be more able than others to produce paranormal effects). Further studies with the I Ching may put us on firmer ground in regard to establishing the form psychopraxia and its correlates may take.

This study was supported by a grant from the Bial Foundation. We acknowledge the statistical advice of Bob Willson and Suitbert Ertel.

(1.) The combined sample was formed only after performance comparisons between Sample 1998 and Sample 1999 were made on the relevant variables. Transliminality scores did not differ significantly between samples, t(198) =-.710, p = .479, two-tailed ([[omega].sup.2] = 0). A significant t value implies the existence of an association, but omega-squared gives an estimate of bow strong that association is. Where omega-squared is less than .09, the association is regarded as "functionally" unimportant because there is little predictive power in that association. Consequently, the samples will be combined on the basis that they may be regarded as coming from the same population. Hexagram hit rates did not differ significantly between samples either, [chi square](1, N= 200) = .12, p = .729, two-sided ([phi] = .03). A phi-squared value (i.e., the coefficient of determination equivalent to [r.sup.2]) that falls below .09 will also normally be regarded as unimportant, but this value does not apply to the categories of sex and academic affiliation and, therefore, is not given in the relevant chi-square tests.

(2.) One commentator (S. Ertel, personal communication, September 9, 2000) advised us to consider the possibility that the ostensible change in Pearson r values across groups may have been attributable to declines in the variance on the transliminality measures for those groups, but this rival hypothesis was not confirmed. There were no significant declines in variances for transliminality across groups, nor were there for hitting and number of changing lines.

(3.) Number of changing lines did not differ significantly between samples, t(198) = 0.56, p = .579, two-tailed [[omega].sup.2] = 0). The samples were therefore combined for this analysis (see the section REMAINING ANALYSES for the result of the transliminality--changing lines correlation for the combined sample).

(4.) The literature on sex differences on paranormal belief is quite substantial, but for studies on sex differences in ESP performance, see Palmer and Johnson (1991), Peretti (1971), and Rao and Kanthamani (1981, 1983). See Parker, Frederiksen, and Johansson (1997) and Parker, Grams, and Pettersson (1998) for studies on ESP performance differences between psychology students and participants recruited from New Age groups or groups with paranormal experiences.

(5.) In the 1999 study, volunteers were sought from all disciplines of Adelaide University, whereas the 1998 study comprised mainly volunteers from the Departments of Psychology, Asian Studies, Architecture, and Computer Science.

(6.) "A person may be said to have a pro attitude toward state S when they would prefer S rather than -S [not S] if those two alternatives were to be brought to their attention (Thalbourne, in press).

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[Figure 1 Omitted]
Table 1

Correlations Between Hitting and 16PF Factors for Female Psychology
Students 1998 (N = 39)

Factor r p

F (Liveliness) .58 <.001
H (Social Boldness) .50 .001
[Q.sub.2] (Self-Reliance) -.40 .012
[Q.sub.4] (Tension) -.48 .002
EX (Extraversion) .48 .002

Note. p values are one tailed.
Table 2

Correlations Between Changing Lines and 16PF Factors for the Four Groups
(Sample 1998 and Sample 1999)

 Male Male Female Female
 Psych. nonpsych. psych. nonpsych.
 (1998: (1998: (1998: (1998:
 n = 8) n = 18) n = 39) n = 28)
 (1999: (1999: (1999: (1999:
Sample and Factor n = 7) n = 42) n = 24) n = 34)

1998
 A (Warmth) -.67 (*) ns ns ns
 C (Emotional Stability) ns ns -.30 (*) -.34 (*)
 [Q.sub.9] (Self-Reliance) ns ns .33 (*) ns
 EX (Extraversion) ns -.45 (*) ns ns

1999 A (Warmth) ns NA NA NA
 C (Emotional Stability) NA NA ns ns
 [Q.Sub.9] (Self-Reliance) NA NA ns NA
 EX (Extraversion) NA -.33 (*) NA NA

Note. psych = psychology students;

NA= not applicable.

(*)p<.05 (Sample 1998: two-tailed; Sample 1999: one-tailed).
Table 3

Correlations Between Hitting and 16PF Factors: Combined Sample (N = 200)

Factor r p

F (Liveliness) .16 .011
H (Social Boldness) .21 <.001
[Q.sub.4] (Tension) -.13 .037
EX (Extraversion) .16 .012
IN (Independence) .12 .042

Note. p values are one-tailed.
Table 4

Correlations Between Transliminality and 16PF Factors: Combined Sample
(N = 200)

Factor r p

A (Warmth) .13 .031
G (Rule Consciousness) -.25 <.001
M (Abstractedness) .33 <.001
TM (Tough-Mindedness) -.26 <.001
SC (Self-Control) -.23 .001

Note. p values are one-tailed.
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Author:Storm, Lance; Thalbourne, Michael A.
Publication:The Journal of Parapsychology
Article Type:Statistical Data Included
Geographic Code:9CHIN
Date:Sep 1, 2001
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