paranormal beliefs, education, and thinking styles

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Personality and Individual Differences 39 (2005) 1227–1236

Paranormal beliefs, education, and thinking styles

Kia Aarnio *, Marjaana Lindeman

Department of Psychology, University of Helsinki, P.O. Box 9 (Siltavuorenpenger 20 D),

00014 University of Helsinki, Finland

Received 4 November 2004; received in revised form 13 April 2005; accepted 19 April 2005Available online 5 July 2005

Abstract

This study examined connections between paranormal beliefs and educational level, discipline, length ofeducation, gender, and analytical and intuitive thinking. Finnish students (N = 3141) from 14 universityand six vocational school disciplines filled in an Internet-based questionnaire. The results showed that uni-versity students had less paranormal beliefs than vocational school students, which was partially due to uni-versity students� stronger preference for analytical thinking. Of the university students, those majoring inmedicine and psychology held the least beliefs and the students of education and theology held the mostbeliefs. Length of university education was, however, only slightly negatively associated with paranormalbeliefs. Intuitive thinking was positively connected with paranormal beliefs. Women�s higher intuitivenessand lower analytical thinking partially explained their higher amount of beliefs compared to men.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Paranormal belief; Education; Discipline; Analytical thinking; Intuitive thinking

1. Introduction

Paranormal beliefs are widespread among Western people: in North America, more than halfof adults believe in psychic powers and extrasensory perception (Orenstein, 2002; Rice, 2003).Some studies indicate that education decreases paranormal beliefs but the empirical evidence is

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1228 K. Aarnio, M. Lindeman / Personality and Individual Differences 39 (2005) 1227–1236

sparse and contradictory (a review: Vyse, 1997). Moreover, the underlying mechanisms of therelationship between paranormal beliefs and education have not been empirically analyzed.

In most studies that have included participants from a wide variety of educational levels, para-normal beliefs have been less prevalent among the more educated (Orenstein, 2002; Otis & Al-cock, 1982; Za�rour, 1972). Besides amount of education, the kind of majors people have seemsto matter: University students of natural and social sciences, and psychology and medicine stu-dents in particular, tend to have less paranormal beliefs than students of art and humanities (Gray& Mill, 1990; Grimmer & White, 1992; Pasachoff, Cohen, & Pasachoff, 1970; Za�rour, 1972).Many studies have also shown contradictory findings: In comparison with students of social sci-ence, students of natural science have either held more (Jahoda, 1968), less (Pasachoff et al., 1970),or equal amount of (Salter & Routledge, 1971) beliefs.

Several methodological issues are relevant when considering the results regarding disciplinarydifferences in paranormal beliefs. First, many of the above mentioned studies date back to fourdecades, and may not reflect the effect of current education. Second, the methods and resultsof the earliest studies are not reported in much detail, which hampers their comparison with morerecent findings. Third, the sample sizes have typically been small, restricting the reliability ofresults concerning the frequency of paranormal beliefs in different disciplines. Fourth, the rangeof studied disciplines has been highly restricted.

Why students of different educational levels and university disciplines show different levels ofparanormal belief is yet poorly understood. The few researchers who have brought up the issuehave proposed that university students have less paranormal beliefs than students of lower edu-cational levels because their education provides them with critical thinking abilities (Otis & Al-cock, 1982; Za�rour, 1972). Likewise, these researchers have proposed that students of art andhumanities have more paranormal beliefs than other students because they lack the need to eval-uate arguments critically. Critical and analytical thinking is thus assumed to be the generativemechanism through which education influences paranormal beliefs. This is possible because somestudies suggest that belief in the paranormal is related to poor critical thinking and low rationality(Gray & Mill, 1990; Musch & Ehrenberg, 2002). Other studies have, however, failed to find such aconnection (Roe, 1999). One study even showed a positive relationship between analytical think-ing and paranormal beliefs (Wolfradt, Oubaid, Straube, Bischoff, & Mischo, 1999). The contra-diction is further deepened by results of some early studies showing relative stability ofparanormal beliefs during the years of higher education (Jahoda, 1968; Parida, 1962; Pasachoffet al., 1970; Salter & Routledge, 1971). To untangle the discrepancies between the previous stud-ies, we examined whether analytical thinking and length of education are negatively related toparanormal beliefs, how level and field of education are related to paranormal beliefs, andwhether analytical thinking mediates these relationships.

Besides analytical thinking, intuitive thinking may influence the relationship between paranor-mal beliefs and disciplines. We hypothesized that intuitive thinking is positively related to para-normal beliefs because in thinking intuitively and in justifying paranormal beliefs assessment ofinformation is based on personal experiences and in neither case justification with objective evi-dence is required; Intuitions and beliefs are rather self-evidently valid (Epstein, Pacini, Denes-Raj, & Heier, 1996; Stanovich & West, 2000). Positive connection between intuitive thinkingand paranormal beliefs has been reported in earlier work (Epstein et al., 1996; Wolfradt et al.,

K. Aarnio, M. Lindeman / Personality and Individual Differences 39 (2005) 1227–1236 1229

1999). As intuitive thinking, paranormal beliefs, and creativity all seem related with each other(Gianotti, Mohr, Pizzagalli, Lehmann, & Brugger, 2001), it is possible that intuitive thinking con-tributes to the enhanced amount of paranormal beliefs in students of creative disciplines such asart and humanities. Thus, we examined whether disciplinary differences in paranormal beliefs aremediated by intuitive thinking.

Finally, we examined gender differences in paranormal beliefs and possible explanations forsuch differences. Earlier work indicates that women hold more paranormal beliefs than men, withfew exceptions such as belief in extraterrestrial life forms (Rice, 2003; Tobacyk & Pirttila-Back-man, 1992; Vyse, 1997). Because men seem to think more analytically and less intuitively thanwomen (Lieberman, 2000; Pacini & Epstein, 1999), we examined whether intuitive and analyticalthinking mediate the relationship between gender and paranormal beliefs.

In sum, the following questions and hypotheses were addressed: First, how frequent are para-normal beliefs among Finnish students? Second, do paranormal beliefs vary according to level ofeducation, discipline, and length of the present education? We assumed that university studentshave less paranormal beliefs than students of vocational school, and that length of education isnegatively connected with paranormal beliefs. Third, we hypothesized that belief in the paranor-mal is connected negatively with analytical thinking and positively with intuitive thinking. Fourth,we predicted that the educational level difference and the effect of length of education on paranor-mal beliefs are mediated by analytical thinking, and that disciplinary differences in paranormalbeliefs are mediated by analytical and intuitive thinking. Fifth, we hypothesized that women holdmore paranormal beliefs and are more intuitive and less analytical than men, and that the differ-ences in paranormal beliefs between genders are mediated by analytical and intuitive thinking.

2. Method

2.1. Participants

The participants (N = 3141) were 16–60 years old (M = 24 years, SD = 4.5 years; 6% over age30) Finnish students, of whom 74% were women. Of the 2414 university students, 77% werewomen, as well as 63% of the 727 students of vocational school or vocational high school (upperlevel of vocational school). The participants were from various disciplines as indicated in Table 2.University students (M = 23.85) and vocational school students (M = 23.93) did not differaccording to their age, t(3124) = �.38, ns. Eighty-eight percent of the students reported studyingfull-time; others were part-time students. Of the original 3282 participants, 20 were excludedbecause of missing data and 120 because they were not part of the target group, that is, students.

2.2. Procedure

The participants were recruited through six universities and 10 vocational schools in Finland bysending requests for participation to student mailing lists. The questionnaire was posted on theInternet and a hyperlink to it was included in the recruitment messages. The web survey wasplaced in a hidden directory where it was unavailable to casual browsers. For some vocational


school students, an employee of the educational institute posted the message on a communicationboard (either real or virtual). To a minority of university students (n = 279) we dealt out paperquestionnaires at the beginning of their lectures.

2.3. Measures

Paranormal beliefs were measured with Tobacyk�s (1988) 26-item Revised Paranormal BeliefScale (RPBS, original scale by Tobacyk & Milford, 1983). Its items form seven subscales: tradi-tional religious beliefs, spiritualism, extraordinary life forms, psi, witchcraft, precognition, andsuperstition. We renamed the superstition subscale as omens of luck because in the literaturethe distinctions between the terms superstition and paranormal beliefs are fuzzy and the termsare often used interchangeably (Vyse, 1997). The five-point scale (1 = strongly disagree,5 = strongly agree) had a reliability (Cronbach�s a) of .92. The reliabilities of the subscales rangedfrom .79 to .88, except for the extraordinary life forms subscale, which reliability was .53.

Individual differences in analytical and intuitive thinking were assessed by the Rational-Experi-ential Inventory (Pacini & Epstein, 1999). The scales for analytical and intuitive thinking bothconsist of 20 items, and are measured with five-point scales (1 = strongly disagree, 5 = stronglyagree). Example items measuring analytical and intuitive thinking, respectively, are ‘‘I enjoy intel-lectual challenges’’ and ‘‘I like to rely on my intuitive impressions’’. The reliabilities were .87 (ana-lytical thinking) and .88 (intuitive thinking).

3. Results

3.1. Differences in paranormal beliefs between genders and students of two educational levels

Frequencies of paranormal beliefs are presented in Table 1. The most common beliefs were tra-ditional religious beliefs, which, according to the results of a pair-wise t-test, were significantly

Table 1Means and standard deviations of paranormal beliefs in Finnish students by gender and educational level

Paranormal beliefs All Women Men University Vocationalschool

M SD M SD M SD M SD M SD

Overall score 2.08 0.64 2.14a 0.63 1.90a 0.64 2.02b 0.61 2.26b 0.69Religious beliefs 2.85 1.21 2.98a 1.17 2.47a 1.23 2.86 1.23 2.82 1.13Spiritualism 2.21 0.99 2.30a 0.98 1.95a 0.97 2.14b 0.96 2.45b 1.06Extraordinary life forms 2.19 0.67 2.14a 0.65 2.33a 0.70 2.14b 0.63 2.35b 0.75Psi 2.06 0.88 2.11a 0.87 1.93a 0.89 1.99b 0.84 2.30b 0.95Witchcraft 1.98 0.96 2.05a 0.95 1.80a 0.96 1.91b 0.93 2.22b 1.03Precognition 1.73 0.76 1.83a 0.78 1.47a 0.63 1.66b 0.71 1.99b 0.86Omens of luck 1.37 0.73 1.40a 0.75 1.30a 0.65 1.32b 0.68 1.54b 0.87

Note: The paranormal belief scale ranges from 1 (unbelief) to 5 (strong belief).a A significant difference between men and women at p < .001 (g2 > .010).b A significant difference between students of university and vocational school at p < .001 (g2 > .010).


more common than the next most popular belief, spiritualism, t(3140) = 29.54, p < .001. With re-gard to the other paranormal beliefs, each of them differed significantly (p < .001) in popularityfrom the next popular belief, except for spiritualism and extraordinary life forms,t(3141) = 1.62, ns, which did not differ from each other, and were thus combined when comparedto the next popular belief.

Next, effects of gender and educational level (university vs. vocational school) on overall para-normal belief were analyzed with separate one-way analyses of variance (ANOVA). The meansand standard deviations are presented in Table 1. Women had more paranormal beliefs thanmen, F(1,3133) = 91.00, p < .001, g2 = .028. As regards the specific beliefs, women scored higherthan men in all the others (g2 ranges from .004 to .043) except in beliefs in extraterrestrial life, inwhich men believed more (g2 = .015). Vocational school students had more paranormal beliefsthan university students, F(1,3140) = 78.09, p < .001, g2 = .024. They scored higher than univer-sity students in all other beliefs (g2 = .016–.034) except in religious beliefs (g2 = .000) in which thegroups did not differ. Age did not correlate with overall paranormal belief (r = �.01, ns).

All the paranormal belief subscales correlated highly with the total scale, r = .46–.84, p < .001.Thus, from this point forward we use the sum score of paranormal beliefs.

To investigate the mediating effects of thinking styles, we first tested whether they are associ-ated, on the one hand, with paranormal beliefs, and with gender and educational level on theother hand. The results showed, first, that paranormal beliefs correlated negatively with analyticalthinking, r = �.14, p < .001, and positively with intuitive thinking, r = .34, p < .001. The twothinking styles were not associated with each other, r = .02, ns. Second, ANOVA results showedthat women (M = 3.37) reported a higher level of intuitive thinking than men (M = 3.14),F(1,3132) = 100.70, p < .001, g2 = .031, whereas men (M = 3.98) showed more analytical think-ing than women (M = 3.84), F(1,3132) = 42.90, p < .001, g2 = .014. Moreover, university stu-dents (M = 3.94) showed a higher level of analytical thinking than vocational school students(M = 3.67), F(1,3139) = 162.49, p < .001, g2 = .049.

In addition, the results of univariate analyses of covariance (ANCOVA) showed that analyticaland intuitive thinking mediated the gender difference in paranormal beliefs. When analyticalthinking was partialled out, F(1,3134) = 51.50, p < .001, g2 = .016, gender had a slightly reducedalthough still significant effect on paranormal beliefs, F(1,3134) = 75.98, p < .001, g2 = .024. Sim-ilarly, when intuitive thinking was partialled out, F(1,3134) = 352.91, p < .001, g2 = .101, genderhad a reduced although still significant effect on paranormal beliefs, F(1,3134) = 43.40, p < .001,g2 = .014.

Further, analytical thinking mediated the educational level difference in paranormal beliefs.The results indicated that when analytical thinking was partialled out, F(1,3134) = 41.40,p < .001, g2 = .013, students of university and vocational school differed less although still signif-icantly from each other, F(1,3134) = 52.48, p < .001, g2 = .016.

3.2. Comparison of disciplines and the effect of length of education

To analyze disciplinary differences in paranormal beliefs, we first carried out an ANCOVA forparanormal beliefs. Discipline and gender were included as independent variables and length ofeducation as a covariate. The three-way interaction between discipline, gender, and length of edu-cation, F(19,3033) = 1.10, ns, g2 = .007, and the two-way interactions between gender and years


of education, F(1,3033) = 0.41, ns, g2 = .000, and discipline and years of education,F(19,3033) = 1.22, ns, g2 = .008, were all non-significant and were dropped from the final model.The results of the final model showed that the main effects of discipline, F(19,3033) = 8.24,p < .001, g2 = .050, length of education, F(1,3033) = 14.07, p < .001, g2 = .005, and gender,F(1,3033) = 35.04, p < .001, g2 = .012, were all significant, as was the interaction between genderand discipline, F(1,3033) = 2.27, p < .001, g2 = .014.

Second, we carried out follow-up analyses in which the effect of discipline on paranormal beliefswas analyzed separately for both genders. The results indicated that the effect of discipline onparanormal beliefs was significant both for women, F(19,2261) = 11.01, p < .001, g2 = .085,and for men, F(19,770) = 4.36, p < .001, g2 = .097. All significant differences between disciplinarygroups are indicated in Table 2 separately for both genders, along with means and standard devi-ations. The results of post hoc comparisons (Bonferroni) revealed that among female universitystudents, students of philosophy and psychology hold the least beliefs and students of businessand theology hold the most beliefs. Among male university students, students of architectureand psychology had the least beliefs and students of education and theology had the most beliefs.Additionally, two things should be noted: the male students of philosophy and, more significantly,

Table 2Paranormal beliefs of female and male students by disciplines

Discipline Women Men

M SD Differs from n M SD Differs from n

University

Philosophy (a) 1.80 0.72 m, n, q–t 35 1.84 0.75 20Psychology (b) 1.81 0.59 h, i, k–t 68 1.65 0.50 l, n 23Medicine (c) 1.87 0.52 h, i, k–t 168 1.70 0.65 l, n 42Other medical1 (d) 2.00 0.52 n, q–t 105 1.75 0.43 9Social science (e) 2.02 0.60 n, r–t 64 1.74 0.64 n 19Natural science (f) 2.02 0.60 n, q–t 402 1.76 0.63 l, n 121Technology (g) 2.09 0.62 s, t 74 1.78 0.56 l, n 95Art and humanities (h) 2.10 0.61 b, c, n, r–t 395 2.00 0.63 47Law (i) 2.15 0.55 a, b, s, t 127 1.79 0.53 n 53Architecture (j) 2.15 0.59 29 1.60 0.51 n 12Forestry (k) 2.18 0.61 b, c, t 79 1.73 0.48 n 25Education (l) 2.19 0.55 b, c, s, t 149 2.41 0.71 b, c, f, g 16Business (m) 2.31 0.65 a–c 55 1.78 0.47 n 24Theology (n) 2.39 0.55 a–f, h 121 2.45 0.55 b, c, e–g, i–k, m 34

Vocational school

Technology (o) 2.19 0.69 a, b, t 79 1.97 0.62 n 197Agriculture (p) 2.26 0.61 a, b 48 1.81 0.62 15Business (q) 2.33 0.71 a–d, f 88 2.20 0.76 22Art (r) 2.39 0.63 a–f, h 83 2.35 0.92 7Health and Education (s) 2.54 0.59 a–i, l 58 2.52 0.30 2Service2 (t) 2.64 0.67 a–i, k, l, o 54 1.71 0.47 7

1 Students of pharmacy, dentistry, and veterinary medicine.2 Students majoring in hairdressing, catering, and customer services.


those of education were the only men who had more paranormal beliefs than their female coun-terparts, and the number of men in the disciplines varied a lot, being negligible in a few disciplines.

We also examined whether analytical or intuitive thinking mediated the disciplinary differencesin paranormal beliefs among university students. Given the 14 disciplines, theoretically there were91 potential disciplinary differences, both among men and women, which might have been med-iated by the thinking styles. In 84 cases out of 91, female students from different disciplines did notdiffer from each other both in paranormal beliefs and the thinking style in question, and thereforethe mediator effect was not possible. As regards the seven remaining disciplinary differences, fivewere not mediated by the thinking styles (p > .05). Among male students, none of the disciplinarygroups differed from another disciplinary group in both paranormal beliefs and the thinking stylein question and the mediator effect was thus not possible. These results indicated that thinkingstyles did not mediate the disciplinary differences in paranormal beliefs.

Finally, the results showed that duration of education was weakly negatively connected withparanormal beliefs, r = �.09, p < .001. When analytical thinking was partialled out, the connec-tion was only slightly reduced, r = �.08, p < .001.

4. Discussion

Previous studies have predominantly indicated that higher educational level and education incertain disciplines such as natural science are related to skepticism toward paranormal beliefs(a review: Vyse, 1997). The reasons have, however, only been speculated about. Moreover, thefew studies that have addressed these issues have been limited to a few disciplines. This study ex-tended the previous research by including students from many disciplines and from two educa-tional levels, and by analyzing whether length of education and intuitive and analyticalthinking explain the relationship between education and paranormal beliefs.

The results showed that university students had fewer paranormal beliefs than vocationalschool students. This was in accordance with our hypothesis, and with the research that has foundparanormal beliefs to be negatively connected with level of education (Orenstein, 2002; Otis & Al-cock, 1982; Za�rour, 1972). The present results also indicated that those who had enrolled in high-er education were more analytically oriented compared with the students of lower level ofeducation and that the lower analytical thinking among vocational school students explainedthe difference in paranormal beliefs between vocational school and university students. Hence,the results indirectly support the argument that students enrolling in university have fewer para-normal beliefs than others because they are more intelligent and more interested in academic pur-suits than other students (Otis & Alcock, 1982; Za�rour, 1972).

Additionally, the results showed that among university students, the students of medicine andpsychology hold the least paranormal beliefs and the students of education and theology hold themost paranormal beliefs. Earlier studies on the connection between paranormal beliefs and differ-ent disciplines have shown quite inconsistent findings. For example, some studies have shown thatstudents of natural science, social science, and psychology have fewer paranormal beliefs than stu-dents of art and humanities (Gray & Mill, 1990; Grimmer & White, 1992; Pasachoff et al., 1970;Za�rour, 1972), whereas other studies have indicated other types of differences (Jahoda, 1968;Parida, 1962; Pasachoff et al., 1970; Salter & Routledge, 1971). The present results offer two


explanations for the inconsistent findings. First, differences between the disciplines were small,which may explain why they have not always been detected in previous studies. Second, thedifferences between the disciplines were somewhat dissimilar among male and female students.This may explain the previous inconsistent results as in some previous studies there were onlymale participants (Jahoda, 1968; Parida, 1962; Pasachoff et al., 1970).

It has been suggested that disciplinary differences in paranormal beliefs may be explained bycritical thinking abilities that university education has been assumed to provide more in disciplinessuch as natural science than in disciplines such as art and humanities (Otis & Alcock, 1982;Za�rour, 1972). The present results did not support this argument: Paranormal beliefs were onlyslightly less prevalent among the students of upper year courses than among students of loweryear courses, and only a fraction of this difference was due to analytical thinking. Furthermore,against our hypotheses, the disciplinary differences in paranormal beliefs were not mediated by thethinking styles. Another assumption on the disciplinary differences has been that the most skep-tical people apply to higher education and to disciplines such as natural science (Vyse, 1997). Ourresults supported that view: The small disciplinary differences that were found seem to haveexisted already when students applied to the different disciplines.

Understanding why analytical thinking was not more strongly connected with paranormal be-liefs is facilitated by regarding information processing as two-dimensional. The assumption thatonly development of analytical thinking reduces paranormal beliefs includes an implicit presump-tion that superstitious thinking is the opposite of analytical thinking. More generally, it assumesthat reasoning can be depicted on one dimension and that poor reasoning is replaced by rationalthinking in the course of education. In contrast to this single-dimension view, dual-process theo-ries suggest that reasoning does not develop from primitive and error-prone processing linearly torational and accurate reasoning but that people have two independent information-processingsystems, intuitive and analytical thinking, which have different neural bases, different rules ofoperation, and a different evolutionary history (Epstein et al., 1996; Stanovich & West, 2000).In this study, belief in the paranormal was more strongly related with intuitive thinking than withanalytical thinking. The results are in line with the basic tenet of dual-process theories in thatbeliefs which are most resistant to change arise from the intuitive, not from a malfunctioning ana-lytical system (Epstein et al., 1996; Stanovich & West, 2000).

Additionally, intuitive and analytical thinking explained gender differences in paranormal be-liefs. Women were less analytical and more intuitive than men as we had predicted and as indi-cated by earlier research (Epstein et al., 1996; Lieberman, 2000; Pacini & Epstein, 1999;Wolfradt et al., 1999), and these differences in thinking styles turned out to be generative mech-anisms for women�s higher endorsement of paranormal beliefs compared to men. These findingsare important given that similar gender differences in paranormal beliefs have been repeatedlyfound in earlier work (a review: Vyse, 1997) but no explanations have previously been offered.

Before concluding, some limitations of the study should be mentioned. Our results indicatedthat paranormal beliefs among students were relatively infrequent. Some beliefs were rarely ac-cepted, such as belief in an unlucky number (6% agreed or strongly agreed with the claim),although some other beliefs were more accepted, for example belief in God (51%). Student respon-dents in this study thus hold considerably fewer paranormal beliefs than respondents of studieswith national samples from Canada and the United States (Orenstein, 2002; Rice, 2003). Similarresults have been obtained in previous cross-cultural comparisons: Finnish students have held


considerably fewer beliefs than American students (Tobacyk & Pirttila-Backman, 1992). In futurestudies, the relationships between paranormal beliefs, thinking styles, and education should beexamined with people who believe more in the paranormal.

Another limitation is that the study was cross-sectional, and thus not the best possible researchdesign for studying the effect of length of education. However, there is no reason to suppose thatthe students of different year courses would differ in any essential way in their thinking styles or inthe education they have received as there have not been any considerable changes in the Finnishschool system or in the university entrance exams during the last years.

Additionally, only a self-report measure of analytical thinking was used. We selected the Ra-tional thinking scale because individuals who score high on it have been shown to have betterproblem-solving abilities and perform better on the Math and Verbal Scholastic Aptitude Testthan others (Epstein et al., 1996; Toplak & Stanovich, 2002). It is nevertheless possible that dif-ferent kinds of results would emerge if more diverse measures of analytical and critical thinkingwere employed.

Finally, it is possible that the gender differences in paranormal beliefs were distorted by differ-ential item functioning (DIF) of the paranormal belief scale, that is, some paranormal belief itemsmight have been responded to differentially by equally believing men and women (see Lange,Irwin, & Houran, 2000). Although similar gender differences have been obtained with severalkinds of measures (Rice, 2003; Vyse, 1997), future studies on paranormal beliefs should pay moreattention to differential item functioning.

Taken together, the results revealed that analytical thinking mediated the educational level dif-ference in paranormal beliefs, and intuitive and analytical thinking mediated the gender differencein paranormal beliefs. However, the effects of discipline and length of university education onparanormal beliefs were small, and were not mediated by the thinking styles. It thus seems thatskepticism toward paranormal beliefs is mostly acquired before higher education.

Acknowledgement

This study was supported by a grant from the Academy of Finland (200828). We thank KaisaAunola for statistical help.

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