Paranormal vs conventional conjunction fallacy

A series of 2 (Conjunction type: Conventional vs. paranormal: Within subjects) x 2 (Level: low vs. high: Between subjects) mixed ANOVAs were conducted (see Tables 9 and 10 below).

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Table 9. Paranormal vs. conventional conjunction fallacy: number of correct responses

(Key: ASGS = Australian Sheep-Goat Scale, MMUpbs = Manchester Metropolitan University Paranormal Belief Scale, RPBS = Revised Paranormal Belief Scale, RT = Reality Testing IPO-RT).

166 Table 10. Summary ANOVA statistics22

(Key: ASGS = Australian Sheep-Goat Scale, MMUpbs = Manchester Metropolitan University Paranormal Belief Scale, RPBS = Revised Paranormal Belief Scale, RT = Reality Testing IPO-RT).

6.5.1. Australian sheep-goat scale (ASGS)

A significant main effect was found for problem type, F(1, 262) = 414.484, p <.001, ηp 2₌ .63. More correct responses were made for paranormal conjunction (M = 2.48, SD = 0.77) than for conventional conjunction (M = 1.19, SD = 1.00).

There was no significant main effect for level, F(1, 262) = 0.526, p = .469, ηp 2 _{= .020.} Participants above the median produced fewer correct answers than those below the median (M = 1.89, SD = 0.79).

There was no significant interaction found for problem type vs. level.

22 _{Cohen (1988) suggests that ηp}2 _{effects be interpreted using the following rule of thumb: values between}

.01-.06 reflect a small effect size, values within the .06–.13 range a medium effect size, and a value of .14 or higher indicates a large effect.

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6.5.2. New paranormal measure (MMUpbs)

A significant main effect was found for problem type, F(1, 262) = 422.491, p <.001, ηp 2 =. 62.More correct responses were observed for conventional conjunction (M = 1.19, SD = 1.01) than for paranormal conjunction (M = 2.49, SD = 0.78).

There was no significant main effect found for level, F(1, 262) = 0.392, p <.532, ηp 2 ₌ .001. Participants above the median produced fewer correct answers than those below the median. (M = 1.89, SD = 0.79). Simple main effects analysis was conducted, which indicated that there no significant interaction between problem type vs. level.

6.5.3. Revised paranormal belief scale (RPBS)

A significant main effect was found for problem type, F(1, 262) = 416.58, p <.001, ηp 2 ₌ .61 Fewer errors were made for paranormal conjunction (M = 2.58, SD = 0.70) than for conventional conjunction (M = 1.15, SD = 0.98).

There was no significant main effect for level, F(1, 262) = 0.339, p <.561, ηp 2 _{= .01.} Participants above the median produced fewer correct answers than those below the median. (M = 1.89, SD = 0.79).

There was no significant interaction found for problem type vs. level.

6.5.4. Reality Testing (RT)

A significant main effect was found for problem type, F(1, 262) = 416.60, p <.001, ηp 2 ₌ .61. Fewer errors were made for paranormal conjunction (M = 2.58, SD = 0.70) than for conventional conjunction (M = 1.15, SD = 0.98).

Whilst there was no significant main effect for level this was approaching significance,

F(1, 262) = 3.215, p <.074, ηp 2 _{= .012. Participants above the median produced fewer} correct answers than those below the median. (M = 1.94, SD = 0.78).

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The interaction between problem type vs. level was not significant. Overall, findings demonstrate that a main effect exists for belief and type. Whilst, more conjunction problems appear solved when framed within a paranormal context: framing effect.

The relationship between study measures and paranormal conjunction problems was assessed further using Pearson’s product moment correlation. Scores on paranormal conjunction problems negatively correlated with the measures of paranormal belief and RT; as level of paranormal belief and proneness to reality testing deficits increased performance on the paranormal conjunction problems decreased (see Table 11).

Table 11. Number of correct responses

**correlation significant at p < .01 (one-tailed).

(Key: ASGSrasch = Australian sheep-goat scale rasch scaled, RPBStot = Revised paranormal belief scale total, TPBrasch = Traditional paranormal beliefs rasch scaled, NAPrasch = New age philosophy rasch scaled, RTtot = Reality testing, MMUpbs = Manchester Metropolitan University paranormal belief scale)

169 6.6. Evaluation of new paranormal measure

The MMUpbs has established face validity, measuring the construct of paranormal belief. The MMUpbs also demonstrated satisfactory content validity; items are drawn from questions encompassing a broad range of paranormal constructs (i.e., astrology, psi, ESP and PK, ET/alien, haunting, religion, superstition, and witchcraft) (see Appendix A. Phase III Booklet, Section 1, pp. 313-317 for the 50-item MMUpbs). It was clear that the new measure of belief in the paranormal performed similarly to the established measures (ASGS and RPBS). Indeed, the MMUpbs shared considerable variance with the ASGS (65%) and RPBS (81%). The MMUpbs also shared significant variance with the two factors of the RPBS (TPB 60% and NAP 68%). Thus, the MMUpbs has good concurrent validity, test-retest reliability; it correlated positively with criterion measures. In addition to this, the MMUpbs demonstrated convergent validity; the MMUpbs correlated positively with other variables (i.e., reasoning measures and reality testing) in a pattern comparable to the ASGS and RPBS, whilst produces a normal distribution of responses, making it an appropriate measure (Peters et al., 2004).

Scores for each of the MMUpbs subscales were calculated and internal reliability assessed. Cronbach’s alpha (α) assessed the internal reliability of each of the paranormal belief subscale measures; astrology (r = .80), ESP (r = .80), ET/alien (r = .93), ghost/haunting (r = .92), PK (r = .88), religion (r = .87), superstition (r = .86) and witchcraft (r = .90) demonstrating good/excellent internal reliability (George and Malley, 2003). All crombach alpha subscales ranged between good (.80) and excellent (.93); consideration of individual items revealed/supported subscale coherence. (see Table 12 below).

Means and standard deviation scores were as follows: astrology (M = 2.91, SD = 1.27), ESP (M = 3.70, SD = 1.32), ET/alien (M = 2.76, SD = 1.31), ghost/haunting (M = 3.62, SD = 1.56), PK (M = 2.33, SD = 1.28), religion (M = 4.10, SD = 1.50), superstition (M = 3.67,

170 Table 12. MMUpbs subscales descriptive statistics

(Key: Astrology = Belief in astrology, ESP = Extra-sensory perception, ET/Alien = Extra- terrestrial/alien beliefs, Ghosts/Hauntings = Belief in ghosts/hauntings, PK = Psychokinesis, Religion = Religious beliefs, Superstition = Superstitious beliefs, and Witchcraft = Belief in witchcraft).

A further set of correlations examined relationships between MMUpbs subscales and established paranormal measures (ASGS and RPBS) (see Table 13).

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Table 13. Correlations for paranormal measures and MMUpbs subscales

**correlation significant at p < .01 (one-tailed).

(Key: TPBrasch = Traditional paranormal beliefs rasch scaled, NAPrasch = New age philosophy rasch scaled, ASGSrasch = Australian sheep-goat scale rasch scaled, RPBStot = Revised paranormal belief scale total)

Analysis found significant positive correlations for all measures and subscales of paranormal belief (RPBS, TPB, NAP and ASGS) and the MMUpbs subscales (astrology, ESP, ghosts/hauntings, extra-terrestrial, superstition, psychokinesis, religion and witchcraft). All of the MMUpbs subscales were significantly positively correlated at the p <.01** level.

172 Table 14. Inter-subscale correlations

*correlation significant at p < .05 (one tailed); **correlation significant at p < .01 (one- tailed).

For the sake of completeness, table 14 contains inter-subscale correlations. All subscales were significantly positively correlated at the p <.01** level except for the following subscales which were positively correlated at the p <.05* level: religion and superstition (r = .11*), extra-terrestrial and superstition (r = .14*) and witchcraft and superstition (r = .15*).