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A RASCH HIERARCHY OF HAUNT AND POLTERGEIST EXPERIENCES.

RENSE LANGE [1]

ABSTRACT: Although it has long been suspected that haunt and poltergeist phenomena form a hierarchy, compelling empirical evidence for this suggestion has been lacking. Using the data of 865 student respondents from 2 previous studies, Rasch scaling of 8 items from the Poltergeist subscale of the Anomalous Experiences Inventory (V. K. Kumar, R. J. Pekala, & C. Gallagher, 1994) revealed the existence of a well-defined probabilistic hierarchy of events. Statistical dimensionality tests validated that the 8 items indeed constitute a unidimensional continuum, and this continuum is not significantly affected by gender-related response biases. The results do not discriminate among the various parapsychological and conventional explanations for these experiences, and several theoretical perspectives on the findings are discussed.

Our research program (e.g., Lange & Houran, 1998, 1999, 2000) has actively focused on constructing a process model of haunts and poltergeists, that is, a mathematical description of what Teguis and Flynn (1983) called "the holistic patterns of interpersonal relationships, background factors, and social-psychological variables ... crucial to understanding the nature, etiology, and meaning of such occurrences" (p. 61). However, we have not examined in detail the holistic patterns among different haunt and poltergeist experiences. A few studies have investigated how qualitatively different phenomena correlate with one another (e.g., Alvarado & Zingrone, 1995; Houran, 2000; Houran & Thalbourne, 2001), but Palmer (1974; Pratt & Palmer, 1976) was the first to propose the interesting notion that phenomena might progress systematically over time. According to Guy Lyon Playfair (1980), there are approximately 19 "symptoms" of the poltergeist, beginning with raps and ending with equipment failure of cameras, tape recorders, and so forth. Individual cases may involve only half a dozen of these symptoms, but Playfair (quoted in Wilson, 1993, pp. 388-389) asserted that: You always get them in the same order. You don't get puddles of water before stone throwing, you don't get fires before raps. So that there is a predictable behavior pattern. They appear to be random to us, but they're obeying some sort of rules that they understand even if we don't.

We are unaware of any published research supporting Playfair's assertion, but Houran and Brugger (2000) similarly argued that haunts and poltergeist experiences could form a hierarchy and that determining the probability of certain anomalies should provide clues to the nature of haunts and poltergeists.

Building on this earlier work, we address the question of whether haunt and poltergeist phenomena form a hierarchy as defined by the self-reported experiences derived from the Poltergeist subscale (Kumar & Pekala, in press) of the Anomalous Experiences Inventory (AEI; Kumar, Pekala, & Gallagher, 1994). The AEI was originally constructed to measure general paranormal belief, experience, ability, drug use, and fear of the paranormal (see Gallagher, Kumar, & Pekala, 1994). However, Houran identified eight items on the AEI that parallel experiences typical of haunts and poltergeists (see Table 1), and Kumar and Pekala (in press) subsequently used these items in a study on how haunt and poltergeist experiences relate to hypnosis-specific attitudes and behaviors.

The 8-item Poltergeist subscale addresses two broad types of occurrences: (a) seemingly subjective phenomena (i.e., not normally perceived collectively), such as apparitions, and (b) more objective phenomena that involve the physical environment, such as object movements (Roll, 1977). The range of specific experiential content measured by the Poltergeist subscale is admittedly limited. For instance, Lange, Houran, Harte, and Havens (1996) identified seven specific categories of haunt and poltergeist experiences,[2] but the Poltergeist subscale covers perhaps only three of these categories (visual, sensed presence/tactile, and object movements).

Two of the items in the subscale deserve brief comment. First, haunts and poltergeists usually elicit intensely fearful reactions in experients (Hufford, 1982, Rogo, 1974), and for this reason the subscale includes an item that reflects having had a psychic experience that scared the experience "to death." Second, it may be controversial to some readers that the subscale includes an item dealing with elves and "little people." Actually, reports of haunts and poltergeists resemble and are significantly correlated with reports of encounters with folklore-type entities (Evans, 1984, 1987; Houran & Thalbourne, 2001). It is not surprising therefore that haunt and poltergeist cases occasionally involve "troll-like entities" (Myers, 1986, pp. 196-200) and devilish "horny things" (McHarg, 1973, pp. 17-19). [3]

Before undertaking a large, detailed study of a possible hierarchy of experiences, we decided to use pre-existing AEI data to test the scaling properties and dimensionality of the items comprising the Poltergeist subscale within a Rasch (1960) scaling framework. Because this approach may be unfamiliar to some readers, in the next section we provide an overview approach as it pertains to the present research. For more general introductions to Rasch scaling we refer interested readers to Embretson and Herschberger (1999) and van der Linden and Hambleton (1997).

RASCH HIERARCHY OF EXPERIENCES

A clear hierarchy exists when the items that assess respondents' experiences (E) obey a Guttman scale; that is, it should be possible to renumber the events such that the occurrence of [E.sub.e] implies that [E.sub.1], ... , [E.sub.e-1] also occurred. As is illustrated by the thick lines in Figure 1, given an appropriate Guttman dimension this is possible only when the probability of an affirmative response follows a step function. Unfortunately, it is unrealistic to expect such patterns to occur in practice as the response probabilities [P.sub.e] of reporting the [E.sub.e], are affected by measurement error. The situation is further complicated by the fact that direct comparisons of the [P.sub.e] are useful only when these probabilities vary along a single dimension. As explained below, both sets of issues can be addressed within a Rasch (1960) scaling framework (see, e.g., Linacre, 1904; Wright & Stone, 1979), which essentially produces a probabilistic Guttman scale (the sloped curves in Figure 1). Although most R asch applications focus on measuring person characteristics (for applications relevant to parapsychology see, e.g., Lange, Irwin, & Houran, 2000a; Lange, Thalbourne, Houran, & Storm, 2000b), our present hypotheses mainly concern the item characteristics. Accordingly, individual differences are largely ignored, except to establish the fit of the Rasch model and the absence of systematic response biases.

In its most basic form, Rasch scaling assigns to each [E.sub.e] a location [[delta].sub.e] on a common underlying dimension such that they form a hierarchy with the property [P.sub.1] [greater than] ... [greater than] [P.sub.e] [greater than] ... over the entire dimension. Naturally, these probabilities also vary with respondents' idiosyncratic tendencies ([theta]) of experiencing anomalous events, and perhaps with other properties of the respondents. Because gender ([gamma]) is the only respondent variable that occurs in our data set (see Method section), we compare men and women. Following Linacre (1994), we therefore analyze our data according to a generalized Rasch model that relates [P.sub.nge] (i.e., the probability that person n, of gender g, reports experience e) to the three facets--[theta], [gamma], and [delta]--as:

log([P.sub.nge]/1 - [P.sub.nge]) = [[theta].sub.n] -[[gamma].sub.g] -[[delta].sub.e].

The log odds ratio (logit) in the left hand side of this equation defines the basic metric of the Rasch scale. This logit scale is determined up to a linear transformation only, and we use the convention that greater [[delta].sub.e] and [[gamma].sub.g] express a lower response probability. The reverse is true for [[theta].sub.n]. This is illustrated by the leftmost Rasch curves in Figure 1, which show the response probabilities associated with two hypothetical experiences, a and b, as obtained by setting [[delta].sub.a] = -1 and [[delta].sub.b] = 1, [[gamma].sub.men] = [[gamma].sub.women] = 0, and solving for [P.sub.nge] in Equation 1. [4] Note that the two response curves never overlap (i.e., [P.sub.nga][greater than][P.sub.ngb] and that the response probability is .5 for Item a (Item b) when [theta] = [[delta].sub.a] = -1 ([theta] = [[delta].sub.b] = 1).

Equation 1 can be fitted by means of the versatile Facets software (Linacre, 1999) by constraining the gender parameters [gamma] to sum to zero and constraining the [theta] parameters to sum to zero for each gender. This software also provides indices to quantify the fit of the items and the respondents in terms of the differences between the observed and predicted response probabilities. In particular, the infit reflects the item (person) fit relative to items (persons) with similar locations, whereas the outfit reflects the items' (persons') fit relative to those with dissimilar locations. The theoretical value of both statistics is 1, and fit values in the range of 0.7 to 1.3 are generally deemed acceptable (Wright & Stone, 1979). In addition, Facets provides tests of significance for the differences in the [[delta].sub.e]s (reflecting a difference in the items' locations) and between the [[gamma].sub.g]s (which corresponds to a main effect of gender).

Such comparisons are meaningful only when the items are unbiased; that is, the items' properties should be the same across different subgroups of respondents (cf. Thissen, Steinberg, & Gerrard, 1986). As indicated by Figure 1 for the two versions of Item b (leftmost two Rasch curves), this means that the response probabilities for men and women with equal propensities should be identical for each item.[5] In other words, all items should assume the same location for men and women--and this holds regardless of the fact that one gender may have a higher average propensity than the other. Violations of this condition (i.e., biases) are evidenced by the finding that the [[delta].sub.e]s are statistically diferent for men and women, resulting in gender interactions involving [delta]. If so, this would greatly limit the generality of Equation 1, because separate item locations would be needed for men and women (i.e., the item parameters would occur as [[delta].sub.eg] rather than [[delta].sub.e] in Equation 1). T he Facets software includes two types of tests for this purpose. First, it provides a chi-square omnibus test that considers the locations of all items by gender simultaneously. Second, it provides a test (z) for group differences in the location of each individual item. In other words, this last test determines for each item e whether [[delta].sub.e(women)] = [[delta].sub.e(men)] is a tenable hypothesis.[6]

Note that gender bias as defined here refers to the measurement distortions that result when the same item is interpreted differently by men and women. Depending on the nature and the magnitude of the items' biases, the removal of biased items might increase as well as decrease the differences between men and women's average measures (cf. Lange et al., 2000b).

In addition, Equation 1 assumes that the Rasch dimension is unidimensional. Although an acceptable fit of this equation supports the assumption of unidimensionality (Hattie, 1985), a more stringent test can be obtained by comparing the relative fit of the intended unidimensional model with that of a competing two-dimensional Rasch model. Facets does not provide such tests, and therefore the ConQuest Rasch software (Wu, Adams, & Wilson, 1998) is used for dimensionality testing purposes.

METHOD

Data Set

We used two data sets from two research projects (Kumar, Pekala, & McCloskey, 2000; Pekala, Kumar, & Marcano, 1995) in which the AFI (Kumar et al., 1994) was administered. These data sets had been gathered for independent research purposes. The first set contains the data of 400 respondents with known gender information (282 women, 118 men). The second data set consisted of 465 respondents of unknown gender. The respondents were students in Introduction to Psychology at West Chester University in West Chester, Pennsylvania, who participated to complete a departmental requirement of participation in a research study or another project. Participation was voluntary inasmuch as the students had a choice among several research projects and they could terminate their participation at any time with impunity.

AEI

The AEI contains 70 items that form five subscales: Anomalous/Paranormal Experience, Anomalous/Paranormal Belief, Anomalous/Paranormal Ability, Fear of the Anomalous/Paranormal, and Drug Use. However, only the eight AEI items that are listed in Table 1 are analyzed (i.e., Items 29,38,48,49,51,55,66, and 67). This Poltergeist subscale was constructed on the basis of the face validity of the items for their relevance to haunt and poltergeist phenomena. This subscale has been used in two published studies (Kumar & Pekala, in press; Houran & Thalbourne, 2001), and Houran and Thalbourne (2001) reported a correlation of .54 (p [less than] .001) between this measure and Item 18 of the Australian Sheep-Goat Scale: "I am completely convinced that persistent inexplicable physical disturbances, of an apparently psychokinetic origin (as for example a 'poltergeist') have occurred in my presence at some time in the past."

We stress that the same items were used as in Kumar and Pekala's (in press) and Houran and Thalbourne's (2001) studies; no items were eliminated because of their lack of fit to the Rasch model.

RESULTS

Preliminaries

The respondents reported relatively few paranormal experiences (M = 0.71, SD=1.17, range: 0-7). In fact, the majority of respondents (n=540 of 865, or 62%) checked none of the eight AEI items studied here, which effectively leaves only 325 cases for analysis (128 with known gender and 197 with unknown gender). No respondent checked each question. Given the small number of items, the classical (person) reliability of the Poltergeist subscale appears satisfactory (KR 20 = 0.70). However, from a Rasch perspective, the items do not constitute a viable person scale, because they are severely "mistargeted" (i.e., we know that 540 respondents are "low," but not how low). Although this does not affect the scaling of the items, it should be kept in mind that the results by necessity concern only those respondents who admitted to experiencing at least one of the anomalies studied here.

The main results of the Rasch item analyses are summarized in Table 1, which shows the percentage of positive responses, the item locations [[delta].sub.i] (in logits) together with their standard errors of measurement ([SE.sub.[delta]]), followed by the items' infit and outfit statistics and the results of the item-level bias tests. We discuss several aspects of the model assumptions before addressing the main findings.

Model Fit and Assumptions

The findings in Table 1 indicate that the AEI items obey the Rasch assumptions, as the infit and outfit of each item lie in the acceptable range of 0.7-1.3. Next, to determine the quality of the individual response records, we tested person misfit using [alpha] = .10 based on the respondents' outfit values. Using this criterion, we found that only 11% of the 325 effective response records deviated significantly from the Rasch model, that, is, about what would be expected by chance. Furthermore, Facets' omnibus bias test revealed that gender differences did not interact with the item locations [[delta].sub.[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]] [[chi].sup.2] (16, N = 128) = 14.3, p [greater than] .50, implying the absence of gender bias. In addition, none of the item = level bias tests are significant at p[less than] .10, because all \[z.sub.e]s\ [less than] 1.65 in the last column of Table 1. In other words, the items as well as the respondents fit the assumptions of the Rasch model, and the responses are not systematically biased with respect to gender.

To test for multidimensionality, we divided the eight AEI items into two factors, depending on their frequency of endorsement (i.e., Items 49, 51, 48, 66 [high frequency] vs. Items 38, 29, 55, 67 [low frequency]), and we fitted a multidimensional Rasch model using the ConQuest software (Wu et al., 1998). Although other choices are possible, we selected these two factors because common experiences might be qualitatively different from rarely reported experiences. In support of the unidimensionality assumption, the correlation between the two latent dimensions was extremely high (r=.90) after correcting for attenuation. In addition, competitive model tests indicated that the two-factor model did not significantly outperform, [[chi].sup.2](3, N = 325) = 3.21, p [greater than] .30, the one-dimensional model that treats all items as belonging to a single factor. It is reasonable to assume, therefore, that the eight experiences studied here are indeed ordered along a single continuum.

Experience Hierarchy

In Figure 2 are plotted the AEI items according to their location on the Rasch dimension in logits. The extremes of this dimension are seeing ghosts and apparitions ([[delta].sub.49] = -0.03), which was reported by 18.6% of all respondents (see Table 1), and seeing elves and fairies ([[delta].sub.67] = 3.48), which was reported by just 1.7% of all respondents. The Rasch location of the eight experiences differs significantly, [[chi].sup.2](7, N= 325) = 228.0, p [less than] .001, and the standard errors, [SE.sub.[delta]], associated with each item's location are listed in Table 1. To illustrate the hierarchical nature of the experiences, also displayed in Figure 2 are the response curves of Items 49, 29, and 67. As the response curves are relatively flat across the range of 0 shown in this figure, it follows that a deterministic model would provide a poor fit to the data. 7 Nevertheless, the item hierarchy uncovered by means of Rasch scaling discriminates admirably among the various experiences. For instance, the modeled probability that a respondent with [theta] = 1.96 (the location of Item 29) will experience his or her body, or nearby objects, levitating is 50%, whereas the corresponding conditional probability of seeing ghosts or apparitions is 88%, and that of seeing elves or fairies is only 18%. [8]

Items 51, 48, 66, and 38 (which deal with possession, communicating with the dead, frightening psychic experiences, and objects appearing and disappearing) assume similar scale locations, and so do Items 29 and 55 (which deal with levitation and being able to communicate with the dead). It appears therefore that the hierarchy begins with experiences that are first perceived to originate within the experient and then are perceived to progressively manifest outside the experient. This is consistent with several hypotheses that emphasize "externalization" for poltergeist-like phenomena, such as attribution theory (Houran & Williams, 1998), dissociation (Ross & Joshi, 1992), or "seizure-related" psychokinesis (Roll, 1977; Roll & Persinger, in press). However, this interpretation is necessarily tentative, because it should be kept in mind that the items' locations on the Rasch dimension depend partly on the way they are phrased. For instance, if Item 67 were reworded as "I may have seen elves or fairies," or as " I have seen entities that remind me of elves or fairies," this may yield a greater number of affirmative responses. Accordingly, the location of "elves and fairies" in Figure 1 would shift to the left. Conversely, the rewording "I see elves and fairies all the time" would push the location further to the right.

Gender

The gender effect [gamma] in Equation 1 is not statistically significant [[chi].sup.2](1, N = 128) = 0.10, p [greater than] .50, as the overall difference between these two groups is negligible (0.04 logits). In terms of raw scores, men checked an average of 0.68 items out of eight, whereas women checked an average of 0.63 (as computed over all 400 respondents with known gender). This difference explains less than 1% of the variance ([[eta].sup.2] = 0.00) in the number of reported paranormal experiences. We note that a gender effect with a similarly low explanatory value ([[eta].sup.2] = 0.01) was obtained by Lange et al. (2000a), who studied men and women's paranormal beliefs as assessed by an unbiased Rasch version of Tobacyk's (1988) Revised Paranormal Belief Scale.

DISCUSSION

The findings indicate that the eight items of the AEI's Poltergeist subscale form a hierarchy according to the assumptions of a generalized Rasch model (Linacre, 1999). This model has three facets because, in addition to respondents and items, it also considers the role of gender. In particular, each of the AEI items shows an acceptable infit and outfit to the Rasch assumptions, and the items show no signs of multidimensionality as determined by competitive model tests. Moreover, the items are unbiased--at least with respect to gender--as their locations are not significantly different for women and men. Finally, the respondent fit is adequate, because the number of response records that do not fit the model barely exceeds what would be expected due to chance. In other words, the eight haunt/poltergeist experiences [E.sub.1],..., [E.sub.e],..., [E.sub.8] addressed by the AEI items can be renumbered such that their response probabilities [P.sub.e] obey the hierarchy condition [P.sub.1] [greater than] ... [greater than] [P.sub.e] [greater than] ... [P.sub.8] across the Rasch dimension. Accordingly, we conclude that these items define an interval-level continuum along which haunt and poltergeist experiences vary according to their intensity.

We take this opportunity to speculate about the theoretical import of our findings. For example, Alvarado and Zingrone's (1995) research on the survival hypothesis for haunts and poltergeists revealed that visual apparitions were not significantly associated with physical events that seemingly reflect intelligence and purpose. Using cases taken from journalistic sources, Houran (2000) found that visual apparitions tended not to occur with any object movements or erratic functioning of mechanical apparatus. However, rather than assuming that "ghosts" and physical manifestations are unrelated phenomena, our findings suggest that they may simply represent different locations on a shared dimension--that is, these are similar phenomena (Houran & Thalboume, 2001) that differ only in their probability of occurring or of being reported. We admit that such reports are not always reliable. For instance, Roll tested Palmer's (1974; Pratt & Palmer, 1976) speculation about a possible structured progression of poltergeist experiences--namely, that sounds precede object movements. Roll (1977) examined 31 historic and well-investigated poltergeist cases in which it was known what type of phenomena came first. In an apparent contradiction of Playfair's (quoted in Wilson, 1993, pp. 388-389) notion that phenomena always follow the same order, 17 cases in Roll's sample began with sounds, and 14 started with movements. However, Roll cautioned that there might be a tendency to ignore or not give credence to sound phenomena. With more details, we might learn that a greater number of cases with movements were preceded by sound, or indeed that sound phenomena and object movements are equally likely to occur or be reported by experients.

Although finding a unidimensional hierarchy provides some support for the early ideas of Palmer and Playfair, it does not help us discriminate between parapsychological and conventional sources for these experiences. In fact, if psychokinesis (and recurrent spontaneous psychokinesis [RSPK] in particular) can be validated, we might find that such phenomena form different hierarchies than events that are due to natural (nonpersonal) causes. Similarly, the dimensionality of experiences might differ between subjective and objective phenomena. If these suggestions bear out, then the methods used in this article may eventually help us classify or solve cases on the basis of the sequence of what has been reported and the dimensionality of the collective experiences.

In this context we note that Persinger has hypothesized that natural or manmade sources of electromagnetism can instigate phenomena suggestive of spirits (e.g., Gearhart & Persinger, 1986; Persinger, 1985; Persinger & Cameron, 1986). In a recent case study, Persinger, Tiller, and Koren (2000) examined the sequence of experiences reported by a laboratory participant who was exposed to magnetic fields. The types of experiences and their reported sequence (pp. 664-665) showed some interesting correspondences to our hierarchy. For instance, the experimental participant perceived visual anomalies prior to feeling possessed or being controlled, and reports of fear preceded experiences of floating or being elevated. Although Persinger et al.'s (2000) data are based on only one individual, we note that two representative surveys of paranormal experiences (Gallup & Newport, 1991; Ross & Joshi, 1992) also parallel our results. Specifically, in both Gallup and Newport's (1991) and Ross and Joshi's (1992) studies, "con tact with ghosts" was reported more frequently than physical manifestations associated with poltergeists. With respect to the other experiences considered in this article, Ross and Joshi's (p. 358) frequency distribution of paranormal experiences showed "possessed by some other power or force" as having the next higher prevalence, followed by "telekinesis." Taken together, these studies lend support to the ecological validity of our findings.

We emphasize, however, that our findings can be variously interpreted depending on theoretical perspective. For the hypothesis of RSPK, our findings could indicate that macro-PK has different probabilities of manifesting in certain ways. Assuming that our hierarchy is valid, it follows that haunt and poltergeist outbreaks initially involve phenomena that are extremely subtle or easily dismissed as imagination due to their private nature, whereas more spectacular events, such as levitations and object movements, come later in the episode. This may mean that haunt or poltergeist episodes have longer durations than previously thought or that experients give credence to anomalous events only when the events are of sufficiently large scale, such as with object movements. The findings might also be telling us something about the nature of specific RSPK events, if RSPK is indeed the underlying dimension to our hierarchy. That is, the findings suggest that visual apparitions require smaller "amounts of RSPK than obj ect movements or levitations.

Alternatively, the findings can be related to our attribution theory view of haunts and poltergeists (Lange & Houran, 1998, 1999, 2000), which revolves around the interrelations of paranormal experience, paranormal belief, fear of the paranormal, and tolerance of ambiguity. Within this framework, two interpretations are immediately apparent. First, the hierarchy could reflect the probability that people will apply certain paranormal labels to ambiguous (but otherwise conventional) stimuli. Second, the hierarchy may refer to the distribution of chance or "freak" events that are subsequently interpreted as having paranormal origins. In either case, the present findings suggest that research into the possible biasing effects of experients' beliefs, fears, and tolerance of ambiguity might provide more detailed insights into the nature of the posited attributional processes.

Additional research clearly is needed over a greater range of experiences in order to validate our results as well as to understand how other haunt and poltergeist experiences not considered here fit into the proposed hierarchy. For instance, it is desirable to study additional experiences so as to fill the gaps among the various items shown in Figure 2. Also, the present research did not distinguish between haunts and poltergeists. Therefore, investigators might want to examine separately these potentially two different classes of phenomena. Finally, greater ecological validity may be obtained in studies of actual haunt or poltergeist cases rather than by using a general sampling technique such as we used here. That is, the AEI could be administered to witnesses of the same haunt or poltergeist episode to determine whether the trends reported here replicate. Furthermore, the Facets software (Linacre, 1999) we used also provides excellent facilities to analyze observational data because it allows the simulta neous study of observer and event characteristics, observer agreement, and contextual effects, as well as their interactions, all within a single framework (cf. Lunz, Wright, & Linacre, 1990).

Despite the limitations of the present study, we believe that the Rasch methods used here have widespread application in parapsychology. The primary strength of this approach is that it allows researchers to construct detailed and verifiable models of how unobservable (latent) variables operate to produce variations in observable data. Already this has produced several scales (Lange et al., 2000a; Lange et al., 2000b) that challenge established findings within parapsychology (Houran, 1999; Irwin, 2000) as well as mainstream psychology (Lange, 1999). Although the aforementioned research (i.e., Lange, 1999; Lange et al., 2000a; Lange et al., 2000b) has primarily addressed the quantification of relatively stable person characteristics, Rasch scaling can also be used to model changes over time (cf. Fischer & Seliger, 1997), possibly as a function of an arbitrary number of independent variables (Linacre, 1994). Moreover, progress has been made in the modeling of continuous physical variables (Roskam, 1997), makin g these analytic techniques compatible with our multi-energy sensor array approach to the on-site study of haunts and poltergeists (Houran & Lange, 1998; Houran, Lange, & Black, 1998). Thus, the analysis of many types of data can be improved by adopting methods similar to those described here. In this way, we will come closer than was possible before to describing the underlying dimension (or dimensions) of haunt and poltergeist experiences.

(1.) We thank V. K. Kumar and Ronald J. Pekala for kindly providing the Anomalous Experiences Inventory data and commenting on an earlier version of this article. Also, the statistical referee provided excellent feedback that helped to clarify the presentation of the Rasch model. Finally, we express our appreciation to the Institut fur Grenzgebiete der Psychologie und Psychohygiene, Freiburg i. Br., Germany, for financial support of this study.

(2.) This includes visual, auditory, olfactory, tactile, sensed presence, object movements, and erratic functioning of mechanical/electrical apparatus.

(3.) We also note that these types of experiences are not uncommon even in contemporary cultures. For example, hallucinations of miniature people, called Lilliputian hallucinations, can occur during the early stages of delirium tremens or other organic states. Furthermore, some medical conditions may produce hallucinations of little folk (see, e.g., Needham & Taylor, 2000).

(4.) The Rasch response curves in Figure 1 were obtained by assuming that all [[a.sup.[sim]].sub.g] = 0. In this case Equation 1 yields:

P ([theta];[delta]) = 1/1 + [e.sup.[delta]-[theta]]

(5.) For purposes of illustration, the rightmost Rasch curve (Item b for men) was obtained by offsetting the curve for Item b for women by 0.2 units. In other words, the equation for the three Rasch curves in Figure 1 (left to right) is given by P(theta];[delta]), where [[delta].sub.1]] = -1 (Item a), [[delta].sub.2] = 1 (Item b for women), and [[delta].sub.3]] = 1.2 (Item b for men).

(6.) To obtain such tests, Facets computes the bias terms [B.sub.eg] relative to [[delta].sub.e], that is, [B.sub.eg] = [[delta].sub.eg] - [[delta].sub.e], as well as the associated standard errors of estimate [SE.sub.eg]. Assuming an approximately normal distribution of the [B.sub.eg], the item specific bias tests are thus obtained by computing

[z.sub.e] [approximate] [B.sub.e(women)] - [B.sub.e(men)]/[square root][[SE.sup.2].sub.e(women)] + [[SE.sup.2].sub.e(men)]..

(7.) The difference in the shapes of the response curves in Figure 2 relative to those in Figure 1 is due solely to the "shrinking" of the x-axis in Figure 2.

(8.) These values are obtained by substituting the appropriate values of [theta] and [delta] into the formula listed in footnote 3.

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TABLE 1
RESULTS OF RASCH SCALING AND TESTS OF GENDER-RELATED ITEM BIAS
 Rasch model b
AEI % of
item Experience sample a [delta]
49. I have seen a ghost or 18.6 -0.03
 apparition.
51. At times, I have felt 11.0 0.99
 possessed by an outside
 force.
48. I have communicated with 10.2 1.12
 the dead.
66. I have had a psychic or 9.9 1.15
 mystical experience
 which scared me to
 death.
38. I have experienced 9.7 1.19
 objects appearing or
 disappearing around me
 (materialization or
 dematerialization).
29. I have experienced my 5.8 1.96
 physical body or objects
 floating in the air
 (levitation).
55. I am able to communicate 4.6 2.24
 with the dead.
67. I have seen elves, 1.7 3.48
 fairies, and other types
 of little peoople.
 Gender
AEI bias c,e
item [SE.sub.[delta]] Infit d Outfit d z
49. 0.12 1.0 1.0 1.61
51. 0.13 1.1 1.1 -0.38
48. 0.14 0.8 0.8 0.54
66. 0.14 1.1 1.1 0.05
38. 0.14 1.0 0.9 -0.10
29. 0.17 1.0 1.3 -1.29
55. 0.18 0.9 0.8 -0.27
67. 0.28 1.0 1.2 -1.57
Note: AEI = Anomalous Experiences Inventory.
(a) Computed over all 865 available respondents.
(b) Computed over all 325 effective respondents.
(c) Computed over 128 effective respondents with known gender.
(d) Facets (computer program) reports values to one decimal place
only.
(e) A negative (positive) z statistic indicates that women (men)
are more likely to answer affirmatively than men (women) with
similar locations ([theta]) on the Rasch dimension.


[Graph omitted]
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Author:HOURAN, JAMES; LANGE, RENSE
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Date:Mar 1, 2001
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