The similarities and differences in dream content at the cross-cultural, gender, and individual levels provide one starting point for carrying out studies that attempt to discover correspondences between dream content and various types of waking cognition. Hobson and Kahn's (2007) conclusion that dream content may be more generic than most researchers realize, and that individual differences are less salient than usually thought, provides the occasion for a review of findings based on the Hall and Van de Castle (1966) coding system for the study of dream content. Then new findings based on a computationally intensive randomization strategy are presented to show the minimum sample sizes needed to detect gender and individual differences in dream content. Generally speaking, sample sizes of 100-125 dream reports are needed because most dream elements appear in less than 50% of dream reports and the magnitude of the differences usually is not large.
The empirical conclusion -- based on a wide range of studies -- that there are cross-cultural, gender, and individual similarities and differences in dream content provides one important starting point in the search for correspondences between dreaming and various types of waking thought, whether fantasies, worries, interests, or more generally speaking, "concerns" (Klinger, 1971, 1999). However, the evidence for this starting point has recently been called into question by Hobson and Kahn's conclusion (2007, p. 850), based on the inability of judges to group dream reports according to their individual authors beyond chance levels, that "This finding indicated that dreams may be at least as much like each other as they are the signatures of individual dreamers." They further noted that "Our results suggest that dream reports cannot be used to identify the individuals who produced them when identifiers like names and gender of friends and family members are removed from the dream report" (Hobson & Kahn, 2007, p. 850). They further state "The corollary assumption, that dreaming is generic, is almost never considered. . ." (Hobson & Kahn, 2007, p. 850). In the discussion section of their article they write that their use of blind analyses may explain why they did not find the individual differences reported in other studies: "An important aspect of our study not previously used by dream researchers was the blinding of the judges who would have probably been more easily able to match the reports to individuals that they knew" (Hobson & Kahn, 2007, p. 855).
Hobson and Kahn (2007) reach these conclusions on the basis of three studies in which judges were asked to match sets of 25 or 50 dream reports to the five participants who contributed them. There were five dream reports from each of three men and two women in the first study, for a total of 25 dream reports; five dream reports from each of two men and three women in the second study, for a total of 25 dream reports; and 10 dream reports from each of three men and two women in the third study for a total of 50 dream reports. Overall, the six psychiatrists, one clinical psychologist, and one physicist who served as judges in one or more of the three studies could not sort the dreams beyond a chance level, defined as .20 by Hobson and Kahn (2007, p. 852).
However, in the discussion of their "surprising hypothesis," Hobson and Kahn (2007, p. 854) noted that systematic quantitative studies using the Hall and Van de Castle (1966) coding system for the study of dream content might lead to different results, and they therefore "encourage such additional studies." Since there are many studies using the Hall and Van de Castle (1966) coding system to examine these issues, their allusion to it provides the occasion for drawing together previous findings in a new format. We also use this article to present new information showing that it takes from 100 to 125 dream reports from each group or person being studied in order to detect many of the systematic differences in dream content that we report. These large sample sizes are needed because (1) many elements in dreams -- e.g., aggressive, friendly, and sexual interactions, misfortunes, and striving to succeed -- occur in fewer than half of all dream reports and (2) the magnitude of the differences between groups or individuals usually is not large.
Based on our empirical and methodological findings, we think there are shortcomings in a matching study of the type carried out by Hobson and Kahn (2007) because the wide range of memories, thoughts, and concerns any human being has, whether waking or dreaming, make it highly unlikely that five or 10 brief dream reports from one individual, ranging in length from 40 to a few hundred words, are going to be similar enough to be distinguished from similar sets of short reports from four other individuals with equally diverse and complex thought patterns. This article therefore focuses on the findings with the Hall and Van de Castle (1966) coding system in order to demonstrate that there is a solid foundation of findings at the cultural, gender, and individual levels that can be useful in studies seeking to link dream content to various forms of waking thought, which always has been the primary empirical essence of the search for "meaning" in dreams (Domhoff, 1996).
The studies we review, usually based on blind analyses by one or more coders who knew nothing about the participants, first show that there are several cross-cultural similarities in dream content as well as a few interesting cross-cultural differences that suggest linkages between dream content and culture. There are also gender similarities and differences that in at least some instances have correspondences in the waking thought patterns and behaviors of men and women. In addition, there are several studies of individual differences that in many instances relate to waking thoughts and concerns. The individual correspondences between dream content and waking thought have been established in two ways: by the use of evidence found in written documents relating to the dreamers' lives and by confirmatory responses by the dreamers and their friends to inferences developed by investigators on the basis of blind analyses.
2. Data and methods
To set the stage for the findings that follow, we present a brief overview, first, of the Hall and Van de Castle (1966) coding system and then of the computationally intensive randomization strategy, "approximate randomization," that we use to determine the minimum sample sizes necessary to replicate our findings (e.g., Franklin, Allison, & Gorman, 1997; Noreen, 1989). The Hall and Van de Castle (1966) coding system is an instance of the general methodology of content analysis, a quantitative approach to the search for meaningful regularities in any kind of written text. It involves four steps: the creation of carefully defined categories; the tabulation of frequencies for the various elements in the text; the use of statistical transformations to change raw frequencies into usable data, and the comparison of findings with control groups or normative standards (e.g., Cartwright, 1953; Holsti, 1969; Krippendorff, 2004; Osgood, 1959). In particular, we focus on 10 general empirical categories in the Hall and Van de Castle (1966) system that make it possible to classify every element that appears in a dream report (e.g., characters, social interactions, activities, misfortunes, emotions, settings, and objects).
The coding system rests on the nominal level of measurement to avoid serious reliability problems with rating systems for dream content, has high reliability when used by investigators in many different countries, and uses percentages and ratios to correct for differences in the length of dream reports (Domhoff, 1996, chap. 2; Domhoff, 2003, chap. 3). These percentages and ratios make possible a wide range of "content indicators," such as "animal percent" (the percentage of all characters that are animals) and "male/female percent" (the percentage of all gender-identified human characters that are male or female). The content indicators are discussed in Domhoff (2003, chap. 3) and briefly defined when they first appear in this article.
Because of the distortions and mistakes created by the use of parametric statistics with nominal data, skewed distributions, and/or non-random samples, especially when sample sizes are uneven, p values are determined using the formula for the significance of differences between two proportions, which has the added virtue of providing the same results as a 2 × 2 chi square with data expressed in percentages (Domhoff, 2003, pp. 63-65, 84-88; Micceri, 1989; Nanna & Sawilowsky, 1998; Reynolds, 1984; Siegel & Castellan, 1988). Effect sizes are determined by the use of Cohen's h statistic (Cohen, 1988), which uses an arcsine transformation calculated for the two samples to correct for the fact that standard deviations cannot be computed for data expressed in percentages (see Domhoff, 1996, Appendix D, for a discussion of the use of the h statistic with Hall and Van de Castle codings). The p and h values for all Hall and Van De Castle content indicators are computed automatically when codings are entered into DreamSAT, then displayed as either tables or bar graphs that we call "h profiles"; DreamSAT is available to all researchers through DreamResearch.net (Schneider & Domhoff, 1995).
Very important for the purpose of this article, the Hall and Van de Castle coding system includes normative findings based on five dream reports from each of 100 American college men and 100 American college women. The general findings with these two samples of 500 dream reports, which range in length from 50 to 300 words, have been replicated several times (Domhoff, 1996, pp. 68-73; Dudley & Fungaroli, 1987; Dudley & Swank, 1990; Hall, Domhoff, Blick, & Weesner, 1982; Tonay, 1990/1991). They therefore provide one basis for cross-cultural comparisons and for finding individual differences in dream content. All of the dream reports used in creating the norms, along with the original codings of them by Hall and Van de Castle, can be viewed and printed using DreamBank.net's "Coding Search" utility (Schneider & Domhoff, 1999). In addition, dream reports with a specific coding or set of codings can be viewed and printed at "Search For DreamSAT Codings" at http://dreambank.net/coding_search.cgi.
Even more crucially here, the large size of these normative samples makes it possible to use approximate randomization to draw thousands of pairs of subsamples of varying sizes to determine the minimum sample sizes needed to replicate findings on gender differences established by using the large normative samples. Like non-parametric statistics, this approach bypasses most of the assumptions necessary for the use of parametric statistics. Random sampling and normal distributions are not necessary, and the techniques work equally well with longitudinal studies of individual cases (Franklin et al., 1997).
Approximate randomization, which is called permutation testing by statisticians, provides an exact p value, not an approximation. It is determined by comparing the difference between the two original samples to a distribution of differences obtained by pooling the data from both samples and then creating a thousand or more pairs of random samples. The p value is the percentage of times that the difference between a pair of randomly drawn samples is equal to or greater than the difference between the two original samples. For example, in a comparison we made of the normative male/female percents for men (67/43) and women (48/52), there were no instances in numerous separate trials using 10,000 randomized pairings where the difference between the randomly drawn pairs of samples was equal to or larger than the difference between the two original samples, so the p value is .0000. This p value is extremely small because gendered human beings appear frequently in dreams and the h of .41 is very large for a dream content indicator. In the analyses we are going to report later in this article, we draw numerous separate subsamples of decreasing size from each of the two large normative samples and then compare 10,000 randomized pairings from each of the new subsamples.
There is one further methodological issue that needs to be discussed before turning to the findings. All of the dream reports used in the Hall and Van de Castle (1966) normative sample and in the other studies we draw upon for this article were collected from volunteers who gave them to investigators a day or more after the dream occurred. This raises the possibility that the reports might be different from the dreams as they actually unfolded because they are filtered through waking selfconceptions and cultural scripts. Because dreams cannot be observed by others or reported by dreamers while they are happening, it is only possible to address this problem indirectly through the comparison of dreams collected immediately upon awakening in a sleep laboratory with "home" dreams collected from the same participants on days when they were not sleeping in the laboratory. Despite early indications that there were more aggressive, sexual, and emotional elements in dreams collected at home (Domhoff & Kamiya, 1964; Hall, 1966), several later studies of laboratory and home dreams from the same participants showed that they were more similar than different (Heynick & deJong, 1985; Hunt, Ogilvie, Belicki, Belicki, & Atalick, 1982; Strauch & Meier, 1996; Zepelin, 1972). Furthermore, most of the originally reported differences disappeared when further controls were introduced (Foulkes, 1979; Weisz & Foulkes, 1970) and when new statistical measures were used by Domhoff and Schneider (1999) in reanalyzing Hall (1966) data. The one consistent difference in the reports from the laboratory and home settings seems to be in the category of aggressive elements, which occur more frequently in the home dream reports of young adults in three different studies (Domhoff & Kamiya, 1964; Domhoff & Schneider, 1999; Weisz & Foulkes, 1970). However, this one difference does not seem to us to be enough to cast general doubt on the usefulness of home-collected dream reports as a good avenue into what people dream about.
3. Findings on dream content
3.1. Cross-cultural results
Despite many limitations relating to language barriers, rapport, and cultural stereotypes about dreams, which are summarized and discussed by Domhoff (1996, chap. 6), the dream reports painstakingly collected by cultural anthropologists in small pre-industrial societies in the first seven decades of the twentieth century provide a starting point for studying universal elements and cross-cultural differences in dream content. Most of these collections were brought together by David Schneider (1969, p. 56), who used content categories paralleling several Hall and Van de Castle (1966) categories to study dream reports from 13 traditional peoples, including Alor, Kwakiutl, Navaho, Tinguian, Truk and Yir Yiront. With sample sizes ranging from 56 to several hundred dream reports, he concluded that his study "seems to support the contention that (1) there are certain regularities in the manifest content of groups of dreams regardless of the society and culture of the dreamer, and (2) there are certain differences between groups of dreams that seem to be a function of the culture of the dreamers." His most striking example is that the people in all these societies were more often victims than aggressors in aggressive interactions, but with variations from society to society in the degree to which they were victims.
Carl O'Nell and Nancy O'Nell (1977) collected five dream reports from each of 66 men and 66 women in a Zapotec Indian village in southern Mexico in the 1960s, when the people still lived a traditional lifestyle. They did a study of aggression in dreams using the Hall and Van de Castle (1966) subcategories for various kinds of aggression, which include nonphysical aggressions (hostile thoughts towards another dream character, insults, rejections, and verbal threats) as well as physical aggressions (stealing or destroying someone's possessions, chasing or being chased, physical attacks, and murder). Like Schneider (1969), O'Nell and O'Nell (1977) found that both men and women were more likely to be victims than aggressors in aggressive interactions. They also found similarities with findings on aggression in American dream reports by Hall and Domhoff (1963a, 1963b), including a higher rate of aggressions per character for men and a higher rate of aggression with male characters for both men and women.
In the 1970s Thomas Gregor (1981, p. 389) collected 276 dreams from 18 men and 109 dreams from 18 women as part of his intensive field work with the Mehinaku, a people in the Amazonian jungle. Based on an analysis of physical aggression, sexuality, and degree of passivity in the dream reports, which included some comparisons with the Hall and Van de Castle (1966) normative findings, he reports findings similar to those of Schneider (1969) and O'Nell and O'Nell (1977) on aggression and suggests that "with additional cross-cultural data it may be possible to show that the dream experience is less variant than other aspects of culture" (Gregor, 1981, p. 389).
In unpublished work carried out in the 1970s and summarized in Domhoff (1996, pp. 115-120), Calvin S. Hall used the Hall and Van de Castle (1966) coding system to make a detailed study of characters and social interactions in the 13 dreams sets from traditional societies provided to him by Schneider (1969). He first of all found that in most of these societies men dreamed more often about other men than they did of women and that women dreamed more equally of men and women, as is the case for males and females from a very young age in the United States (Hall, 1984; Hall & Domhoff, 1963a, 1963b). In addition, there were always more individual characters than group characters and more familiar than unfamiliar characters. The rate of aggressions per character was higher than the rate of friendly interactions per character with one exception, and physical aggressions were usually more frequent than nonphysical aggressions, as expressed by a physical aggressions percent (physical aggressions divided by physical aggressions plus nonphysical aggressions). As in the Schneider (1969) and O'Nell and O'Nell (1977) studies, men and women dreamers were more often victims than aggressors in aggressive interactions. Finally, the dreams with any references to sexuality, whether a sexual thought, a sensual touch, or something more, were usually fewer than 10% in number, which is similar to Hall and Van de Castle (1966) normative findings. Similarly, and more briefly, cross-national studies in Canada (Lortie-Lussier, Cote, & Vachon, 2000; Lortie-Lussier, Schwab, & de Koninck, 1985), the Netherlands (Waterman, Dejong, & Magdelijns, 1988), Switzerland (Strauch & Meier, 1996), Germany (Domhoff, Meyer-Gomes, & Schredl, 2005-2006; Schredl, Petra, Bishop, Golitz, & Buschtons, 2003), India (Prasad, 1982), and Japan (Yamanaka, Morita, & Matsumoto, 1982) show more similarities than differences with the Hall and Van de Castle (1966) norms for the subsets of content indicators used in each study (see Domhoff, 1996, pp. 100-115, for a summary of these studies).
At the same time, there are some differences among these societies. First, animals constitute a greater percentage of the characters in dream reports from people in hunting and gathering societies, a seemingly trivial and obvious finding that is nonetheless useful because it suggests that variations from society to society may reflect differing ways of life. Then, too, there are variations in the occurrence of aggressive acts from society to society, especially in the physical aggressions percent. As shown in Table 1, most small traditional societies have a higher physical aggressions percent than industrialized societies, in part because they are often fighting with or attacking animals, while Americans have a higher physical aggression percent than do people in the few other industrialized societies where this dream element has been analyzed. In summary, these findings suggest both similarities and differences in dreams across societies. Many of the similarities can be summarized by saying that dreams often seem to be enactments of worst-case scenarios, as seen most starkly in the greater degree to which both men and women are victims of aggression in their dreams. This negativity in dreams can be illustrated with findings based on the 1000 dream reports from college men and women in the Hall and Van de Castle (1966) normative sample. Nearly 80% of both men and women's dreams have at least one of several "negative" elements -- aggression, misfortune, failure, or one of four negative emotions (apprehension, anger, sadness, and confusion).
On the other hand, only 53% of men and women's dreams have at least one "positive" element -- a friendly interaction, a good fortune, a success, or a positive emotion (happiness). Generally speaking, then, it can be concluded that dream content is usually more "negative" than "positive" (Domhoff, 2007). At the same time, there are variations in categories such as the percentage of characters that are animals and in the rate of aggressive interactions per character. The variations suggest that dreams include cultural scripts as well as universal elements (see Domhoff, 1996, chap. 6, for more detailed examples of this point).
3.2. Gender similarities and differences
The Hall and Van de Castle (1966) normative study revealed a pattern of gender similarities and differences that will be briefly overviewed here, and then supplemented by a listing of the six largest differences in the section in which new findings on minimum necessary sample sizes are presented. Aside from two methodologically flawed studies that have been critiqued in detail by Domhoff (1996, pp. 79-82, 1999, pp. 133-134), subsequent studies have replicated the patterns found by Hall and Van de Castle (1966), as we also noted in the Introduction to this article (Domhoff, 1996, pp. 68-73; Dudley & Fungaroli, 1987; Dudley & Swank, 1990; Hall et al., 1982; Tonay, 1990/1991). However, there is evidence that one of the differences, the large difference in the percentage of men appearing in men and women's dreams, may have disappeared among college students in Germany; this finding would be of great theoretical interest if it can be replicated and linked to increased gender equality or some other cultural change in that country (Domhoff, Meyer-Gomes, & Schredl, 2005-2006; Schredl et al., 2003).
The dreams of men and women in the United States are similar in several ways, such as the same percentage of dreams with at least one aggression and friendliness, and they have the same high negative emotions percent (80% of all the emotions in men and women's dreams are either anger, apprehension, sadness, or confusion). They also show several gender differences that seem to parallel gender differences in waking life, which is evidence for the meaningful relationship of at least some dream content to waking consciousness. For instance, there is a higher percentage of physical aggressions in men's dreams and a higher percentage of rejections and exclusions in women's dreams, which parallels the waking finding that boys engage in more physical aggression than girls and that girls are more likely to engage in "social aggression" -- exclusion, rejection, and criticism (Underwood, 2003). Differences in the activities and objects categories seem to parallel differences in the general waking concerns of men and women. For example, men's dreams have more physical activities and women are more likely to be engaged in conversations. There are more appearances of tools and cars in men's dreams, more appearances of clothing and household items in women's dreams (Hall & Van de Castle, 1966).
3.3. Individual differences in dream content
A large majority of dream reports, perhaps as many as 75-80%, revolve around common preoccupations with family, friends, lovers and ex-lovers, leisure activities, and interactions with people at school or work, as seen in studies with American (e.g., Foulkes, 1985; Hall, 1951; Snyder, 1970), Swiss (Strauch, 2004; Strauch & Meier, 1996), and German (Domhoff et al., 2005-2006; Schredl et al., 2003) participants. For that reason, most of the individual differences in dream content discovered with the Hall and Van de Castle (1966) coding system are likely to concern the frequency with which certain characters (e.g., mother, husband, girlfriend) and social interactions (e.g., aggression, sexual interactions) appear. Thus, individual differences are not likely to be detected with small samples of dream reports unless they involve large differences on frequently occurring elements.
However, there is strong evidence that individual differences do exist, that they persist over years and decades, and that at least some of them reflect the same interests and concerns the individual dreamers express in waking life (Domhoff, 1996, chaps. 7 and 8; Domhoff, 2003, chaps. 4 and 5, for summaries and references). This point was first demonstrated with very long dream journals, a kind of archival document that has long been valued in psychological studies as an unobtrusive or nonreactive measure (e.g., Allport, 1942; Baldwin, 1942). The results are most convincing when dream journals kept for diverse reasons -- e.g., out of curiosity, for personal discovery, as a source of plots for stories -- all lead to the same conclusion (Webb, Campbell, Schwartz, Sechrest, & Grove, 1981). Findings from studies of dream journals reveal two crucial points.
First, the frequency with which a dream element occurs reveals the intensity of the dreamer's concern with it, as demonstrated by comparisons with biographical documents or the dreamer's corroboration of inferences drawn by the dream investigator based on blind analyses of the dream reports. Second, this continuity between dream elements and waking concerns is present in waking thought, but not always in waking behavior, as seen most directly in studies in which waking aggressive or sexual thoughts are expressed in dramatic fashion in dream scenarios, but never in actions undertaken during waking life (e.g., the murder of a parent or sexual relations with a wide range of women) (Domhoff, 1996, pp. 178-180).
One of the first examples of these points can be drawn from a detailed study of 1368 dreams written down between 1965 and 1968 by a child molester in his 30s for his own personal reasons, during a time when he was confined in a state facility for sexual offenders (Bell & Hall, 1971). A blind analysis of the dream reports by Hall, who knew nothing but the age and gender of the dreamer at the outset, revealed a very low male/female percent when compared to the normative sample for men's dreams, as well as a striking lack of friends (a low friends percent) and a higher than expected percentage of characters under age 18. There was also an extremely low rate of friendly interactions per character. However, it is his sex dreams that are of the most relevance in terms of this article. There are no sexual interactions with male or female children or teenagers in the Hall and Van de Castle (1966) normative sample for men, but half of the child molester's sexual interactions were with female and male children and teenagers. Since the dreamer was close to the male baseline of 12% in terms of the number of dreams with at least one sexual element, the way in which his sexual dreams mirror his waking fantasies and actions would not be detected with five, 10 or even 100 dream reports (see Domhoff, 1996, pp. 166-171, for a summary of the main quantitative findings from this study).
A dream series with over 1000 dream reports given to Hall by an engineer in his early 30s provided the opportunity to demonstrate that sexuality in dream reports is not always accompanied by waking behavior related to the same activities as occurred in the dreams. Over the course of a 3-year period, the dreamer had sexual relations in his dreams with 38 different female characters, most of them women he knew and to whom he felt attracted in waking life. But in waking life he had not had intercourse with any of these women. Instead, the continuity was with his waking sexual fantasies, which were accompanied by masturbation once or twice each day (Domhoff, 1996, pp. 180-181; Hall & Nordby, 1972, pp. 119-126). A detailed study of 3116 dreams written down over a 20-year-period by a middle-aged woman made it possible to demonstrate that her patterns of aggressive and friendly interactions with family and friends were very similar to her feelings about these people in waking life, as corroborated by the dreamer and four of her friends who were each interviewed separately (Domhoff, 2003, chap. 5). Her main waking interests, such as acting in theatrical productions, are the most frequent activities in her dreams. For purposes of this paper, however, her dreams about a man she became infatuated with in her early 50s are of the most relevance because they show a connection with waking thoughts, but not with waking behavior. Her 43 dreams about this man over a 2-year period initially dramatize her sexual fantasies about him: 13 of the first 16 dream reports contain sexual or intimate physical interactions with him. Later dreams reflect her growing realization that he had no interest in her, which she expressed in her dreams by portraying him as cruel to her when in fact he did not even know she wanted to have a romantic relationship with him. (Her dreams about this man can be viewed and printed on DreamBank.net (Schneider & Domhoff, 1999) by selecting the Barb Sanders series and then putting his pseudonym, Derek, in the search box).
4. Determining minimal sample sizes
We now turn to the important issue of what sample sizes are needed to replicate the findings we have reported. We begin with a brief review of our earlier studies of necessary sample sizes that used rudimentary methods. Then we turn to the new studies carried out for this article using approximate randomization that led to the same results as the earlier studies.
Our first study of minimum necessary sample sizes was based on numerous subsamples drawn from the 500 dream reports in the male normative sample, the only one we had available to us at the time (Domhoff, 1996, pp. 64-67). Using three different tables of random numbers, we first drew six random samples of 250 dream reports and determined an "average departure" from the findings with the full sample. The results were usually within 1-3% points of the findings for the full sample for all of the Hall and Van de Castle indicators, which suggested that 250 dream reports are adequate to replicate our norms. When we drew 12 samples of 125 dream reports, the average departure was within 3-10% points of the findings for the full sample with frequently occurring elements, but differed by 14-22% points with less frequent elements, which suggests that 125 dream reports may be a minimal sample size for elements that occur relatively infrequently. At the other extreme, the average departure from the norms was over 10% points for most indicators with 30 random sets of 50 dream reports and 60 random sets of 25 dream reports. Based on these results, Domhoff (1996) concluded that it takes samples of at least 100 dream reports to make comparisons using most Hall and Van de Castle indicators.
These findings were later refined by using the 1000 dream reports in the men and women's normative samples to calculate the mean number of times that various elements appeared in each dream report. This calculation made it possible to determine the number of dream reports needed for statistical significance at the .05 level of confidence for differences of varying magnitudes. Based on the empirical finding that the effect size h ranges from .20 to .40 for most content categories in most dream studies (a difference of roughly 10-20% points, except at the extremes of the distribution), Domhoff (2003, pp. 92-94) concluded that it takes anywhere from 22 to several hundred dreams in each sample to detect known differences at just the .05 level. For example, 100 dream reports are needed in both samples to detect an effect size of .20 on the male/ female percent, but only 16 dream reports are needed in each sample if the effect size is .50 (Domhoff, 2003, Table 3.7). Since the magnitude of the differences between two samples usually cannot be predicted before the study is carried out, the necessity of analyzing large samples of dream reports becomes apparent.
We now extend our analysis and empirically test our previous claims by using our more recently developed approximate randomization algorithm to determine the sample sizes that are necessary to detect the six largest gender differences in the Hall and Van de Castle (1966) normative samples and the five largest differences between the Barb Sanders series and the women's normative sample at the .05 level. Recalling that approximate randomization begins by combining two different samples into one sample and then drawing many thousands of pairs of samples from the common pool, we drew numerous subsamples of decreasing size. We created 10,000 randomized pairings in each case to determine how often the differences between the two random samples drawn from a subsample are equal to or greater than the difference between the two original samples. To maximize the possibility that smaller sample sizes could be found useful, we defined the minimum sample size as the point where at least half of 10 subsamples of a given size yielded a p value equal to or lower than .05. As shown in Table 2, the normative samples based on 500 dream reports from men and 500 dream reports from women reveal that men dream far more often about other men (a higher male/female percent), have fewer familiar characters in their dreams (a lower familiarity percent), and have a higher physical aggression percent. Men also have a higher rate of aggressions per character, a lower indoor settings percent (indoor settings divided by indoor settings plus outdoor settings), and a lower familiar settings percent (familiar settings divided by familiar plus unfamiliar settings). As also can be seen in Table 2, the frequency of these elements and the magnitude of their differences varies greatly, which means that it takes larger numbers of dream reports to have the necessary observations to detect differences on infrequently appearing elements that are not large in magnitude.
We first of all found that all six gender differences have a p value of .05 or lower with subsamples of 250 dream reports, and that all but the familiar settings percent have a p value of .05 or lower for subsamples with 125 dream reports. We further determined that it takes samples of 100 dream reports to detect differences on indoor settings percent and physical aggressions percent half the time at a p value of .05 or lower. The differences on familiarity percent and the aggressions per character ratio do not have p values of .05 or lower with sample sizes below 60. On the other hand, differences on the male/female percent can still be detected at the .05 level or lower half the time with samples sizes of 30 because the relevant elements for this indicator appear frequently and the gender difference on male/female percent is large.
We now compare codings for a random sample of 250 dream reports from the Barb Sanders series (which was discussed briefly at the end of the section on individual differences) with the normative sample for women. We started our highly detailed study of Barb Sanders with 250 dream reports because of our earlier finding (Domhoff, 1996) that 250 dream reports from the male norms replicated the findings for 500 dream reports almost exactly. This starting point is supported by the fact that findings using one of our other intensive randomization algorithms with 125 of Barb Sanders' dream reports replicated the findings with 250 dream reports (Domhoff, 2003, p. 113). For this article we use approximate randomization to determine what sample sizes are necessary to detect the five largest statistically significant differences between the Barb Sanders dreams and the women's norms. As shown in Table 3, Sanders' has a very low friends percent, which means her dream reports contain more unknown characters than is usually the case. She is the aggressor in aggressive interactions (aggressor percent) more often than women in the normative sample, and she has higher rates of aggressive and friendly interactions per character. (The finding on her high rate of friendly interactions per character is not in conflict with her low friends percent because it is possible to have friendly interactions with family members and unknown characters and for friends to appear in dreams without the dreamer having friendly interactions with them.) She also has a far higher percentage of dreams with at least one sexual element than do the women's norms.
When we drew subsamples of decreasing size from the Barb Sanders and female normative samples, and then drew 10,000 approximate randomization pairings for each new combined subsample, we found that all five differences were detected at the .05 level of significance or lower with 125 dream reports per sample. However, the differences on aggressor percent and aggressions per character were not detectable at the .05 level when 100 reports per sample were compared. The difference on friendly interactions per character could not be detected when there were less than 75 dream reports per sample. On the other hand, the difference on the percentage of dreams with at least one sexuality could be detected with a p value of .05 or lower with 25 dream reports in each sample and the difference on friends percent could be detected with a p value of .05 or lower with 15 dream reports per sample because the h difference in both cases is large. As in our comparison of the two normative samples, it takes 100-125 dream reports to detect the full range of differences found with larger sample sizes, which is what we expected based on statistical grounds. (Readers who want to repeat the analyses based on the norms and the Barb Sanders series, or extend them to two other dream series, can obtain a url and password from Adam Schneider to make use of our randomization programs, but we may have to limit the number of randomizations at times so that we can be sure that our shared server can sustain the load.)
5. Discussion and conclusion
The findings on dream content reported by a wide range of investigators using the Hall and Van de Castle (1966) coding system show that there are cultural, gender, and individual differences as well as more generic or universal dream elements discovered through comparisons of dream reports from a wide range of cultures. Within this context, it does not seem useful to state that dreams are more generic than previous investigators realized, or that individual differences are relatively minor, as Hobson and Kahn (2007) do, because it is likely that universal, cultural, gender, and individual factors are always intertwined in complex ways for each dreamer. In addition, we want to stress that our findings on necessary sample sizes are crucial if the systematic study of dream content and its relationship to waking thought is to advance. Our findings on necessary minimum sample sizes may even imply that many earlier studies using small sample sizes rejected hypotheses that should not have been rejected. Thus, large sample sizes are needed to determine the degree to which further psychological and cultural meaning can be extracted from dream reports.
Parenthetically, we also think our findings show that aggression may be a very useful indicator in future studies of cultural, gender, or individual changes in dream content, as well as in studies of the effects of medications and life stressors on dreams. This is because aggression, as indexed from different angles by several content indicators, is the element in dreams that differs the most by culture (Domhoff, 1996, chap. 6), gender (Hall & Van de Castle, 1966), age (Avila-White, Schneider, & Domhoff, 1999; Foulkes, 1982), sleep state (Faucher, Nielsen, Bessette, Raymond, & Germain, 1999; McNamara, McLaren, & Durso, 2007; McNamara, McLaren, Smith, Brown, & Stickgold, 2005), and method of dream collection (home vs. laboratory) (Domhoff & Schneider, 1999; Foulkes, 1979; Weisz & Foulkes, 1970). In addition, in a pilot study of the effects of sertraline (Zoloft) on the dream content of a young woman with generalized anxiety disorder and panic attacks, it was found that various content indicators relating to aggression moved closer to the normative findings for women (Kirschner, 1999). Although we think our findings relating to sample size are very robust and useful, in closing we want to express our agreement with Cohen (1990, 1994): there is no substitute for replication studies because all statistical analyses have weaknesses that are often overlooked. Thus, the fact that most of the empirical findings stressed in this paper have been replicated several times is an additional reason why we think that there are cultural, gender, and individual differences in dreams that are a useful starting point for those who want to understand dreaming or try to determine what the relationship is between dreaming and various forms of waking thought.
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