Assessing Autocorrelation in Studies Using the Hall and Van de Castle Coding System to Study Individual Dream Series

G. William Domhoff & Adam Schneider

University of California, Santa Cruz

NOTE: If you use this paper in research, please use the following citation, as this on-line version is simply a reprint of the original article:
Domhoff, G. W., & Schneider, A. (2015). Assessing autocorrelation in studies using the Hall and Van de Castle coding system to study individual dream series. Dreaming, 25, 70-79.


This article reports statistical findings concerning the presence of autocorrelation in studies using the Hall and Van de Castle (1966) coding system to quantify various aspects of dream content in samples containing multiple dream reports from 1 person. It employs the Wald and Wolfowitz (1940) runs test, which tests for randomness in time series that are based on the categorical level of measurement, to search for autocorrelation in 10 subsets of dream reports from 4 different dream series — a total of 125 runs tests in all. The results provide no indication of autocorrelation. These findings are discussed in the context of relevant empirical studies in laboratory and nonlaboratory settings, which suggest that any individual dream is likely a random occurrence drawn from the dreamer's large storehouse of cognitive abilities and semantic memories. Possible practical applications of these findings for studying dream series from atypical individuals are suggested.

Autocorrelation in time series data (i.e., the lack of independence among a series of responses from a single individual) is an issue in several different areas of psychology because most statistical tests are based on the assumption that each response is an independent data point. In psychological studies, autocorrelation is thought to be increasingly likely as the time between responses decreases because it becomes more plausible that the prior responses — and/or some underlying factor(s) — are influencing subsequent responses.

The possibility of autocorrelation in studies of dream content arises because such studies sometimes rely on samples that include two or more dream reports from one person. This is especially the case with studies using dozens or hundreds of dream reports from a single individual, most of which have employed the Hall and Van de Castle (1966) coding system. This coding system is a form of content analysis, a methodology for turning narratives into numbers through (a) creating well-defined categories, (b) determining frequency counts for the various categories, (c) carrying out appropriate statistical tests on the findings, and (d) making comparisons with norms (e.g., Cartwright, 1953; Hall, 1969; Krippendorff, 2004; Smith, 2000). The Hall/Van de Castle system includes 10 general categories, rests on the categorical (also called "binary" and "nominal") level of measurement, and uses percentages and ratios to correct for differences in the length of dream reports (Domhoff, 1996, Chapters 1 and 2; Hall, 1969; Van de Castle, 1969). This article examines the issue of autocorrelation in dream series by means of the Wald and Wolfowitz (1940) runs test, a statistical technique designed to test for randomness in categorical time-series data of the kind that is generated by the Hall and Van de Castle (hereafter HVdC) coding system. As a test of randomness, it can detect any form of dependencies in a categorical binary dataset, including cyclical patterns. The results from the Wald-Walkowitz tests lead to the hypothesis that any given dream is a random event drawn from the dreamer's vast cognitive Rolodex — that is, his or her cognitive storehouse of conceptions, semantic memories, personal concerns, and interests; it is a storehouse that creates dreams that share some content in common with human beings cross-culturally as well as having many unique personal concerns (Domhoff, 1996, Chapters 6-8).

The issue of autocorrelation in individual dream series

Personal dream journals that contain hundreds or thousands of dream reports are a form of unobtrusive, nonreactive archival data when they later become available to researchers by happenstance (Allport, 1942; Baldwin, 1942; Webb, Campbell, Schwartz, Sechrest, & Grove, 1981). At least 22 dream journals containing from several dozen to a few thousand dream reports have been analyzed in varying detail and discussed in articles or books using the HVdC content indicators. These studies resulted in the empirical generalization that there is consistency in dream content over time, as well as continuity between the conceptions and concerns expressed in dreaming and waking thought in relation to family members, friends, avocations, and leisure-time interests (Domhoff, 1996, Chapter 7 and 8 for summaries; Domhoff, 2003, Chapter 5, for the most detailed study of the longest dream series analyzed to date). However, these studies were carried out without the issue of autocorrelation in mind. Over and beyond statistical concerns, autocorrelation is an issue that has potential theoretical implications because its presence might mean that there are one or more cyclical patterns in the dream series that could be of psychological interest.

Runs testing of individual dream series

Wald and Wolfowitz's (1940) runs test can detect the presence of any form of dependency within a dataset, including monthly or seasonal cyclical patterns. It is the best-suited test for categorical data because the well-known Durbin-Watson test assumes at least an interval level of measurement. The Wald-Wolfowitz test checks for randomness by determining whether or not there is any pattern in the runs that appear, with a run defined as one or more similar observations followed by a dissimilar observation. For example, the sequence 1 0 1 0 contains four runs, as does 111 00 1111 0. The runs test's ability to detect randomness is greater with longer datasets of the kind used in this study. In addition, the p value for the runs test can be supplemented with a one-period lagged phi coefficient (a measure of correlation between two categorical variables) to provide a descriptive measure of the strength of the first-order autocorrelation. The one-period lagged phi coefficient is computed from a 2 x 2 contingency table with the binary responses for period t as rows and the binary responses for period t = 1 as columns. The lower the first-order autocorrelation, the more likely it is that the Wald-Wolfowitz results are solid ones.

The application of the runs test begins by counting the observed number of runs and comparing them with the expected number of runs — the latter via a formula that takes into account the number of runs and the overall frequency of occurrence for each type of observation. Using a formula based on the difference between observed and expected proportions, a Z score and p value are calculated. The utility used to perform the runs tests for this article was created by the authors and is available to other researchers on request via a Web page on dreamresearch .net. It takes plain text as input, with observations represented by single characters and separated by white space or commas. The output includes the observed and expected number of runs, a Z score, and a p value.

For purposes of this article, the ideal dataset for a runs test would be a lengthy dream series that spans a relatively short time, because autocorrelation would be most likely to occur in consecutive dream reports. Therefore, our strongest evidence is based on four samples drawn from 2,222 dream reports that were provided by a young man who wrote down every dream he remembered during his first three years of college. On many occasions there were two or more dream reports from the same night. He offered his dream journal to investigators while he was in graduate school, well after he had stopped documenting his dreams. The four samples in this study consisted of the first 100 dreams he wrote down in 1996, the first 100 he wrote down in 1997, the first 100 he wrote down in 1998, and the last 100 dreams he recorded, which occurred between September 16 and December 30 of 1998. All 2,222 dream reports can be found on dreambank.net, under the pseudonym "Kenneth" (Schneider & Domhoff, 1999).

The Kenneth dream reports had been previously coded for aggressions, friendliness, and sexuality, which made it possible to apply the runs test to the presence or absence of five coding elements for all four sets: aggression, physical aggression, nonphysical aggression, friendliness, and sexuality. Of the 20 tests, none had a p value below .384 — except for sexuality in the final set, which had a p value of .017. However, at least one significant difference at the .05 level would be expected by chance among a suite of 20 tests.

The second series consists of 171 usable dream reports (those with 50 or more words) written down between July 2003 and September 2004 by a 15-year-old girl out of an interest in dreams and with no knowledge of any dream theories. Six years later, during her senior year at an academically prestigious private college, she happened on an article on dreams in The New Yorker that led her to offer her dream series to investigators (Bulkeley, 2012, for background information and an analysis of this series using 40 word strings). This dream journal can be found in its entirety on dreambank.net under the pseudonym "Bea." This series is of interest not only for the dreamer's age and gender, but because it had been coded for more categories than the Kenneth series, with 19 separate content elements available for runs testing. None of the tests showed a statistically significant result at the .05 level. The third analysis is based on a dream series that was offered to investigators by a professor who had retired several years earlier from the humanities division at a major university. He first regularly recorded his dreams at age 15, then again in his late 20s, and then again in his early 60s, shortly after his retirement. His entire series of 506 dream reports can be found on dreambank.net under the pseudonym "Phil." Sixteen previously coded content indicators were used; the samples consisted of 86 dream reports from age 15, 86 from age 29, and 86 from age 63. Out of 48 runs tests, three were statistically significant at the .05 level: family characters and misfortunes at age 15, and negative emotions at age 29.

The fourth and final analysis was carried out on 100 dream reports written between 1960 and 1963 and another 100 written between 1977 and 1979 by a mother of four children who was also a lay Jungian analyst and an artist; she volunteered her dream series to dreambank.net (under the pseudonym "Emma") well after she had retired. There were 19 previously coded categories (Van Rompay, 1999, 2000), which made it possible to carry out 38 runs tests. There were two statistically significant results in her 1977-1979 series: characters (p < .05) and aggressions (p < .01). Overall, 125 runs tests were carried out, which resulted in six statistically significant results, five at the .05 level and one at the .01 level. The percentages of statistically significant differences that were found — 4.8% at the .05 level and 0.8% at the .01 level — are close to what would be expected by chance. It is also noteworthy that the three statistically significant differences for the 48 applications of the runs test to the Phil series were for three different content categories, and they occurred in two different subsets; they therefore provide no evidence for autocorrelation in his specific series.

Since a failure to reject the null hypothesis of randomness can be attributable to either a small time series or very weak autocorrelation, one-period lagged phi coefficients were therefore computed for each dream series. The first-order phi coefficients are extremely small, which helps to explain why most of the runs tests were nonsignificant. The numerous nonsignificant results are not attributable to a lack of power, because the power of the runs test depends on the length of the time series, which ranged from n = 86 to n = 171 in this study. The overall nonsignificant results are therefore most likely attributable to extremely weak autocorrelations within each dream series. The results for the Wald-Walkowitz test and the phi coefficient are presented in Table 1.

Table 1. Wald-Wolfowitz Runs
4 sets, 100 per set
5 categories, 20 tests
1 set of 171
5 categories, 20 tests
3 sets, 86 per set
16 categories, 48 tests
2 sets,100 per set
19 categories, 38 tests
Any characters    .913
Unfamiliar characters    .679
Familiar characters    .563
Friends    .363
Family    .712
Animals    .165
Physical aggression.384
Non-phys. aggression.539
Success    .377
Failure    .063
Misfortune    .512
Bodily misfortune    .464
Good fortune    .555
Emotion    .052
Negative emotion    .142
Positive emotion    .550

Note: each cell contains p values (in regular type) and first-order (AR(1)) phi coefficients (below the p values, in italics) for various Hall/Van de Castle content elements in ten long dream sets from four different dream series. Number of sets, number of dreams per set, number of categories analyzed, and number of tests carried out follow the names of each dreamer.

*p < .05    **p < .01


This article finds no indication of autocorrelation in dream series from two men and two women of varying ages using categorical data to analyze the dream reports. This finding is supported by an earlier study that used a regression test appropriate for interval- and ratio-level datasets to test for autocorrelation for word count, number of female characters, and number of male characters in two series of 100 consecutively reported dreams from the same young man. The investigator concluded that "the dream-to-dream correlation is very small, approximating a white noise process," and that "statistical procedures assuming independent observations seem to be appropriate" for at least these three variables (Schredl, 2000, pp. 915-916).

The findings presented in this article provide a good baseline for future studies of dream series from average teenagers and adults. If such future studies show similar results, then the results of this study would be strengthened. In the meantime, if the current results were used as a temporary "normative" baseline for typical teenagers and adults, then they may have practical uses in the study of future dream series. For example, a finding of autocorrelation in one or another content category in a dream series could lead to a search for the reasons for the nonrandomness — cycling in and out of seasonal depression, for example. Perhaps people suffering from PTSD would show a cyclical pattern in the appearance of upsetting or frightening dreams.

These findings make it possible to distinguish between autocorrelation and consistency in the content of an individual's dream reports over time. Although there is evidence for consistency for the main HVdC quantitative indicators for subsets of 100 to 125 dream reports in long dream series (Domhoff, 1996, Chapter 7), this is not the same thing as autocorrelation because there is no pattern to the appearance of these various kinds of content. If, for example, aggression appears in about 25% of every 100 dream reports in a dream series consisting of several hundred dream reports, this is not evidence for autocorrelation because the appearance of aggression in the dream reports is random. In other words, the appearance of aggression is more akin to a coin flip because there is no regular pattern as to when the 25 dream reports out of 100 that contain aggression will appear. It is in this sense that dreaming involves a spin through the person's cognitive Rolodex, as suggested (without using that particular metaphor) by Foulkes (1985, Chapter 1) when he concluded on the basis of the 25 years of laboratory studies up until that point that dreaming was an involuntary but organized mental act that generates credible world analogs, which draw on dissociated elements of memory and knowledge.

A laboratory study that tried to match detailed presleep verbal reports of daily concerns with dream reports from the first REM period of the night may provide a useful empirical context for the idea that dreams appear randomly but have psychological meaning. It found that blind judges could not reliably perform such matches. However, the content of the dream reports often revolved around the same kind of concerns with family, friends, and school that were expressed in the presleep reports, although the routine concerns were less frequent and the longstanding interpersonal concerns were more frequent in the dream reports (Roussy et al., 1996) This finding is consistent with studies showing low levels of episodic memory in dreams (Baylor & Cavallero, 2001; Fosse et al., 2003).

Several earlier laboratory and nonlaboratory studies, when taken together, appear to provide further empirical evidence that dreams happen randomly but have psychological meaning. For example, several early lab studies based on REM period awakenings showed that there is little or no thematic or quantitative relationship between dream reports collected on the same night. In the first of these studies, there was a connection between two or more dream reports on only seven of 38 nights, based on a thematic examination of dream reports from eight participants. The few linkages varied from "single, seemingly trivial details to occasions of similarity in plot" (Dement & Wolpert, 1958, p. 569). A study of 106 REM dream reports from two participants over a total of 32 nights did not find any relationship between a dream's position in the sequence of dream reports for any of 12 dimensions, such as emotionality, hedonic tone, and interpersonal involvement, according to ratings by independent judges. Only one of the 32 sets of nightly dream reports showed any thematic sequence (Trosman, Rechtschaffen, Offenkrantz, & Wolpert, 1960, pp. 604-606). To take a more recent and comprehensive example, in a systematic study of 24 male and female participants in Zurich in the 1990s — in which a search was made for thematic continuities from one REM awakening to another — only six of 36 nights contained at least one repeated theme; in most of the infrequent incidences of a repeated theme, there appeared to be thematic connections only between two or three REM dream reports, not for all of the REM reports throughout the night (Strauch & Meier, 1996, p. 206).

Similar findings resulted from a methodological study concerned with the possible influence on dream content from collecting two or more dream reports on the same night in the sleep lab (Domhoff & Schneider, 1999, for an accessible summary; Hall, 1966, for the detailed results). This study is of further interest because it is one of the few lab studies in which dream reports were collected on several nights of the same week, an intensified collection method made possible by the fact that each of the 12 male participants had the exclusive use of a room in a suburban house (specially equipped for laboratory dream studies) during the month of his participation. The analysis included a HVdC comparison of REM dream reports from single and multiple awakenings on the same night; on multiple-awakening nights, the participants were awakened during every REM period. The study found that only two of 26 comparisons (based on the Wilcoxon matched-pairs, signed-rank tests) were statistically significant at the .05 level, which could be expected by chance: there was a greater proportion of individual males among all dream characters in the multiple-dreams sample and a greater proportion of sexual interactions in the single-dreams sample (Hall, 1966, p. 21). The investigator notes that the number of sexual interactions in both samples was very small, and he concludes, "single dreams and multiple dreams are comparable samples of dream life" (Hall, 1966, p. 21). Nor were there any differences between the single-sample and multiple-sample dream reports on several questions answered by each dreamer after he finished recounting each dream report. These questions concerned, among several issues, the vividness, bizarreness, and emotional tone of the dream, along with the familiarity of the setting (Hall, 1966, pp. 26-27).

The absence of autocorrelation in the 121 runs analyzed with the Wald- Walkowitz test in this article also suggests that autocorrelation is not likely to be a confounding factor in analyses of findings from the numerous nonlab studies of dream reports (in which participants are asked to voluntarily keep a dream diary for a week, a month, or a semester). This is because the reports are not often from consecutive nights, and even more rarely are there two or more reports from a single night. In most diary studies, participants typically record from three to five dreams over a 2-week period, although some people report more or fewer. In one large-scale study, the mean number of dreams recalled over a 2-week period was 4.93 for 350 women and 3.63 for 63 men (Schredl, 2010, p. 100, Table 1). Similarly, the Wald-Walkowitz results suggest that autocorrelation is not an issue in the normative samples of men's and women's dream reports that were developed as part of the HVdC coding system; these normative findings are based on five dream reports that were drawn randomly from dream journals containing between 12 and 18 dream reports collected over the period of 16 to 18 weeks (Hall & Van de Castle, 1966, p. 158).


The findings in this study using subsets of consecutive dream reports from the dream series of two men and two women of differing ages strengthens the claim that dream journals are a useful form of archival data for the study of psychological meaning in dream reports. Although experimental designs are preferable when feasible for the study of most psychological issues, the fact is that numerous laboratory studies concluded decades ago that dreaming cannot be triggered by external stimuli, and that it is very difficult to influence dream content with either presleep stimuli, such as fear-arousing or exciting movies, or with concurrent stimuli administered during REM periods, such as the sound of a bell, the names of significant people in their lives that were whispered to the dreamers, or tactile stimulation (Arkin & Antrobus, 1991; Foulkes, 1985; Rechtschaffen, 1978, for summaries). Foulkes (1996, p. 614) concluded:

Probably the most general conclusion to be reached from a wide variety of disparate stimuli employed and analyses undertaken is that dream are relatively autonomous, or "isolated," mental phenomena, in that they are not readily susceptible to either induction or modification by immediate presleep manipulation, at least those within the realm of possibility in ethical human experimentation.

This conclusion is consistent with the concept of stimulus-independent thought, which emerged from the study of mind-wondering, and led to the suggestion that dreaming is a form of mind-wandering (Domhoff, 2011b; Fox, Nijeboer, Solomonova, Domhoff, & Christoff, 2013).

At the same time, there is accumulating evidence, including gender and cross-cultural comparisons, that most dream reports are embodied simulations and enactments of personal conceptions, concerns, and interests (Domhoff, 2010, 2011a). Given the large number of dream reports that are contained in many personal dream journals, subsets of which can be compared statistically after testing for autocorrelation, it may be that intensive studies of such journals can deepen the understanding of psychological meaning in dreams and better identify those aspects that may be meaningless filler. This is especially the case because inferences drawn from blind quantitative analyses of dream reports can be checked against biographical and autobiographical information, as well as against personal responses to those inferences by the dreamers and by people who know the dreamers well (Bulkeley, 2014; Bulkeley & Domhoff, 2010; Domhoff, 2003, Chapter 5).


Our thanks to Douglas G. Bonett, director of the Center for Statistical Analysis in the Social Sciences at the University of California, Santa Cruz, for suggesting the use of the runs test, and for carrying out an additional analysis using the phi coefficient, which showed that the first-order correlations in the dream sets we tested are very low.


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