Showing posts with label Poisson distributions. Show all posts
Showing posts with label Poisson distributions. Show all posts

Cognitive bias in the McGrew and McFall experiment

Review of “A scientific inquiry into the validity of astrology” [Download]

This article has been peer reviewed and published by ISAR International Astrologer, 41, No. 1, pp. 31-37. Copyright © 2014 by Kenneth McRitchie. [Download PDF]

Abstract. The McGrew and McFall experiment attempted to resolve a weakness that the authors identified in Shawn Carlson’s 1985 double-blind astrological chart matching and self-selection experiment. Both the astrologers and the test subjects in Carlson’s experiment might have failed to make correct selections because of the same non-astrological problem. The authors performed a replication yet they introduced their own problems and failed to acknowledge how cognitive biases influenced their results. One of these biases was the “birthday paradox” that the authors implemented in reverse as a counter-intuitive illusion based on a Poisson distribution. This illusion acted to raise astrologers’ confidence in their abilities. Another was the known tendency for people to have overly-positive illusions about themselves that the authors implemented by using a non-standard, open-ended questionnaire. The authors also neglected to test the self-selection ability of their experimental test subjects, thereby ignoring their own criteria of validity and the justification for their experiment.

The double-blind experiment, “A scientific inquiry into the validity of astrology” by psychology professors John N. McGrew and Richard M. McFall (1990), herein referred to as “the authors,” has long stood as one of the definitive tests against astrology. The Dutch researcher Rob Nanninga (1996) gave the experiment additional weight by his successful replication. Australian statistician Geoffrey Dean and Canadian psychologist Ivan Kelly described the experiment and its replication in their influential study “Is Astrology Relevant to Consciousness and Psi” (2003). For them, the McGrew and McFall experiment was convincing evidence that they used to support their arguments against astrology.

The McGrew and McFall experiment was intended to cover what its authors regarded to be a “methodological inadequacy” in Shawn Carlson’s (1985) famous double-blind test of astrology published in Nature. Carlson had tested whether reputable astrologers (N=29) could accurately identify the California Psychology Inventory (CPI) profiles of test subjects (N=100+ mostly University of California at Berkley students). For each subject’s natal chart, the astrologers were given the real CPI profile and two others randomly chosen from the other subjects. The astrologers were asked to rate the individual sections of the three CPIs compared to the natal chart and then to rank their first, second and third choice CPI. By using the same rating and ranking procedure, Carlson tested whether each test subject could identify their own natal chart profile, written by the astrologers, which they had to choose from two others. Also by the same procedure Carlson asked the test subjects to identify their own CPI profiles from two others. (1)

In his analysis, Carlson found that the astrologers did not perform their tasks any better than chance expectancy. For the test subjects’ tasks, Carlson became suspicious of the rating task and discarded the data. The astrologers never learned how well they performed on the individual sections of their written profiles. Although the results for the test subjects’ ranking task (first, second, and third choice) was unusual, Carlson accepted that data. That task had a control group whose members were not given their real astrological profiles, yet the control group successfully chose the pre-selected profiles at a significantly low probability against chance (p<.01, where significance is p<.05), whereas the actual test subjects chose their profiles at chance expectancy. Carlson attributed the surprising result for the control group to a “statistical fluctuation.” Carlson also found that the test subjects could not identify their own CPI profiles any better than would be expected by chance.

Despite these negative results for both the astrologers and the test subjects, the discarded data, and the statistical anomaly, Carlson concluded, “We are now in a position to argue a surprisingly strong case against natal astrology as practiced by reputable astrologers” (Carlson, 425).

The Carlson experiment has been controversial and its strengths and weaknesses have been discussed in various papers (Currey, 2011; McRitchie, 2011; Ertel, 2009; Vidmar, 2008; McGrew & McFall, 1990). For their part, McGrew and McFall argued that because Carlson’s test subjects had failed to identify their own CPI profiles, the astrologers might have failed to match natal charts to CPIs for the same non-astrological problem. Both the astrologers and the test subjects might have had difficulty in understanding the terminology and the graphical scales that the CPI used to describe personality and traits. The evidence required to validate the Carlson experiment, the authors argued, was inconclusive (M&M, 76).

More recently than McGrew and McFall’s 1990 paper, German psychologist Suitbert Ertel (2009) published a critical review of Carlson’s experiment in which he raised the serious issue that Carlson did not actually test his hypothesis but had incorrectly calculated his analysis. Ertel tested the stated hypothesis using Carlson’s data and, in a remarkable turnabout, the evidence showed that the astrologers had successfully matched the CPI profiles to natal charts in their two tasks at a statistically significant probability (p=.054 marginal, and p=.037). To this date, Ertel’s reassessment and the discovered evidence have remained unchallenged. As an intriguing example of scientific reversal, the Carlson experiment has since become one of the leading scientific studies in support of astrology.

Avoiding some biases but not others

The changed fortunes of the Carlson experiment occurred years after McGrew and McFall conducted their experiment and the authors could not know what would happen. McGrew and McFall were concerned with a specific weakness in the Carlson experiment. They designed their own independent research that stands as a separate inquiry into whether astrology is scientifically valid. The transformation of Carlson’s evidence did not directly affect the McGrew and McFall research and this is why their experiment deserves critical review.

To study the weakness they identified, McGrew and McFall, like Carlson, recruited a group of astrologers (N=6)  and a group of test subjects (N=23). However, unlike Carlson, they tested the identification abilities of the astrologers only. Although the authors could have done so, they did not test whether their test subjects could identify their own natal chart profiles that the astrologers could have written. Carlson had understood that such a test would be close to what astrologers actually do in practice and this would ensure the validity of his experiment. It is therefore disappointing that McGrew and McFall did not replicate this part of Carlson’s experiment. Even more so because Carlson had rejected this part of his data, other than a result that contained a large anomaly. Because the authors’ experiment did not test a method that was close to what astrologers do in practice and they did not try to resolve the anomaly, this represented a bias against astrology. McGrew and McFall gave no reasons for not testing their own test subjects.

McGrew and McFall developed their experimental protocol with the participation and approval of the six participating astrologers, all members of the Indiana Federation of Astrologers. Each astrologer would be asked to match the birth charts of the 23 test subjects to 23 packages of information, which included face photographs, for the subjects. To eliminate age clues, all 23 subjects were aged 30 or 31. This narrow age range meant that there was some similarity in the subjects’ astrological charts, which would make them difficult to differentiate. The information package for each subject was extensive, including answers to 61 personal, open-ended questions that the authors had asked the astrologers to create. Besides the photographs and the 61 questions, the package included important life events and the results of the two standardized psychological tests. The authors called their resultant information package the Personal Characteristics and Life History Summary (PCLHS).

The 61 questions in the PCLHS asked about such personal lifestyle characteristics that astrologers may be concerned with, including “hobbies, interests, religious beliefs, physical characteristics, personal talents and achievements, family background, dates of parent or sibling deaths, dates of moves across the country, health problems, attitudes toward authority, sex and commitment, pet peeves, favorite colors, punctuality, dependability, and variations in the personal energy cycle” (M&M, 77).

In the McGrew and McFall experiment or any double-blind test of astrology, care must be taken to ensure that preconceptions regarding astrology do not bias the results. This precaution applies to the experimenters themselves as well as to the test subjects. However, unlike Carlson, who isolated his own influence and carefully screened out subjects who had strong opinions about astrology, McGrew and McFall did not follow a similar test protocol. They did not try to avoid their own sampling bias when they selected a sample of test subjects from the respondents to their newspaper advertisement.

Instead of screening their test subjects for bias, McGrew and McFall relied on a cover story, but this method was not robust and provided leading clues. The authors told their test subjects that the research was about the possible effects of hormone levels associated with the diurnal cycle during birth and the subsequent development of children (M&M, 79). Each test subject had to provide certified documentation of the precise date, time, and place of their birth. The 61 questions in the PCLHS asked the subjects to describe very personal information and life events of the sort that would have been familiar from popular astrology columns. Referring to these questions, the authors state, “Neither the CPI nor any other standard psychological instrument contains this type of information” (M&M, 77). When asked after the test, two of the 23 subjects said they had guessed that the experiment was about astrology (M&M, 79). Evidently, the experiment’s cover story did not provide a reliable screen for potential biases.

A statistical illusion

In addition to the above weaknesses, an even more serious problem was that the design of the experiment included a statistical peculiarity that can bias an experiment, whether the content is astrology or anything else. In the Carlson experiment and its forerunners, participants tried to match each natal chart against a set of only two (Clark, 1961) or three (Marbell, 1981; Carlson, 1985) personality descriptions. The chance expectancy for each choice in these tests was always the same and did not diminish. The matching protocol that McGrew and McFall used in their experiment employed a known cognitive bias, a mathematical illusion.

By selecting specifically 23 test subjects, the authors seem to have been aware of the counter-intuitive effect known as the “birthday problem” or “birthday paradox” (Ma, 2010). Due to a cognitive bias, we do not expect that out of 365 days in a year there is at least a 50% chance of finding matching birthdays in any group of only 23 people. However, if we go in the opposite direction, it seems intuitively easy to confidently match at least 50% from one group of 23 to another group of 23 where we know that all members in the two groups have matches. The actual probability of making half of the matches is not 50% but nearly zero. The authors reinforced this illusion of overconfidence by stating that there were only “23 possibilities” in their experiment (M&M, 82).

The reason for the illusion is that matching problems, where each attempt removes a member from each group, fall into a Poisson distribution. Counter-intuitively, the chance of finding the matches converges quickly to very small, very similar probabilities regardless of the number of pairs to be matched, whether it is 10, 23, or 200. The probability of making 1 match is approximately .37, of 2 matches is .18, of 3 matches is .06, of 4 matches is .015, and of 10 matches is .0000001 (Ma, 2010). There is a high sensitivity to error that quickly escalates with each attempt. The probability of matching all 23 pairs is vanishingly small. For the results to reach the level of statistical significance, assuming significance at p<.05, the astrologers needed to match an average of slightly more than three charts. The authors did not suggest that they knew their method created an illusion of overconfidence and they did not warn the astrologers. They gave no reasons for changing the test design that Carlson and others had used, where this illusion was not possible.

Idiosyncratic strategies

Each astrologer worked alone to match each of the 23 charts with the corresponding 23 PCLHSs. The authors did not publish any tables or graphs of their test data and it is not possible to scrutinize the mean values of correct matches. The authors reported that correct matches ranged from zero to three with a median value of one match and none of the astrologers performed better than chance (M&M, 80). The astrologers had rated their confidence at a mean value of 73.5%, which implied making at least six correct matches. The correlation between their accurate matches and their confidence was non-significant (Pearson correlation r=.03). The authors found that the results were inconsistent among the astrologers in both their correct and incorrect matches, with a mean value of only 1.4 agreements for the 23 test cases, which was not significant (M&M, 81). Importantly, as the authors pointed out, the astrologers had adopted idiosyncratic strategies, as evidenced by the hodgepodge of questions they provided for the PCLHS and their lack of agreement in making matches (M&M, 81).

This observation of idiosyncratic strategies is crucial to understanding the results. One must ask why the astrologers made the unusual departure from their normal practice. Astrology texts contain descriptions of personality and potential development for the different natal chart configurations. These are fairly standard in agreement and astrologers normally apply these descriptions in their chart interpretations. However, McGrew and McFall did not ask the astrologers to interpret any natal charts but only to match them. If the astrologers did not interpret charts, then whose personality interpretation skills were being tested?

It is normal for astrologers to simply tell their clients what their personality, character development, achievements, and other potentials can be, based on what the astrological literature says about natal charts. These areas of personal potential may or may not have been acted upon, and it is up to the client to recognize their patterns of behavior and lifestyle through the consultative process. It is not normal for astrologers to ask clients to describe their own potentials. It is not normal for astrologers to use a questionnaire to ask clients about their potentials. Applied astrology does not assume that clients know their potentials. The McGrew and McFall experiment went against normal astrology and this represented a bias against the astrologers.

The authors’ experimental design reversed the astrologer and client roles. It placed the interpretive discipline on the wrong party. The test subjects had to describe their own potentials (normally done by the astrologer) by answering an ad hoc questionnaire that McGrew and McFall required the astrologers to create. The astrologers then had to judge the accuracy and usefulness of the descriptions they received (normally done by the client).

Astrology is concerned with providing descriptions of one’s personal potentials and how to make the best choices at different stages in life. This is not the same sort of information that is generated by psychological tests, which typically only measure the dimensions of personality traits. The astrologers in the McGrew and McFall experiment might have had the best intentions but they were given an enormous task. In their attempt to create a questionnaire that would cover the entire spectrum of human potential, the astrologers tended to adopt idiosyncratic strategies and they resorted to open-ended questions, perhaps hoping that the test subjects could provide enough insight into themselves through their own self-descriptions and narratives.

The problem with this approach is that it introduced an additional cognitive bias that astrological chart readings normally prevent. Psychological studies have shown that people tend to hold unrealistically positive illusions about themselves (Taylor and Brown, 1988). For example, tests have consistently shown that almost 80% of drivers perceive themselves as being in the top 50% in terms of driving skills (McCormick, Walkey and Green, 1986). Of course this is not mathematically possible. Positive illusions of self image in virtually all areas of life are not what astrologers would want to hear, but by asking non-standard open-ended questions about personal potential and interests, these were very likely the types of responses the astrologers got. The authors’ research methodology implemented a cognitive bias that worked against the astrologers.


Because the astrologers accepted McGrew and McFall’s suggestion of creating questions for an ad hoc questionnaire, they accepted a flawed methodology and by their participation they committed themselves to the authors’ test design. McGrew and McFall did not suggest that they knew their questionnaire was open to the bias of positive self-illusion, and they did not warn the astrologers. This bias and the Poisson mathematical effect were cognitive biases or non-intuitive illusions that the authors introduced. These biases did not exist in the designs of prior double-blind astrological experiments, including the Carlson experiment that the authors were replicating.

Unlike the idiosyncratic, open-ended questionnaire created for the McGrew and McFall experiment, the Carlson experiment had used only the standardized CPI questionnaire. Ertel’s reassessment of Carlson’s experiment showed that the astrologers were able to use the CPI profiles to identify natal charts at a statistically significant probability (Ertel, 2009). Although astrologers are not in the habit of using standard psychological questionnaires, the positive results of the Carlson experiment suggest that McGrew and McFall’s astrologers might have fared better if they had restricted their evaluations to the information from the two psychological tests included in the PCLHS and ignored their own questionnaire. Standardized multiple-choice questionnaires force respondents to make specific choices and thereby reduce illusions of self image. Judging by Ertel’s reassessment of Carlson’s test, it is conceivable that targeted testing programs might show correlations between some astrological chart patterns and profiles from standardized personality questionnaires.

Although the astrologers used the information from the two psychological questionnaires to help identify charts, McGrew and McFall did not ask their test subjects to identify their own psychological profiles, as had been done in prior double-blind experiments. This missing psychological validation protocol presents a serious problem for the authors because it is uncertain how much the astrologers relied, or should have relied, on these psychological profiles. This uncertainty raises the same “methodological inadequacy” question that the authors identified in the Carlson experiment. The astrologers might have failed in their task for the same non-astrological reasons as before. Remarkably, by failing to test the test subjects, the authors did not try to resolve the psychological validation problem that they used to justify their experiment! Consequently, by their own reasoning the authors would have to judge their own experiment as equally inconclusive as Carlson’s.

Lessons to be learned

McGrew and McFall conclude their article with a sweeping rationalization. “Because each individual is unique, in practice an astrologer must use the birth information to ‘select’ the one correct interpretation that uniquely matches that individual from nearly countless possibilities, not just from 23 possibilities. Thus, our task can be seen as a simplification of the task that astrologers routinely undertake as a part of their daily practice” (M&M, 81-82).

This claim reverses the complexity of the astrologers’ normal practice compared to their tasks in this experiment. The claim that astrologers in practice must “select” a unique hit from countless possibilities of combined chart features is a misrepresentation. Astrologers read natal charts in much the same way as one would read any other type of map that has clear reference points, desired destinations, and indicators of opportunities and hazards. As anyone can understand, there is more than one way to read a map and reach a goal. Matching 23 pairs was not a simplified task and McGrew and McFall made a misleading claim. There were only 23 possibilities provided each match was performed correctly. The number of possible mismatches was staggering and cognitively incredible.

A replication the McGrew and McFall experiment was performed in 1996. Dutch researcher Rob Nanninga modeled his “Astrotest” double-blind experiment directly on the McGrew and McFall experiment and it contained all the same problems. Nanninga challenged 50 Dutch astrologers to correctly match seven natal charts to seven sets of personal information. In similar fashion to the McGrew and McFall experiment, Nanninga developed his questionnaire of non-standardized open-ended questions from ideas gathered from the participating astrologers. The questionnaire covered personal interests and background such as education, vocation, hobbies, interests, main goals, personality, relationships, health, religion, and so on, plus dates of important life events. To these, Nanninga added 24 multiple-choice questions taken from a standard personality test (Nanninga, 1996/97). Needless to say, the astrologers did not succeed in matching the charts any better than in the McGrew and McFall experiment.

Astrologers, students, researchers, and critical thinkers can learn from the McGrew and McFall experiment. The authors appeared to follow a strict scientific methodology by presenting an impressive analysis of their data. Yet, the authors failed to implement basic scientific protocols against biases, which they introduced through their test subject selection process, a Poisson matching process, and an ad hoc questionnaire of open-ended questions. The authors failed to evaluate the validity of their psychological test methodology, the very same problem that they had identified as the “methodological inadequacy” in the Carlson experiment that they used to justify their research. For these reasons the McGrew and McFall experiment can be regarded as inconclusive and might even qualify as a notable example of cognitive bias in a scientific experiment.

In retrospect, it is enlightening to read the authors’ account of how they worked their way through a “protracted negotiation period” to gradually gain entry and eventually win the trust of the initially skeptical astrologers. “The astrologers, understandably, were wary of becoming involved with research that might be biased against them or that would provide no opportunity for success” (M&M, 77). At least the authors were understanding towards the astrologers.


I am grateful to David Cochrane and Mark Urban-Lurain for their help on the birthday problem and Poisson distributions. I wish to thank International Astrologer for critical peer review, which provided valuable clarifications and suggestions.

Drafts of this article were sent to Professor Ivan Kelly and to Professor Christopher French for comment, but there were no replies.


1. The “profile self-selection” experiment authored by Neil Marbell in 1981, a forerunner leading to the Carlson experiment, attempted to methodically standardize the astrological interpretations presented to the test subjects in a way that the Carlson experiment did not do.
“The personality profiles were composed by individual astrologers from birth data alone, using all of the basic Ptolemaic factors of chart interpretation. Each profile was then revised by a committee of five astrologers, also blind to the subjects. This revision was necessary to review the interpretations and to make the profiles uniform in style, content, and overall presentation.” (Marbell, 1981, p. 4). 
Marbell claimed his experiment to be definitive in its successful outcomes, with high percentages of the subjects selecting their own chart interpretations from three presented. Despite the high percentages, the statistical probabilities of two of the tests were not significant (assuming significance at p<.05) due at least in part to the very small numbers of test subjects (N=5 or 6). Test 1 (using rigorous profiles in a laboratory setting): N=5, with 100% correct responses, and p<.000001. Test 2 (using less detailed profiles, mailed to subjects’ homes): N=6, with 66-2/3% correct responses and p=.1. Test 3 (biorhythm cover story, using both rigorous and less detailed profile items, conducted in subjects’ workplaces): N=5, with 75% correct responses, and p=.111. The Marbell experiment was notable for its cross-disciplinary participation, involving the design and review assistance of leading astrologers, notable academics, prominent skeptics, and even U.S. congressional representatives.

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© 2014 Kenneth McRitchie