Report on Astrology-Schizophrenia Study

Introduction

On 22 March 2022, Pumpkin Person posted on my behalf a solicitation for volunteers to complete a survey where they ranked supposed personality descriptions of people born under astrological zodiac signs by their similarity to the imagined personality of someone experiencing Schneider’s first-rank symptoms of schizophrenia. Thank you, PP! The survey is no longer available, but if I gain access to a sufficiently large and properly responding sample of volunteers, I might reopen it or study this hypothesis again with a different method. Note that the volunteers were not informed that these personality descriptions were borrowed from astrology, nor what the survey was intended to study, although I expect that at least some of them figured those out.

I doubt that the alignment of celestial bodies causally influences individual differences in human temperament, but could the stargazers have gotten something right by coincidence? This study was intended to test my hypothesis that astrological knowledge might reflect nascent, semi-conscious knowledge of the fact that a person’s risk of eventually developing schizophrenia varies based on their month of birth. Statistical studies have found that this risk follows an approximately sinusoidal curve with a period of one year. Compared to the baseline of June, relative risk ranges from about 1.1 in February and March to 0.85 in August and September, a difference of about 30% between peak and trough. [1] This is thought to be caused by maternal vitamin D deficiency due to lack of sunlight in the coldest months, and perhaps also by prenatal exposure to certain seasonal infections. [2] [3]

Methodology

My first task was to define my null and alternative hypotheses:

H0: There is no positive relationship between: (1) the similarity of characteristic symptoms of schizophrenia to supposed personality traits of an individual born under a zodiac sign; (2) the risk that someone born under that sign will eventually develop schizophrenia.

H1: There is a positive relationship between (1) and (2).

From there, I mapped out the following research program:

  1. Rank zodiac signs by schizophrenia risk: starting with Pisces, since it most overlaps the highest-risk month of March; and ending with Virgo, which most overlaps the lowest-risk month of September. Note that each zodiac sign partially overlaps two months, so I determined schizophrenia risk for each sign by consulting Figure 1 in [1] for the schizophrenia risk of the month with which that sign shares the most days, e.g., Capricorn spans from December 21 to January 20, so it’s linked to January. This shift should be too small to affect the overall results much. A problem is that I couldn’t always discern the slight differences in Figure 1, the source I was using for this ranking. I decided on the following ordering, from highest to lowest expected risk, and did so before receiving any survey responses so as to prevent researcher bias: Pisces, Aquarius, Capricorn, Taurus, Aries, Sagittarius, Gemini, Scorpio, Cancer, Libra, Leo, Virgo.
  2. Present volunteers with: (1) a description of Schneider’s first-rank symptoms of schizophrenia; (2) descriptions of supposed personality traits of persons born under certain zodiac signs, all from the same source which was not created for the purpose of this study, and without selectively presenting only some of those traits. For this source, I chose [4]. Ask volunteers to rank those personality descriptions from greatest to least resemblance to the schizophrenia symptoms. Personality descriptions are presented in a random order for each participant, to reduce possible bias from order, e.g., less-attentive respondents tending to give lower numbers to options which appear earlier.
  3. Calculate each zodiac sign’s schizophrenia rating as the average rank of schizophrenia resemblance which volunteers assigned to it, from 1 (highest) to 12 (lowest).
  4. Calculate the rank-order correlation between zodiac signs’ schizophrenia risks from step 1 and volunteer-rated schizophrenia similarity ratings of zodiac signs from steps 2 and 3.
  5. Calculate a p-value for the correlation found in step 4. Because the alternative hypothesis H1 seems unlikely, not to mention that any research pertaining to astrology will have to overcome especial skepticism, the significance threshold was set beforehand at (p < 0.01), well below the usual (p < 0.05). Incidentally, I advocate for (p < 0.000001) to become the standard significance threshold in academia, but under the presumption that professional academics are, or should be, more able to recruit a large and high-quality sample than is an independent amateur researcher such as myself, so I did not hold myself to that standard here.

Results

My prior concerns, expressed in the previous sentence, about poor quality and quantity of responses were vindicated. While about 60 people started the survey, only 10 completed it, and of these: 5 responded as instructed; 4 gave faulty responses by leaving one or more ratings blank and/or assigning the same ranking to multiple personality descriptions; and 1 was an obvious troll, whose ‘name’ was a racial slur and who assigned the same ranking to every description. This atrocious audience engagement may reflect that the survey required substantial reading, totaling about 1700 words for the instructions, schizophrenia symptoms, and personality descriptions, as well as laborious judgment to rank every sign. If I repeat this experiment, I will almost certainly do so with a shorter and easier survey.

Because these data were so exiguous and suspect, I calculated the rank-order correlation, as discussed in step 4 under Methodology, for each of several different amalgamations of the responses. First, I calculated it with only the 5 fully correct responses. Then, I calculated it again, including the 4 faulty responses by interpolating missing rankings and reassigning reused rankings with a random number generator. In each case, if there was one or more tie(s) in the month rankings, I calculated the rank-order correlation for each possible tiebreak, e.g., if Capricorn and Aquarius were tied, I would calculate it once with Capricorn above Aquarius and once with Aquarius above Capricorn.

None of these rank-order correlations were remotely significant even at p < 0.05, and a fortiori not significant at p < 0.01. Ah well. You win some, you lose some, and I lost this one; at least, perhaps, until I try again with a better sample.

Intriguingly, Pisces and Aquarius were consistently ranked among the most schizophrenic signs, and Virgo among the least, all of which concord with my hypothesis. However, this is only one of practically infinitely many possible post hoc pseudo-confirmations, each of which could have happened by sheer chance, and thus it cannot be considered strong statistical evidence.

Because this study was a failure, this report’s purpose is more to present the hypothesis than the results I found. I call it a failure because of the deficient data, not because of the null result, as, from a proper scientific perspective, a null result is a success if the null hypothesis is true.

Additional Note

Different sources give slightly different tabulations of schizophrenia risk by birth month, but there is apparent agreement that risk is highest near the beginning of the year when the weather is coldest, and lowest about three-quarters of the way through the year when the weather is warmest. Would this reverse in the Southern Hemisphere, relative to the Northern?

References

[1] Effects of Family History and Place and Season of Birth on the Risk of Schizophrenia
(See Figure 1.)

[2] Seasonality and infectious disease in schizophrenia: the birth hypothesis revisited
(This study found that winter birth month predicted higher schizophrenia risk, but that rates of influenza and measles did not, which by exclusion supports the hypothesis that the causal factor here is vitamin D deficiency.)

[3] Season of Birth – Low Sunlight Exposure/Vitamin D deficiency is associated with higher risk of schizophrenia

[4] Your guide to all 12 zodiac signs: Dates, symbols, compatibility (I mildly edited these descriptions to shorten them and make it less obvious that they were drawn from astrology. This source is one of many which I could have used.)

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The Two-Sigma Advantage Hypothesis

Here I present my hypothesis that an activity will be trivially, insultingly easy if you’re 2 standard deviations above the mean of people who engage in it. This means 2 standard deviations of the primary trait which confers success in that activity. Also, for convenience, I’m using normalized distributions against the general population, rather than real and potentially non-normal distributions or standard deviations of the group itself.

I formulated this in the context of IQ and academic success, but it extends to other traits and fields. For example, military service:

The largest impediment for today’s young people is health problems — specifically, obesity. Twenty-seven percent of young people in that age group aren’t eligible to join the military because of obesity, the report states, with another 37 percent ineligible due to other health problems such as asthma or joint problems.

If 64% of young adults are physically unfit for military service, then the average military-fit young adult is at the 82nd percentile relative to young adults. That will almost certainly be even higher among the general population because young adults are at the time of their life where they have the highest (potential, and often actual) physical fitness. Let’s round up to a clean 85th percentile. Then the average military-fit young adult has an F.Q. (“Fitness Quotient”) of 115. Therefore, we estimate that with an F.Q. of 145 (~99.7th %ile), you’ll be able to pass basic training without feeling particularly strained. Since almost everyone with an F.Q. of 145 or more will be male, we’ll double that and say this is the 99.4th %ile for American males.

Can anyone think of other examples which would lend support for or against this hypothesis?

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THINKfast recovered

After months of searching culminating in about six hours of frustrating VirtualBox setup, I’m finally able to play THINKfast, albeit on a Windows 98 virtual machine.

THINKfast was marketed as “brain-training software.” As far as I know, the evidence that any such software produces gains in intelligence transferred beyond the game itself is minimal. What’s important about THINKfast is that it’s a good measure of general intelligence, even promoted for that purpose by legendary psychometrics researcher Arthur Jensen. You can read about THINKfast’s psychometric properties on pumpkinperson’s blog here.

THINKfast won’t run on Windows 10, even in compatibility mode. Setting up the virtual machine required to play it on a modern system is time-consuming and requires following instructions fastidiously. If you’re nevertheless interested in playing it, contact me for instructions and technical support, but I won’t hold your hand through the entire process.

A possible problem is that scores may vary between systems due to lag in input or output. My VirtualBox setup seems as responsive as a typical personal computer, but even imperceptible delays might warp both norms and individual performances against those norms. Nonetheless, I’ll post my scores once they’ve stabilized. This may take a while as: (1) the games usually show large practice effects over initial runs; (2) eventual plateau scores correlate much more highly with intelligence than initial scores do; and (3) the games get harder, and thus make higher scores feasible, as long as you are improving. I am currently at Alpha-Gold after 5 runs.

THINKfast running in a VirtualBox virtual machine of Windows 98.
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A hypothetical method for estimating IQ rarity on the right tail

The distribution of IQ, like that of many other quantitative traits in nature, appears to approximate a normal distribution around the mean, but deviates from normality beyond roughly plus or minus 2 standard deviations from the mean. For example, a score four or more standard deviations above the mean would occur a rate of about 1 in 30,000 if IQ were normally distributed, but such scores are far more common than that in practice. Furthermore, we can only estimate how many standard deviations above the mean that score truly is, since we have no way to directly measure “absolute” intelligence levels, only relative ones. This poses a serious obstacle to meaningfully estimating the rarity, relative to the general population, of an IQ score far above the average (and also below the average, but that’s not what I’m concerned with here).

This barrier could be overcome by combining two possible psychometric tools:

  1. An IQ test which yields a score at the interval or ratio level of measurement.
  2. A theoretical distribution which closely approximates the actual distribution of IQ in the general population, even at extreme heights.

As far as I know, neither of these things truly exist, but they both have potential substitutes which might be accurate enough to be scientifically meaningful.

Tool 1 manifests as Rasch scoring. This has already been extensively studied and even implemented in freely available psychometric test analysis software, so I won’t discuss it further here.

Tool 2 is a hitherto a subject of arcane speculation, and I’m not aware of any studies into the true distribution of intelligence at the high end. However, by combining statistical theory with knowledge about the biological underpinnings of IQ, it may be possible to determine a distribution which corresponds reasonably well to reality. Cyril Burt, studying this question in 1963, concluded that the IQs of schoolchildren matched well with a Pearson Type VII curve. Because the IQs of adults and children undoubtedly have the same biological underpinnings, like number of neurons, glucose processing efficiency, etc., I suspect that this curve would, if its parameters were correctly adjusted, also closely approximate the true distribution of adult intelligence.

Because finding the correct parameters, even roughly, for such a curve is currently beyond my research capacity, I instead propose using the log-normal distribution, for which a conversion table from the normal distribution can be found at the bottom of this webpage.

Therefore, my proposed approach for estimating the true rarity of an extremely high IQ score:

  1. Design an IQ test with generous ceiling for exceptional scorers and administer it to a sample of people known to have high IQs, possibly along with an “anchoring” sample of people with less than high IQs.
  2. Perform Rasch analysis on the test.
  3. Convert the person’s Rasch score on that test, in estimated standard deviations above the mean of the general population, to a log-normal rarity score.

Example: Person A takes this test and scores 5.33 standard deviations above the mean of the general population in “absolute” intelligence, as estimated by their Rasch score. This corresponds to a “normalized” IQ of 180. According to our normal to log-normal conversion table, this score is as rare as an IQ of 162.6 would be if intelligence were perfectly normally distributed, giving us a final rarity estimate of about 1 in 60,000.

Obviously, this is all preliminary at best. The details certainly need to be ironed out, and even the fundamental ideas may turn out to be flawed. I’m currently thinking of this as the “Bob Semple tank” of right-tail psychometrics: it doesn’t fully work, but I don’t see anyone else coming up with better ideas.

Edit (April 8, 2021): This article was inspired by a letter from Grady Towers to Darryl Miyaguchi.

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Shiny IQ

The probability of someone having an IQ of 155 of higher, assuming a mean of 100 and standard deviation of 15, is 1 in 8,137.

The probability per encounter of a wild Pokémon in a main series Pokémon game from Generations II to V being shiny is, with a few exceptions, 1/8,192.

Hopefully a comparison like that will help readers, especially those in a certain age bracket, to understand how exceptional such high IQs are by statistical necessity, and how skeptical you should be whenever figures like that are casually tossed around. You can easily play through all of Pokémon Emerald, Diamond, etc., without encountering a single shiny Pokémon.

I probably played those games for a total of hundreds if not thousands of hours, but that was before I was a confident Google user, so I didn’t know what shiny Pokémon were. I wonder how many I missed without knowing…

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