Debunked: serial killers are more likely to be born under certain zodiac signs than others [misundertanding of probability and sample size]

[Rory]

A 2021 study of 485 serial killers proposed that certain astrological signs were overrepresented (and others therefore underrepresented) with "key findings" being:

* Four signs — Cancer, Pisces, Sagittarius, and Scorpio (46 each) — account for almost 40 percent of serial killers. Gemini and Taurus combined account for only 11 percent.

* Killers born in the sign of Capricorn accounted for more victims total and on average than those in any other sign. Combined, they killed more than 800 people, or 19 on average; the lowest average was for Virgo killers, with seven victims each.

* The water signs (Cancer, Pisces, and Scorpio) accounted for the highest number of killers and victims in our analysis — 28 percent of killers and 27 percent of victims.

https://www.astrology-zodiac-signs.com/blog/most-common-zodiac-signs-of-serial-killers/

A different 'study' of 487, however, found different results, with Capricorn (55) and Leo (46) topping the charts, and Taurus (22) and Cancer (34) being the most sedate.

Now, while these results - different though they are - might appear "statistically significant" (and therefore lend some much-needed credence to astrology) there's quite a simple explanation: what we're seeing here is an example of Yonezawa's Fallacy. In a nutshell, despite a sample size of almost 500, it's still nowhere near enough to provide anything approaching a usable result.

To demonstrate this I made a simple spreadsheet that simulates 485 occurences of a thing that can be split into 12 equally sized 'pots'.

Here in column A I list the numbers 1 to 485 and in column B I use =randbetween(1,12) to generate a random number between 1 and 12:

Each number stands for a sign in the zodiac and the test is repeated 10 times to give more accuracy (one hundred or one thousand times would be better though):

As we can see, random chance suggests that a normal result using 485 occurences/12 'pots' predicts an expected range of around 18 to 58 - which encompasses the whole range of figures discovered by the studies (in repeating the test I received highs of 64; while 18 was the low).

The results therefore are entirely what is expected due to chance.

The fallacy seems to be built on two things: 1) the idea that 500 is a reasonable sample size (I would say several tens of thousands would be more like it, and even then there would be noticeable variations); and 2) a misunderstanding of how probability works, even among academics and those who understand p-factors, which leads them to expect the "result by chance" to equal occurences divided by 'pots' - eg, 40 to 41 - whereas the actual chance result is a range that varies massively from the mathematical average (in this case, around 50%).

Good news for Capricorns and Cancers.

 

[Rory]

Also related: an older claim that the FBI released a study ranking the connection between likelihood of criminal behavior and zodiac signs. This has already been debunked in several places, such as:

https://www.snopes.com/fact-check/fbi-revealed-the-most-dangerous-zodiac-signs/

 

[Mendel]

Four signs — Cancer, Pisces, Sagittarius, and Scorpio (46 each) — account for almost 40 percent of serial killers. Gemini and Taurus combined account for only 11 percent.

If you pick 4 signs at random, you'd expect an average of 33% of all killers. However, if you pick the 4 highest star signs, which are all above average, you'd necessarily get a bit more: say, 40% instead of 33%, which is actually not even a quarter above the average.

If you pick 2 signs at random, you'd expect an average of 17% of all killers; but if you select the two lowest signs, you'd necessarily get a lot less: say, 11% instead of 17%, which is about a third less.

So all of that is just mathematical mumbo-jumbo based on the observation that if you only look at outliers, you get outlier results; and anyone who actually knows about p-values ought to see right through it.

It's kinda like if you have 30 kids in a class, and make them do sprints, and then proudly present the finding that the 3 slowest kids did a lot worse than the class average, and that the 10 fastest kids did noticeably better than the class average. You'd wonder if Captain Obvious was waiting somewhere in the wings...

 

[Rory]

I don't think it's quite that: if they had a sample size of 5 million serial killers and found that some zodiac signs were 3 times higher than others then it would be correct to highlight that. The probability of results like that occurring by chance would be incredibly small. So definitely a reason to sit up and take notice.

It's really the small sample size that's the key here.

 

[NorCal Dave]

As a Capricorn, I'm a pretty laid-back friend with everyone, though I can be very judgmental in my head. So far, this dichotomy hasn't led to any bloodshed (that anyone knows of) so I'm keeping my fingers crossed that I wont be on the FBI most wanted list any time soon.

 

[Mendel]

It's really the small sample size that's the key here.

Or the small effect size.

The concept that links the two is the "power" of a study, i.e. what sample size is needed to detect a certain effect size, or conversely, what effect size can be reliably detected with the sample size you have. If it had turned out that one sign was 3 times more likely than average to kill with the sample size you've got, that'd probably be significant. But you're not seeing an effect that strong.

And the next question is always, "does the finding replicate", and you pointed out it doesn't.

 

[captancourgette]

Also the distribution of birthdates is not the same throughout the year, more people tend to be born in the summer vs the winter. In the USA
AFAIKS most common = Virgo, Least = Aquarius
I'm Aquarius, but from the southern hemisphere where I assume its one of the more common ones.

 

[Mauro]

Many interesting and insightful points about statistics and probabilities here, really a cool thread. Thanks all.

 

[Rory]

If it had turned out that one sign was 3 times more likely than average to kill with the sample size you've got, that'd probably be significant.

Good point. The simple spreadsheet test shows around +/- 50% of average would be "normal" - so something some distance outside that range could be considered significant. Certainly +200% of average (120 versus an average of 40) would appear "outside the bounds of chance".

There are probably fancier ways to illustrate this simple demonstration - a chi-squared test, for example - but I think the RNG spreadsheet way makes it really clear and easy to understand, and shows that the "intuitive" assumption of an even spread isn't correct.

Also the distribution of birthdates is not the same throughout the year, more people tend to be born in the summer vs the winter.

That's true. This is a chart of number of births per star sign for the US (1994-2014):

Variance from the average is +7/-10%.

For Australia I'm not sure because I only have monthly rather than daily data to hand (from a previous project). But here are average Australian births per day from 1975 to 2015:

Looking at that I think I'd go with Libra as Australia's most common sign and probably Capricorn as the least.

Of course, we mustn't forget that the signs are all made up, that their lengths should vary, and that there should be 13 of them now. Plus that there's almost certainly nothing in astrology anyway. But that's a story for another day.

 

[FatPhil]

A 2021 study of 485 serial killers proposed that certain astrological signs were overrepresented (and others therefore underrepresented) with "key findings" being:

* Four signs — Cancer, Pisces, Sagittarius, and Scorpio (46 each) — account for almost 40 percent of serial killers. Gemini and Taurus combined account for only 11 percent.

Can you add some Chi-squared statistics (https://en.wikipedia.org/wiki/Pearson's_chi-squared_test#Calculating_the_test-statistic ) for the real and your random data, please?

 

[Rory]

Can you add some Chi-squared statistics for the real and your random data, please?

I don't really understand how that works - but I did get an online calculator to do it for me. It said:

"Chi squared equals 19.050 with 11 degrees of freedom."

Any idea what that means?

 

[Ann K]

Despite the grim news from around the world, I just hope we never have enough known serial killers with which to do a proper statistical analysis.

 

[deirdre]

Despite the grim news from around the world, I just hope we never have enough known serial killers with which to do a proper statistical analysis.

I do. because all these 'studies' only look at serial killers who were caught. The title should be "you're more likely to get caught for your serial killing if you were born under these signs".

 

[Rory]

Despite the grim news from around the world, I just hope we never have enough known serial killers with which to do a proper statistical analysis.

While these 'studies' reference ~490 serial killers and Wikipedia lists 500+ from the US alone, there's a 2016 report from Radford University (who maintain the Radford University/FGCU Serial Killer Database) that contains information on 4,743 serial killers worldwide and 3,204 from the US.

http://maamodt.asp.radford.edu/Serial Killer Information Center/Serial Killer Statistics.pdf

It looks like these stats have been cited by several websites as emanating from the FBI - but this seems not to be the case (though the report does use the FBI's definition of a serial killer).

On the plus side, it looks like serial killing is significantly on the wane since its 1970s-1990s heyday.

Maybe cos they've got the internet now instead?

 

[deirdre]

Maybe cos they've got the internet now instead?

more likely home alarm systems, home camera systems, gals aint hitchhiking anymore (i used to hitchhike), gay guys have more normal social outlets now, cell phones vs running 5 miles to find a pay phone, and forensics have greatly improved.

 

[Mendel]

Maybe cos they've got the internet now instead?

Article:

Vronsky has another hypothesis to add to the list: he believes the rise of the North American serial killer in the late 20th century can be traced to the ravages of World War Two, which lasted from 1939 to 1945, and the children of men returning from battlefields in Europe and the Pacific.

It's an idea he put forward in his newly published book Sons of Cain: A History of Serial Killers.

He realised that many were children during World War Two and the ensuing post-war era - a time when the psychological impact of the global conflict and its savagery was not being discussed.

It was a war that "was far more vicious and primitive than we have been able to acknowledge", Vronsky says.

Many of the killers from that period have not spoken on the record about their fathers, he said, but those that have often referred to them coming back from the war in a traumatised state.

He said there was a less pronounced but noticeable increase in serial killings from 1935 to 1950, following World War One, and hopes sociologists and criminologists look more closely at the war experiences of the fathers of these killers, and their paternal relationships.

Source: https://www.bbc.com/news/world-us-canada-45324622

 

[Rory]

He said there was a less pronounced but noticeable increase in serial killings from 1935 to 1950, following World War One

Not sure about that...

Source: Radford University/Florida Gulf Coast University Serial Killer Database

Probably the other potential reasons put forward in that BBC article are much more likely:

• Major changes in society
• Increase in "broken families"
• People moving more
• Less likely to know their neighbours/community
• Lots of hitchhiking/casual rideshares
• Pre-DNA analysis
• Pre-computerised databases
• Media and public fascination with serial murder creating copycats/a snowball effect
• Development of the interstates giving killers a wider geography to roam
• Lead exposure from petrol

I might add that more young people had their own cars; more mobility made strangers and transients less conspicuous; maybe more prostitution, drugs, and general rowdiness, chaos, and declining levels of mental health; and, hey, it was post-hippy days when everybody stopped being so uptight and just, ya know, let it all hang out, got into expressing themselves, and did their own thing - whatever that might be.

The SKDB also suggests stricter parole policies resulted in less potential serial killers being put back on the streets; less walking to school; less insurance fraud (eg, "black widow") killers; and less "good samaritan" victims.

I wonder too about the math of Vronsky's idea: the median age of serial killers is 26 to 32, which may not work so well for his connection to the years 1939-1945 (the rise seems to start in about 1960). Not that it debunks it - but to say "the killers of the 70s to 90s were either children in WWII or the children of people who were affected by WWII" seems a bit of a catchall - especially when considering all the other potential contributing causes.

Anyways, it's good that it's in decline.

 

[deirdre]

he believes the rise of the North American serial killer in the late 20th century can be traced to the ravages of World War Two,

looking at Rory's chart, it can also be traced to more women becoming more ... promiscuous/independent?

of course how they would know how many serial killers there were in the 40s i have no idea. it was hard to collate data back then. even the Zodiac had to tell the police "i did this other murder in x town too". and he at least did all his killings in the same state. (granted california is a big state.). They knew about Jack the Ripper because all the murders were in the same district and he had a rather unique signature that garnished attention.

while its plausible men got the idea from newspaper accounts of other men (like how mass shootings are popular now in disgruntled young men/boys), it could just be that police finally started looking for the patterns more once they realized "this is a thing that is making the newspapers" ie. the public is now aware.

 

[FatPhil]

Anyways, it's good that it's in decline.

It's only one stat. Might the US be migrating towards more one-event "spree" killers as society migrates away from rewarding delayed gratification? I wonder if they would skew the stats back up again.

One chart that I'd like to see, and I think the authors should have the data, is that of plotting the birth year histogram. That might show a clearer ramp up than the year of the offences themselves if there is indeed a societal change that's a strong influence. Of course, if the societal change has a slow ramp up, even the clearest correlation with it will look like a slow ramp up, so it's hard to know if you've found possible causation, or whether there's something stronger that's still being smoothed by something as yet unknown.

 

[FatPhil]

looking at Rory's chart, it can also be traced to more women becoming more ... promiscuous/independent?

The paper addresses the some familial aspects of the perpetrator:

9. SERIAL KILLER CHILDHOOD
Research Questions Addressed
* What percentage of serial killers were abused as children?
* Compared to the general population, were serial killer more likely to be raised by adoptive or foster parents?
* Is the birth order of serial killers different from the population in general?
* What is the typical education level for a serial killer?

The signal seems weak for the some of the questions asked, but strong for others. Alas, nothing they ask is a useful proxy for your question.

I'd like to see the birth order raw data, which does have some strong correlations, as the question I'd like to ask is "what proportion are last-but-one?", as the last but one child is the one who gets to have their special position as youngest taken away from them, but never gets to see that special position taken off the younger sibling who stole it from them. It might be nothing, but, as they say, there are no stupid questions.

 

[Rory]

I think "number of killers by birth year" would be a very good stat to have - it would link well with a question I had, which was whether killers' ages have changed significantly over the decades (other demographics have).

More specific info on birth order could be interesting too. Definitely not silly questions.

I notice that they conclude middle-children are more likely and only-children less likely to be serial killers:

Interesting to note the same trend among US presidents - which reminds me of other studies which proposed that presidents, prime ministers, CEOs, etc were more likely to have psychopathic tendencies.

Here's the main man if you want to give him a try.

 

[Rory]

On a related note to both the question of whether certain personality types are more likely to be born at certain times of the year, and also issues of interpreting probability, I've been reading about studies which appear to show a link between things like schizophrenia, bipolar disorder, depression, and drug and alcohol dependencies (among other diseases and conditions) and the month/season of a person's birth.

It's quite fascinating. It's not a vindication for astrology - far from it - but it may show that time of birth (or perhaps conception) does result in a significant impact on the personality.

Some of the studies appear to fall foul of Yonezawa's Fallacy, with too small sample sizes or results that fall within the range of chance, despite what their fancy p-factors and chi-square tests are telling them. But some pass the test.

Effects are small. But if certain birth months are more prone to debilitating mental illnesses than others then it stands to reason that certain star signs could result in an increased number of psychopaths and serial killers. Not because of any influence from the planets or the stars, but due to other factors that just so happen to coincide and correlate.

Interesting stuff. Though perhaps beyond the bounds of this particular thread.

 

[FatPhil]

Here's the main man if you want to give him a try.

Mailed - will report back if a response appears.

 

[deirdre]

I think "number of killers by birth year" would be a very good stat to have - it would link well with a question I had, which was whether killers' ages have changed significantly over the decades (other demographics have).

again, "number of CAUGHT killers". for ex:

Article:

The FBI states that the average male serial killer has a "career" span of 2-3 years, with female serial killers lasting almost 11 years. Often females are rarely caught as (1) they don't hang around after the murder, (2) they tend not to take souveniers, and (3) they usually kill by poisoning, which means they don't have to be in the same room, street or country as their victim.

Source: https://www.murdermiletours.com/blog/category/killers-by-age

then you have those "angel of death" types, who are health care workers who kill their charges.

etc.

 

[deirdre]

a small stat

Article:

We compiled a list of 179 serial killers from 31 different countries. Furthermore, these were the worst killers that we could find. Between them, these people took the lives of at least 3,065 victims.

.....

Most common year for the birth of serial killers.

The top year on our list was 1959. Out of the 179 offenders, 10 were born in 1959. In other words, that is 5.59%. This was followed by 1952, which saw the birth of 9 serial murderers. 1946 was next on the list, with 8.

The mean year for a killer to be born in was 1953.

However, in the United States, the top year was 1950 (6) (8.7%), followed by 1945 (5) (7.25%). In addition to this, we calculated that the mean year for a serial killer to be born in the United States was 1949.

Source: https://thisinterestsme.com/decades-serial-killers-born/

but that website also says

Article:

The FBI started studying these killers in the 1970s.

Source: https://thisinterestsme.com/decades-serial-killers-born/

which jives, if they start killing in their 20s or 30s (most popular) ..with the idea that law enforcement wasnt really tracking them much prior to this time.

 

[Rory]

Well, for some strange reason I decided to scrutinize a few of those studies that propose connections between season/month of birth and various psychiatric illnesses to see if they pass my amateur test:

Study: https://sci-hub.se/10.1111/j.1530-0277.2000.tb02055.x
Sample size: 42,430 (17,660/3,300 in specific category)
Key finding: Alcohol-dependent men were more likely to be born between the months of October and December (19.0% relative to unaffected controls) and less likely to be born during the winter (27.6%)

Their results:

Potential issues: Results in women, though less pronounced, were different, with winter and spring being found most likely and summer least likely (fall as expected). Similarly, while illicit drug use (IDU) in men mostly matched alcohol dependence (AD), in women there was no such correlation:

Also, while their various statistical tests (p-factor, chi-squared, Wald's Test) suggested the male alcohol dependence result for winter/fall (880 out of 4402) was significant my own Simple Spreadsheet Test (SST) showed that this result was well within the bounds of chance. Plus, other similar studies found differing results (not in agreement with one another).

Finally, if looked at on a month-by-month basis:

then a pattern appears much less pronounced. For example, taken in two-month groups June and July would be the most likely.

My conclusion: it looks like a well-intended and high-minded paper but, ultimately, their sense that "an unusual birth pattern was observed among male alcoholics" is more likely explained by random noise and chance.

Study: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0034866
Sample size: 57,971
Key findings: Schizophrenia (SC) had a statistically significant peak among January births (p<0.0001) and a significant trough exactly six months later in July (p=0.02). Bipolar Affective Disorder (BAD) patients were more likely to be born than expected in January (p=0.002) and less likely in August and September (p=0.02 and 0.005). In Recurrent Depressive Disorder (RDD) an almost significant May peak (p=0.08) and a significant November deficit (p=0.02) were observed.

As we can see, January SC differs by +1.03% from control; July SC by -0.38%; January BAD is +0.7%; August and September BAD are -0.52 and -0.64%; and May and November RDD are +0.38 and -0.46% respectively.

Other months that perhaps also could have been highlighted include: January RDD (+0.35%), March SC (-0.34%), and May BAD (+0.45%).

Potential issues: first thing I notice is that their control - derived from ONS statistics for births between 1950 and 1990 - differs somewhat for average births per month in more recent decades (figures also from ONS):

I'm not sure if and/how this would change things. But it's perhaps worth considering.

Second thing is to test and see whether the figures they obtained could be arrived at by chance. So I ran my SST (adjusting for the 1950-1990 birth month frequencies) and (for SC) it came up with:

So it does appear that 2,502 incidences of January-birth SCs is unusually high. Though the idea that July could represent a significant low (2,186 incidences) isn't convincing. I suspect it arises more from the pleasing notion that the opposite side of the year would result in an opposite outcome (those excess January incidences have to come from somewhere).

Next for BAD (14,549 incidences):

So, again, January incidences of BAD (1,318) are somewhat outside the range arrived at by chance, while August (1,141) is within and September (1,118) just outside.

For RDD (14,759 incidences):

Which shows that the seemingly significant figures for May and November (1,539 and 1,211) could just as easily have been arrived at by chance.

In conclusion, it does look like there's something going on with January births with regard to schizophrenia and bipolar affective disorder, and this is supported by other studies. Other connections however seem weak. And I'd be curious to see a more narrow breakdown, possibly by day or week: months, after all, are pretty arbitrary lines to draw and it seems strange that January could be so "off" while neighbouring February appears completely normal.

Other studies I've browsed but haven't delved into include:

• The impact of month of birth on children's cognitive and non-cognitive skills (related to the relative age effect)
• Season of birth is associated with birth weight, pubertal timing, adult body size and educational attainment (~450,000 sample size - one rather striking table here)
• Birth month affects lifetime disease risk: a phenome-wide method (1.75 million person sample size, which apparently found "55 diseases that were significantly dependent on birth month")

In a nutshell: though the proposed findings don't all pass muster it does look like something's going on - but it's not the stars that affect you, it's probably how much vitamin D your mum is exposed to during your final months in the womb; it's what pollutants are in the air when you're readying to pop out; and it's how much older or younger you are than the kids they put you in a room with (among other things).

Anyway, that all seems a bit mad and I can't quite figure out why I did that. But then again, I was born in January in the grey north of England so what can I expect?