I knew Subway was bad for our health...

A student sent me the following infographic which is an excellent illustration of our tendency to confuse correlation with causation:

The image displays a  meme that compares 5G coverage with the hot spots for COVID-19 implying that one caused the other. It then shows a variety of other maps with similar distributions. This illustrates how we often mistake correlation for causation.

Lisa, I want to buy your rock!

This is one of the best examples of the Post Hoc fallacy out there. For a long time, a clip of this was unavailable on the internet (I don't know why), but today I finally came across one, and here it is:


The key here is Homer's confusion about the rock. If we reconstruct his argument it goes like this:

1. Lisa has a rock.
2. There are no tigers.
3. Therefore, the rock kept the tigers away.

It is the assumption that the rock caused the tigers to stay away which is the Post Hoc fallacy. 

Does Nicholas Cage cause people to drown in their swimming pools?

A great new website, Spurious Correlations, has just appeared on my radar, and it fantastically illustrates the Post Hoc fallacy. The website takes data sets, and then hunts through the web to find data sets that correlate with the initial data and then presnts it in the form of a chart. The headline for the post comes from this chart:



As this chart nicely shows, there is a correlation between Nicholas Cage films and drowning deaths in swimming pools. There is clearly no causal relation that I can think of here (though Cage has certainly appeared in some dire films recently), but there is a clear and obvious correlation. This entire website does a great job of illustrating the mantra that "correlation does not equal causation." I encourage everyone to take a look at the site because many of the correlations are interesting and quite humorous.

The Power of Barking

Saw this on Facebook and I couldn't resist. This is a great example of a Post hoc fallacy. The dog thinks that because she barks and then the mailman doesn't murder the family that the barking causes the mailman to not murder. The post hoc in a nutshell.

Antivaccine Post Hoc, Ignorant Reasoning

In a recent edition of BMJ Case Studies, Deirdre Therese Little and Harvey Rodrick Grenville Ward from Australia published a report in which they suggest that a 16-year old girl suffered early menopause as a result of Gardasil, the HPV vaccine. Several anti-vaccine blogs including the Population Research Institute and Gaia Health and  have picked up on the story and run with it, presenting it as further evidence of the dangers of vaccines. Unfortunately, all these people miss the obvious point that the entire case against Gardasil rests on a Post Hoc fallacy in which a temporal correlation is assumed to be a causal relation and an Argument from Ignorance. Let's take a look at the actual case study and the reporting on it to see how this entire case is based on fallacious reasoning.

In the summary of their case study published on the BMJ website Little and Ward write:

Although the cause is unknown in 90% of cases, the remaining chief identifiable causes of this condition were excluded. Premature ovarian failure was then notified as a possible adverse event following this vaccination.

See what little and ward do here. They begin by noting that 90% of the cases of premature menopause have no known cause.  They then conclude that, because they eliminated the 10% of known causes the early onset menopause must have been caused by the vaccine. This is a great example of the Argument from Ignorance. We have no idea what causes this condition, therefore it must have been Gardasil. In addition, the reason for assuming Gardasil must have been the cause is that about a year before she became menopausal, the woman had received Gardasil. So, we have a Post Hoc fallacy combined with an Argument from Ignorance to reach the conclusion that Gardasil caused the amenorrhoea (fancy medical jargon for early menopause). Let's look now at how several antivaccine websites pick up and amplify these errors.

First, Steven Mosher and Elizabeth Crnkovich writing for the Population Reasearch Institute describe the case study as follows:

Dr. Deirdre Little, the Australian physician who treated the girl, has published a complete account in the British Medical Journal. (BMJ Case Reports 2012; doi:10.1136/bcr-2012-006879) Her report explains that the girl's menstrual cycles were regular until she received the Gardasil vaccination in the Fall of 2008. By January 2009, her cycle had become irregular. Over the course of the next two years, her menses became increasingly scant and irregular, until by 2011, she had ceased menstruating altogether.

Look at the reasoning here. In the Fall of 2008 the women gets the HPV vaccine. She then stops menstruating in 2011. We are looking at a roughly three year gap between the event and its supposed cause. I am sure that there were many things that this young girl did in 2008. Why are these not considered as causally related to her amenorrhoea? We need more than a remote temporal correlation to establish a causal relation between these two events. Later in the same post Mosher and Crnkovich write:

While Dr. Little could not confirm that Gardasil caused the destruction of the girl's reproductive system, she was able to rule out all other possible causes. The circumstantial evidence implicating Gardasil is strong.

As we know from the original case study, 90% of these cases have no known cause. Thus, by eliminating all known causes, we are still left with a gaping hole of ignorance. To try and fill that hole by asserting that is must have been the Gardasil is clearly an Argument from Ignorance. Furthermore, as I noted above, the circumstantial evidence implicating Gardasil is actually incredibly weak, amounting to nothing more than Post Hoc reasoning.

We see a similar error in a post by Heidi Stevenson at Gaia Health. She writes:

The girl has been thoroughly examined and tested. There is no known explanation other than the series of three Gardasil vaccinations she had.

This is, again, a classic Argument from Ignorance. Stevenson is arguing that because we eliminated a bunch of known causes it had to have been Gardasil. But, as I noted above, one can't base a conclusion on a lack of knowledge or information. Given that we know so little about what actually causes amenorrhoea, the most that we can conclude is that we don't know.

As a critical thinker, it is very disturbing for me to see such an elementary logical error used as the basis for a case study that was then accepted by a fairly reputable medical journal. These kinds of basic reasoning errors would be grounds for failure if they were committed by my students, yet here are actual medical practitioners committing them in a reputable journal, and these errors are then being amplified by various ideologically motivated bloggers. This point to a sad state of affairs for medicine and science.

h/t to Orac

Black people run faster because they are descended from slaves?

Sometimes, when one tries to come up with a ridiculous title, it turns out that you can't out ridicule reality. As a case in point, check out this "commentary" on black athletes from the BBC:

According to the commentator in this clip, black people are good at running because slavery exerted an evolutionary pressure on them that made them faster runners. This is a good example of a Non Sequitur and a Post Hoc fallacy combined with a bit of straw manning. The straw manning comes from the misrepresentation of evolutionary theory and the ideas of eugenics. The commentator in question clearly doesn't have a very good grasp of this topic and uses a very cursory analyis of evolutionary theory to develop his points.

The non sequitur arises in that his conclusion just does not follow from his premise. The reconstructed argument seems to be as follows:

1. Evolution proceeds by natural selection and survival of the fittest.
2. West Africans were slaves and were subject to enormous evolutionary pressure such that only the fittest West Africans survived the slave passage and made it to the Americas.
3. All successful (in terms of Gold medals and world records) runners are of West African descent.
4. Therefore, their success is due to their descent from slaves.

It should also be clear that this is a post hoc fallacy in that the commentator is assuming a causal relation between slave ancestry and skill at running, when there is, at best, a correlation. There are likely a variety of other factors at work here besides mere descent from slaves. Furthermore, as PZ Meyers notes,  the evolutionary story doesn't even make sense:

…because, obviously, being able to survive shackling in a slave ship and a lifetime of menial stoop labor in the cotton fields clearly selects for genes of benefit in short foot races.

If anything, it would seem that slavery would select against speed over short distances as the last thing a slave owner would want is for his slaves to be able to run away!

Through the looking glass

It is with some reluctance that I write this post as I have generally been avoiding news reports concerning the massacare in Aurora, Colorado. As is often the case with tragedies that get a great deal of traction in the media, people come out of the woodwork exploiting that tragedy as a way to garner support for their particular political cause. There has obviously been a great deal of discussion about gun control (though apparently no one's opinion is changing), but I want to focus on a slightly different angle, promoted most recently by Jon Rappoport.

In an article published today on NaturalNews, and reprinted from his blog Rappoport suggests that the accused Aurora, Colorado shooter, James Holmes, was either (a) the patsy for some large conspiracy designed to change public opinion on gun control or (b) driven crazy by psychiatric drugs or (c) driven crazy by psychiatric drugs so that he could be used as the patsy or perpetrator of a mass killing designed to change people's opinions on gun control. The article itself is poorly written and reads more like a rant than any kind of thoughtful analysis, but I will do my best to unpack some of the fallacies lurking in it.

The first and most obvious is the post hoc fallacy. Rappoport doesn't quite come out and say that Holmes was driven violently insane by pharmaceuticals (though he does make that claim in his blog), but that does appear to be the major point of the article.  After making a number of unsubstantiated claims about the pressure being exerted by pharmaceutical manufacturers on law enforcement and the judicial system to suppress the medical records of Holmes in order to prevent tarnishing the reputation of the drugs Holmes was taking thereby causing people to refuse to take them thus hurting the profits of Big Pharma, Rappoport then launches into a lengthy (but more substantiated, at least there are references though almost all of them are over 20 years old) discussion of the potential psychotic side effects of Prozac. The clear inference here is supposed to be that Holmes took Prozac (even though there is no evidence that this was a drug he was taking, we will probably know more when his medical records are released during the court proceedings), this made him psychotic, and this psychosis led him to commit the crimes for which he is accused. This is a clear example of a post hoc fallacy in that the author is assuming a causal relation when all we have evidence for is a correlation (a correlation Rappoport invented for the sake of his article). Assuming that Holmes was taking some sort of psychiatric medicine, it seems far more likely that his underlying mental condition caused him to commit his crimes, rather than the medication he was taking to treat that crime. As a quick note, I have no evidence concerning Holmes' psychiatric condition or medication he may have been taking, I am merely trying to unpack and evaluate the argument Rappoport makes. For all I know, Holmes may have been perfectly sane and was not prescribed nor taking any medication.

Moving on, Rappoport then commits a rather large Hasty Generalization when he suggests that because there is some evidence of people becoming psychotic when they take certain classes of anti-depressants that therefore everybody who takes them will become psychotic. Again, there is no direct quote which shows a clear example, but the article as a whole is clearly trying to make the case that this generalization is true.

Lastly, Rappoport's article is filled with what can best be described as Bullshit. Bullshit occurs when one has no concern for the truth and just makes up whatever facts or stories will support one's position. For example:

So right now, in Aurora, there are pharmaceutical people on the scene. Not just low-level goofballs, but competent investigators. They want to know what drugs James Holmes was prescribed. They need to know. And behind the scenes, people with clout are making phone calls. These pharma types are talking to government agents and it's crazy time and damage-control time, and nobody is laughing. This is a high-stakes game. WHAT DRUGS WAS HOLMES TAKING?

Rappoport provides no evidence whatsoever that any of the things he describes in this paragraph are actually taking place. Similiarly, he writes:

[If] they could get to Holmes in his cell, they'd erase him. They'd make it look like a suicide. Today. What do you think "lone shooter" is all about? Yes, the covert op that very well may have used Holmes as the patsy, to push the government into banning guns, is a major piece here. But that work is done. Now it's "lone shooter" because getting rid of Holmes by killing him or warehousing him for the rest of his life in a mental prison, with brain-hammer drugs making him into a vegetable, means that the names of the psychiatric drugs he was taking before the massacre will be lost to history, and no one will take the criminal investigation any further.

Again this appears to have no basis in reality, and no evidence beyond Rappoport's wild speculations. This is, quite simply, bullshit.

It's that time of the month: Hasty Generalizations and Post Hoc reasoning.

A recent press release from Concordia University in Montreal has announced the publication of a paper by lead author Gad Saad linking shopping habits among women to their menstrual cycle. In particular, the study seemed to indicate that women were more likely to buy clothing and beauty related products and spend more time on appearance related activities (manicures, tanning salons, sun-bathing etc.) during the fertile phase of their menstrual cycle, and more likely to consume high-caloric foods during the infertile phase of the menstrual cycle. Of particular interest for me is the linking of these behaviors to evolution, with Saad essentially arguing that women are biologically determined to engage in these sorts of behaviors.

"In ancestral times,” he explains, “women had to focus more time on mating-related activities during the fertile phase of the menstrual cycle, when the likelihood of conception was highest. Those same psychological and physiological mechanisms now lead women to engage in greater consumption of products relevant to reproductive drives during the fertile phase of their cycle."

Now I don't want to get into too much detail about the science behind this article since I want to focus on the press-release, but I do want to highlight one element of the research conducted:

Working with his doctoral student and co-author Eric Stenstrom, Saad recruited hundreds of participants by canvassing classes at Concordia university. Through a careful selection process, 59 female participants were chosen. Over a period of 35 days, the women kept detailed diaries that chronicled beautification behaviours, clothing choices, calorie consumption, and purchases.

So what we have here is a very limited sample size. The study is only looking at 59 women over a period of 35 days. All these women are college students, and given that Concordia is a public university they are all likely Canadian citizens. In addition, Montreal is about 75% Caucasian, so it is likely that a majority of the participants in this study are college-age white women (Let me be clear that I am just making estimates based on the press release and some quick Google searches). Given this small, limited sample size, it is clear that the conclusions drawn about the research by the author of the press release is a good example of a Hasty Generalization. A Hasty Generalization occurs when one draws a general or universal conclusion from a small or limited set of data, and this is exactly what we see here in drawing a conclusion about the evolutionary origins of female behavior from a sample size of 59. There are roughly 7 billion people on earth and about half of them are women. That amounts to about 3.5 billion women in the world, so a sample size of 59 would equal about .00000000842% of the population (please check my math and leave a comment if I got ti wrong!). This is really too small a percentage to draw a general conclusion about the evolutionary origins of this behavior.

Beyond this, the authors also appear to be guilty of a Post Hoc fallacy. Here I am less confident about whether or not a fallacy has been committed. Having not read the original paper, perhaps the authors of the study do correct for this, but given the limited information in the press release, I think we can reasonably question whether or not there is a causal link between the behaviors identified and the menstrual cycle. First, the study had a very short duration, just 35 days. The average menstrual cycle is about 28 days, but there is enormous variation among women, and even the same woman can have significant differences between the lengths of her menstrual cycles. Given this, a 35 day study is far too short to draw a causal inference between the cycle and the behavior. Furthermore, given that all of these women were in essentially the same environment (college students at a public university) it seems that there could be numerous other factors causing or contributing to the behavior of the women. Given a study performed under these constraints, the authors have at best identified a correlation, but one can't assume this correlation to be equivalent to causation. This is a Post
Hoc fallacy.

Finally, even if the authors have discovered a causal connection between menstruation and consumption behaviors, it doesn't seem that one can assume that the latter causes the former. For example, it might well be the case that cultural factors play a much larger role in determining behavior than genetic or biological factors. It might be that women are told by their cultures to engage in certain behaviors at certain times of their menstrual cycle. If this were true, then it wouldn't be biology causing behavior, but rather culture causing behavior during certain times of a woman's menstrual cycle. Given that all the participants in the study were members of a similar culture group (women at a large, Canadian public university), this hypothesis seems as reasonable as the conclusion drawn by the authors. I am not claiming that this hypothesis is correct, but merely noting that it is another possible explanation that appears to be neglected, and when one assumes a particular causal relation beyond the available evidence, one is is committing a Post Hoc or False Cause fallacy.

For more on the relation between genetics, culture and behavior generally, I recommend this podcast.

h/t to Pharyngula

Family Guy and the Post Hoc Fallacy

For this post, I want to discuss and provide an example of the Post Hoc Fallacy (full name: Post hoc ergo propter hoc; after this, therefore because of this). The Post Hoc fallacy is a type of False Cause fallacy, and a False Cause is a fallacy in which some kind of correlation is mistaken for a causal relation. In the case of the Post Hoc, the fallacy lies in the assumption that because one event follows another the first event must have caused the second. This fallacy is clearly illustrated in the following clip:

The Post Hoc fallacy here lies in the assumption that because contracting herpes came after buying the car from a newspaper ad the two events must, therefore, be causally connected. The fallaciousness of the Post Hoc Fallacy is revealed by the extreme temporal distance between the two events.

A similar example of the fallacy can be found in the Simpson's episode "Much Apu About Nothing." Unfortunately, video clips of this scene are unavailable, so I will refer you to this discussion of it.