The post hoc fallacy

The post hoc fallacy is the logical error that because event B followed event A, A must have caused B. It comes from the Latin post hoc ergo propter hoc, or “after this, therefore because of this.” Along with a similar fallacy, cum hoc ergo propter hoc (“with this, therefore because of this”), it’s important to avoid if you want to do good science—or to understand science stories in the news.

We’ve discussed various aspects of the scientific method in previous blogs. Correlation is not causation. If A and B occur together, A may have caused B, B may have caused A, both could be due to another cause, C, or they may simply be coincidental. Deconvoluting one from the other takes discernment.

The post hoc fallacy in action

An infamous case of the post hoc fallacy is the false attribution of autism to childhood vaccines. This stemmed from a 1998 paper in the British medical journal The Lancet by Andrew Wakefield and coauthors. The paper had numerous serious deficiencies, at least some of which should have been apparent to the original reviewers. For example, it reported on only 12 cases—a collection of anecdotes, not data. Worse, each anecdote contained some false information. But Wakefield also had a financial interest in drawing his conclusions. The MMR (measles-mumps-rubella) vaccine he implicated as a cause of autism conferred immunity to all three diseases. He was promoting his own vaccine formulations, each of which targeted one disease at a time.

Unfortunately, it took years for all of this to come to light. In 2004, 10 of Wakefield’s coauthors retracted the paper. But it wasn’t until 2010 that The Lancet itself retracted the paper. Later the same year, Wakefield’s license to practice medicine in the UK was revoked. Numerous subsequent scientific papers have thoroughly debunked his claims regarding any causal connection between the MMR vaccine and autism.

Even so, Wakefield is still actively campaigning against vaccines from his home in Texas. His latest venture is a feature film seeking to discredit the mumps vaccine. Periodic outbreaks of measles in the US have resulted in 151 cases and 82 hospitalizations so far in 2024, the vast majority in unvaccinated people.


Video: Britain’s National Health Service on safety and efficacy of MMR vaccines.

The post hoc fallacy provides a better explanation for the apparent connection between vaccines and autism. The age at which the CDC recommends children receive their first MMR vaccine is 12 to 15 months. That’s about when parents might notice that their child isn’t responding to stimuli as other children do. They start seeing signs of autism following the administration of the MMR vaccine and make an erroneous causal connection.

Cum hoc ergo propter hoc

In forensic engineering, one must also take care to avoid the cum hoc ergo propter hoc fallacy. Normally we don’t go to the trouble or expense of coring and examining concrete unless it’s showing visible signs of distress. By that time, petrographic examination will show the damage itself, along with normal signs of aging that may or may not be related. In particular, the presence of ettringite crystals may or may not be significant. They may be signs of sulfate attack, or they may just be harmlessly recrystallizing from the smaller crystals that were there from the beginning. You need additional evidence to determine what’s really going on.

In the 1990s, pavements in the upper Midwest began to deteriorate at the joints. Cores of the distressed concrete showed signs of freeze-thaw deterioration, and ettringite crystals had formed in the cracks and air voids. Some engineers attributed the damage to the clogging of air voids with the ettringite, while others maintained that the ettringite was simply opportunistic. That is, after the cracks formed, the ettringite migrated to where it had room to grow.

Deconvoluting cause and effect

To test these hypotheses, a colleague and I sought to recreate the deterioration in the laboratory. By examining the sequence of events we could determine whether either was false. So we based our concrete mixtures on those that had performed poorly in the field. We exposed them to cycles of freezing and thawing in salt solutions to mimic the deicing salts in the field, allowing them to dry out each weekend. We monitored the deterioration via mass loss, length change, and relative dynamic modulus. Although we tested most of the specimens to destruction, we sacrificed some companion specimens for petrographic examination. This program allowed us to reconstruct the sequence of events.

In every case, the deterioration occurred before the deposition of large crystals of ettringite. The ettringite depositions could not have caused the deterioration because they occurred either afterwards or not at all, depending on the rate of deterioration.

Another useful observation was that the smaller air voids appeared to be filled with ettringite deposits, while the larger ones appeared to be lined with them. A concrete thin section is about 20 μm thick—thin enough to see through, but not infinitesimal. By focusing the microscope on the top surface and then the bottom surface of the thin section, the petrographer could see the curvature of the air void. What appeared to be smaller air voids were actually those that had been sectioned near their poles; the “larger” air voids had been sectioned near their equators. Near the poles, the ettringite lining looked as if it were filling the voids. But there was still room for water to migrate in and freeze. That is, the ettringite wasn’t clogging the pores at all; its presence merely showed that they were functioning as intended.